Skeletal animation is a concept that has been used in the areas of motion pictures and computer games to create realistic motion for the animation of articulated characters. Recent work (Merrick & Dwyer 2004, Murray et al. 2004) has applied skeletal animation techniques from inverse kinematics and dynamics to the field of graph interaction. The motivation for this paper is to evaluate the dynam...

We examine bootstrap percolation in d-dimensional, directed metric graphs in the context of recent measurements of firing dynamics in 2D neuronal cultures. There are two regimes, depending on the graph size N . Large metric graphs are ignited by the occurrence of critical nuclei, which initially occupy an infinitesimal fraction, f∗ → 0, of the graph and then explode throughout a finite fraction...

We study the spreading dynamics on graphs with a power law degree distribution pk approximately k-gamma, with 2<gamma<3, as an example of a branching process with a diverging reproductive number. We provide evidence that the divergence of the second moment of the degree distribution carries as a consequence a qualitative change in the growth pattern, deviating from the standard exponential grow...

We investigate the problem of minimizing entropy production for a physical process that can be described in terms Markov jump dynamics. show that, without any further constraints, given time-evolution may realized at arbitrarily small production, yet expense diverging activity. For fixed activity, we find dynamics minimizes is conservative forces. The value minimum expressed graph-distance base...

Abstract Physical systems are commonly represented as a combination of particles, the individual dynamics which govern system dynamics. However, traditional approaches require knowledge several abstract quantities such energy or force to infer these particles. Here, we present framework, namely, Lagrangian graph neural network ( LGnn ), that provides strong inductive bias learn particle-based d...

The biologically inspired framework of port-graphs has been successfully used to specify complex systems. It is the basis of the PORGY modelling tool. To facilitate the specification of proof normalisation procedures via graph rewriting, in this paper we add higher-order features to the original port-graph syntax, along with a generalised notion of graph morphism. We provide a matching algorith...

This is the second part in the series of papers where we are looking for new connections between computer science, mathematics and physics. These connections go through the central notions of computer science grammar and graph grammar. In section 2 main de nitions concerning random graph grammars are given. Section 3 and 4 are devoted to the simplest models of graph dynamics: we study the large...

let $g$ be a non-abelian finite group. in this paper, we prove that $gamma(g)$ is $k_4$-free if and only if $g cong a times p$, where $a$ is an abelian group, $p$ is a $2$-group and $g/z(g) cong mathbb{ z}_2 times mathbb{z}_2$. also, we show that $gamma(g)$ is $k_{1,3}$-free if and only if $g cong {mathbb{s}}_3,~d_8$ or $q_8$.

we define minimal cn-dominating graph $mathbf {mcn}(g)$, commonality minimal cn-dominating graph $mathbf {cmcn}(g)$ and vertex minimal cn-dominating graph $mathbf {m_{v}cn}(g)$, characterizations are given for graph $g$ for which the newly defined graphs are connected. further serval new results are developed relating to these graphs.