Related papers: Stabilization Time in Minority Processes
We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a…
A coagulation process is studied in a set of random masses, in which two randomly chosen masses and the smallest mass of the set multiplied by some fixed parameter $\omega\in [-1,1]$ are iteratively added. Besides masses (or primary…
The minimum status of a graph is the minimum of statuses of all vertices of this graph. We give a sharp upper bound for the minimum status of a connected graph with fixed order and matching number (domination number, respectively), and…
The Colour Refinement procedure and its generalisation to higher dimensions, the Weisfeiler-Leman algorithm, are central subroutines in approaches to the graph isomorphism problem. In an iterative fashion, Colour Refinement computes a…
This paper deals with the boundary stabilization problem of a one-dimensional wave equation with a switching time-delay in the boundary. We show that the problem is well-posed in the sense of semigroups theory of linear operators. Then, we…
We study spreading processes in temporal graphs, i. e., graphs whose connections change over time. These processes naturally model real-world phenomena such as infectious diseases or information flows. More precisely, we investigate how…
We consider vertex partitions of the binomial random graph $G_{n,p}$. For $np\to\infty$, we observe the following phenomenon: in any partition into asymptotically fewer than $\chi(G_{n,p})$ parts, i.e. $o(np/\log np)$ parts, one part must…
Stable gonality is a multigraph parameter that measures the complexity of a graph. It is defined using maps to trees. Those maps, in some sense, divide the edges equally over the edges of the tree; stable gonality asks for the map with the…
Sublinear time algorithms represent a new paradigm in computing, where an algorithm must give some sort of an answer after inspecting only a small portion of the input. The most typical situation where sublinear time algorithms are…
The \textit{node reliability} of a graph $G$ is the probability that at least one node is operational and that the operational nodes can all communicate in the subgraph that they induce, given that the edges are perfectly reliable but each…
We study discrete time linear constrained switching systems with additive disturbances, in which the switching may be on the system matrices, the disturbance sets, the state constraint sets or a combination of the above. In our general…
A coloring of edges of a finite directed graph turns the graph into finite-state automaton. The synchronizing word of a deterministic automaton is a word in the alphabet of colors (considered as letters) of its edges that maps the automaton…
The zero-temperature Ising model is known to reach a fully ordered ground state in sufficiently dense random graphs. In sparse random graphs, the dynamics gets absorbed in disordered local minima at magnetization close to zero. Here, we…
We study the fixation time of the identity of the leader, i.e., the most massive component, in the general setting of Aldous's multiplicative coalescent [4, 5], which in an asymptotic sense describes the evolution of the component sizes of…
We propose quasi-stable coloring, an approximate version of stable coloring. Stable coloring, also called color refinement, is a well-studied technique in graph theory for classifying vertices, which can be used to build compact, lossless…
We study a graph-based generalization of the Galam opinion formation model. Consider a simple connected graph which represents a social network. Each node in the graph is colored either blue or white, which indicates a positive or negative…
Population protocols are a model of distributed computing, in which $n$ agents with limited local state interact randomly, and cooperate to collectively compute global predicates. An extensive series of papers, across different communities,…
We study the mixing time of the unit-rate zero-range process on the complete graph, in the regime where the number $n$ of sites tends to infinity while the density of particles per site stabilizes to some limit $\rho>0$. We prove that the…
We study the self-stabilizing leader election problem in anonymous $n$-nodes networks. Achieving self-stabilization with low space memory complexity is particularly challenging, and designing space-optimal leader election algorithms remains…
We consider a system in which a group of agents represented by the vertices of a graph synchronously update their opinion based on that of their neighbours. If each agent adopts a positive opinion if and only if that opinion is sufficiently…