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The dynamical discrete web is a system of one-dimensional coalescing random walks that evolves in an extra dynamical time parameter. At any deterministic dynamical time, the paths behave as coalescing simple symmetric random walks. This…
We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle / functional central limit theorem) to hold for observables of compact group extensions of nonuniformly…
High-order accurate, $\textit{entropy stable}$ numerical methods for hyperbolic conservation laws have attracted much interest over the last decade, but only a few rigorous convergence results are available, particularly in multiple space…
We address the correspondence search problem among multiple graphs with complex properties while considering the matching consistency. We describe each pair of graphs by combining multiple attributes, then jointly match them in a unified…
This paper is Part II of a two-part series devoting to the study of systematic measures in a complex bio-network modeled by a system of ordinary differential equations. In this part, we quantify several systematic measures of a biological…
We study the stability of orbits in large Boolean networks with given complex topology. We impose no restrictions on the form of the update rules, which may be correlated with local topological properties of the network. While recent past…
Results for estimating the convergence rate of non-stationary distributed consensus algorithms are provided, on the basis of qualitative (mainly topological) as well as basic quantitative information (lower-bounds on the matrix entries).…
We study an approximation by time-discretized geodesic random walks of a diffusion process associated with a family of time-dependent metrics on manifolds. The condition we assume on the metrics is a natural time-inhomogeneous extension of…
The Miller-Abrahams (MA) random resistor network is given by a complete graph on a marked simple point process with edge conductivities depending on the marks and decaying exponentially in the edge length. As Mott random walk, it is an…
The aim of this paper is to develop a method for proving almost sure convergence in Gromov-Hausodorff-Prokhorov topology for a class of models of growing random graphs that generalises R\'emy's algorithm for binary trees. We describe the…
This paper deals with the convergence time analysis of a class of fixed-time stable systems with the aim to provide a new non-conservative upper bound for its settling time. Our contribution is fourfold. First, we revisit the well-known…
A copolymer is a chain of repetitive units (monomers) that are almost identical, but they differ in their degree of affinity for certain solvents. This difference leads to striking phenomena when the polymer fluctuates in a nonhomogeneous…
Functional networks of complex systems are obtained from the analysis of the temporal activity of their components, and are often used to infer their unknown underlying connectivity. We obtain the equations relating topology and function in…
We map the problem of diffusion in the quenched trap model onto a new stochastic process: Brownian motion which is terminated at the coverage "time" ${\cal S}_\alpha=\sum_{x=-\infty} ^\infty (n_x)^\alpha$ with $n_x$ being the number of…
We study the influence of network topology and connectivity on the synchronization properties of chaotic logistic maps, interacting with random delay times. Four different types of topologies are investigated: two regular (a ring-type and a…
Robustness of ecological flow networks under random failure of arcs is considered with respect to two different functionalities: coherence and circulation. In our previous work, we showed that each functionality is associated with a natural…
In this paper, we explore the relationship between the topological characteristics of a complex network and its robustness to sustained targeted attacks. Using synthesised scale-free, small-world and random networks, we look at a number of…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
Consensus over networked agents is typically studied using undirected or directed communication graphs. Undirected graphs enforce symmetry in information exchange, leading to convergence to the average of initial states, while directed…
Let $(W_n(\theta))_{n \in \mathbb{N}_0}$ be Biggins' martingale associated with a supercritical branching random walk, and let $W(\theta)$ be its almost sure limit. Under a natural condition for the offspring point process in the branching…