Consider a graph whose vertices are populated by identical objects, together with an algorithm for the time-evolution of number objects placed at each vertices. The discrete dynamics these can be observed and studied using simple inexpensive laboratory settings. There many similarities but also differences between such population quantum particle hopping on same graph. In this work, we show tha...

In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and  the icosahedral graph.

We consider the statics and dynamics of distinguishable spin-1/2 systems on an arbitrary graph G with N vertices. In particular, we consider systems of quantum spins evolving according to one of two hamiltonians: (i) the XY hamiltonian HXY , which contains an XY interaction for every pair of spins connected by an edge in G; and (ii) the Heisenberg hamiltonian HHeis, which contains a Heisenberg ...

Abstract: The aim of this paper is to present a modelling of rowing dynamics using bond graphs and to replace it by a modelling of mixed reality rowing dynamics using Mixed Reality Bond Graphs. Continuous-time dynamics for real environments, discrete-time dynamics for virtual environments, and their HyperBond interfaces in a mixed reality rowing dynamics will be described together using the mix...

a signed graph (marked graph) is an ordered pair $s=(g,sigma)$$(s=(g,mu))$, where $g=(v,e)$ is a graph called the underlyinggraph of $s$ and $sigma:erightarrow{+,-}$$(mu:vrightarrow{+,-})$ is a function. for a graph $g$, $v(g),e(g)$ and $c(g)$ denote its vertex set, edge set and cut-vertexset, respectively. the lict graph $l_{c}(g)$ of a graph $g=(v,e)$is defined as the graph having vertex set ...

Graph transformation units are rule-based devices to model graph algorithms, graph processes, and the dynamics of systems the states of which are represented by graphs. Given a graph, various rules are applicable at various matches in general, but not any choice leads to a proper result so that one faces the problem of nondeterminism. As countermeasure, graph transformation units provide the ge...

The theory of dynamical networks is concerned with systems of dynamical units coupled according to an underlying graph structure. It therefore investigates the interplay between dynamics and structure, between the temporal processes going on at the individual units and the static spatial structure linking them. In order to analyse that spatial structure, formalized as a graph, we discuss an ess...

let $g$ be a group. the order graph of $g$ is the (undirected)graph $gamma(g)$,those whose vertices are non-trivial subgroups of $g$ and two distinctvertices $h$ and $k$ are adjacent if and only if either$o(h)|o(k)$ or $o(k)|o(h)$. in this paper, we investigate theinterplay between the group-theoretic properties of $g$ and thegraph-theoretic properties of $gamma(g)$. for a finite group$g$, we s...

We study the coevolution of a generalized Glauber dynamics for Ising spins with tunable threshold and of the graph topology where the dynamics takes place. This simple coevolution dynamics generates a rich phase diagram in the space of the two parameters of the model, the threshold and the rewiring probability. The diagram displays phase transitions of different types: spin ordering, percolatio...

Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system’s constituent parts. In this work, we introduce the neural relational inference (NRI) model: an unsupervised model that learns to infer interactions while simult...