Related papers: Stabilization Time in Weighted Minority Processes
Temporal graphs are a popular modelling mechanism for dynamic complex systems that extend ordinary graphs with discrete time. Simply put, time progresses one unit per step and the availability of edges can change with time. We consider the…
The minority game (MG) model introduced recently provides promising insights into the understanding of the evolution of prices, indices and rates in the financial markets. In this paper we perform a time series analysis of the model…
We study the behavior of simple models for financial markets with widely spread frequency either in the trading activity of agents or in the occurrence of basic events. The generic picture of a phase transition between information efficient…
This paper derives a somewhat surprising but interesting enough result on the stabilizability of discrete-time parameterized uncertain systems. Contrary to an intuition, it shows that the growth rate of a discrete-time stabilizable system…
A self-stabilizing processes $\{Z(t), t\in [t_0,t_1)\}$ is a random process which when localized, that is scaled to a fine limit near a given $t\in [t_0,t_1)$, has the distribution of an $\alpha(Z(t))$-stable process, where $\alpha:…
This paper is concerned with the stability analysis of continuous-time switched systems with a random switching signal. The switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part…
Many graph coloring proofs proceed by showing that a minimal counterexample to the theorem being proved cannot contain certain configurations, and then showing that each graph under consideration contains at least one such configuration;…
The \emph{slow-coloring game} is played by Lister and Painter on a graph $G$. Initially, all vertices of $G$ are uncolored. In each round, Lister marks a nonempty set $M$ of uncolored vertices, and Painter colors a subset of $M$ that is…
We prove a metric space scaling limit for a critical random graph with independent and identically distributed degrees having power-law tail behaviour with exponent $\alpha+1$, where $\alpha \in (1,2)$. The limiting components are…
A power dominating set of a graph $G=(V,E)$ is a set $S\subset V$ that colors every vertex of $G$ according to the following rules: in the first timestep, every vertex in $N[S]$ becomes colored; in each subsequent timestep, every vertex…
A dynamical model consists of a continuous self-map $T: \mathcal{X} \to \mathcal{X}$ of a compact state space $\mathcal{X}$ and a continuous observation function $f: \mathcal{X} \to \mathbb{R}$. This paper considers the fitting of a…
We study the signum consensus protocol in continuous-time systems over arbitrary weighted directed graphs with bounded disturbances. The right-hand side of the differential equation is discontinuous on a codimension-$n$ manifold ($n > 1$).…
We investigate the stabilization of unstable multidimensional partially observed single-sensor and multi-sensor linear systems driven by unbounded noise and controlled over discrete noiseless channels under fixed-rate information…
This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the…
The stability analysis of synchronization in time-varying higher-order networked structures (simplicial complexes) is one of the challenging problem due to the presence of time-varying group interactions. In this context, most of the…
We present a detailed study of the evolution of the number of connected components in sub-critical multiplicative random graph processes. We consider a model where edges appear independently after an exponential time at rate equal to the…
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…
Balanced and swap-robust minimal trades, introduced in [1], are important for studying the balance and stability of server access request protocols under data popularity changes. Constructions of such trades have so far relied on paired…
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…
We study noise sensitivity of the consensus opinion of the voter model on finite graphs, with respect to noise affecting the initial opinions and noise affecting the dynamics. We prove that the final opinion is stable with respect to small…