Related papers: Dynamics of weighted shifts on directed trees
Positive dependencies have been compared in the literature under rather strong assumptions such as equality of conditional distributions, exchangeability, or stationarity. We establish supermodular ordering results for distributions that…
Many networks describing complex systems are directed: the interactions between elements are not symmetric. Recent work has shown that these networks can display properties such as trophic coherence or non-normality, which in turn affect…
This letter examines the controllability of consensus dynamics on matrix-weighed networks from a graph-theoretic perspective. Unlike the scalar-weighted networks, the rank of weight matrix introduces additional intricacies into…
The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
We characterise digraphs of directed treewidth one in terms of forbidden butterfly minors. Moreover, we show that there is a linear relation between the hypertree-width of the dual of the cycle hypergraph of D, i. e. the hypergraph with…
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…
We investigate the evolutionary dynamics in directed and/or weighted networks. We study the fixation probability of a mutant in finite populations in stochastic voter-type dynamics for several update rules. The fixation probability is…
We study, using simulations, the steady-state flow of dry sand driven by gravity in two-dimensions. An investigation of the microscopic grain dynamics reveals that grains remain separated but with a power-law distribution of distances and…
Phylogenetic networks are a type of directed acyclic graph that represent how a set $X$ of present-day species are descended from a common ancestor by processes of speciation and reticulate evolution. In the absence of reticulate evolution,…
Evolutionary dynamics and patterns of molecular evolution are strongly influenced by selection on linked regions of the genome, but our quantitative understanding of these effects remains incomplete. Recent work has focused on predicting…
When animal groups move coherently in the form of a flock, their trajectories are not all parallel, the individuals exchange their position in the group. In this Letter we introduce a measure of this mixing dynamics, which we quantify as…
A staged tree model is a discrete statistical model encoding relationships between events. These models are realised by directed trees with coloured vertices. In algebro-geometric terms, the model consists of points inside a toric variety.…
In some applications of matching, the structural or hierarchical properties of the two graphs being aligned must be maintained. The hierarchical properties are induced by the direction of the edges in the two directed graphs. These…
A non-local model describing the growth of a tree-like transportation network with given allocation rules is proposed. In this model we focus on tree like networks, and the network transports the very resource it needs to build itself. Some…
This article investigates the topological pressure of isotropic axial products of Markov subshifts on the $d$-tree. We show that the quantity increases with dimension $d$. To achieve this, we introduce the pattern distribution vectors and…
Motivated by the abundance of directed synaptic couplings in a real biological neuronal network, we investigate the synchronization behavior of the Hodgkin-Huxley model in a directed network. We start from the standard model of the…
We consider the randomly biased random walk on trees in the slow movement regime as in [HS16], whose potential is given by a branching random walk in the boundary case. We study the heavy range up to the $n$-th return to the root, i.e., the…
Most real-world networks display not only a heterogeneous distribution of degrees, but also a heterogeneous distribution of weights in the strengths of the connections. Each of these heterogeneities alone has been shown to suppress…
We analyze variational inference for highly symmetric graphical models such as those arising from first-order probabilistic models. We first show that for these graphical models, the tree-reweighted variational objective lends itself to a…
The varying-coefficient model is a strong tool for the modelling of interactions in generalized regression. It is easy to apply if both the variables that are modified as well as the effect modifiers are known. However, in general one has a…