Related papers: On a Local Version of the Bak-Sneppen Model
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
We exploit a result by Nerman which shows that conditional limit theorems hold when a certain monotonicity condition is satisfied. Our main result is an application to vertex degrees in random graphs, where we obtain asymptotic normality…
A common model for social networks are Geometric Inhomogeneous Random Graphs (GIRGs), in which vertices draw a random position in some latent geometric space, and the probability of two vertices forming an edge depends on their geometric…
Understanding generalization and robustness of machine learning models fundamentally relies on assuming an appropriate metric on the data space. Identifying such a metric is particularly challenging for non-Euclidean data such as graphs.…
Let the Kneser graph $K$ of a distance-regular graph $\Gamma$ be the graph on the same vertex set as $\Gamma$, where two vertices are adjacent when they have maximal distance in $\Gamma$. We study the situation where the Bose-Mesner algebra…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
We study the discrete Bak-Sneppen model introduced by Barbay and Kenyon (2001) "On the discrete Bak-Sneppen model of self-organized criticality". We extend their results as well as the non-triviality result of Meester and Znamenskiy (2002)…
The Bak--Sneppen model is a simple stochastic model of evolution that exhibits self-organized criticality and for which few analytical results have been established. In the original Bak-Sneppen model and many subsequent variants,…
We study the random graph G_{n,\lambda/n} conditioned on the event that all vertex degrees lie in some given subset S of the non-negative integers. Subject to a certain hypothesis on S, the empirical distribution of the vertex degrees is…
Dependency networks (Heckerman et al., 2000) provide a flexible framework for modeling complex systems with many variables by combining independently learned local conditional distributions through pseudo-Gibbs sampling. Despite their…
The Bak Sneppen (BS) model is a very simple model that exhibits all the richness of self-organized criticality theory. At the thermodynamic limit, the BS model converges to a situation where all particles have a fitness that is uniformly…
Variance-Gamma distributions are widely used in financial modelling and contain as special cases the normal, Gamma and Laplace distributions. In this paper we extend Stein's method to this class of distributions. In particular, we obtain a…
Extremal dynamics is the mechanism that drives the Bak-Sneppen model into a (self-organized) critical state, marked by a singular stationary probability density $p(x)$. With the aim of understanding this phenomenon, we study the BS model…
We initiate the algorithmic study of retracting a graph into a cycle in the graph, which seeks a mapping of the graph vertices to the cycle vertices, so as to minimize the maximum stretch of any edge, subject to the constraint that the…
We generalize the poissonian evolving random graph model of Bauer and Bernard to deal with arbitrary degree distributions. The motivation comes from biological networks, which are well-known to exhibit non poissonian degree distribution. A…
We investigate the mean-field dynamics of stochastic McKean differential equations with heterogeneous particle interactions described by large network structures. To express a wide range of graphs, from dense to sparse structures, we…
Traditional statistical learning theory relies on the assumption that data are identically and independently distributed (i.i.d.). However, this assumption often does not hold in many real-life applications. In this survey, we explore…
Multiscale shape skeletonization on pixel adjacency graphs is an advanced intriguing research subject in the field of image processing, computer vision and data mining. The previous works in this area almost focused on the graph vertices.…
Let $F$ be a probability distribution with support on the non-negative integers. Two algorithms are described for generating a stationary random graph, with vertex set $\mathbb{Z}$, so that the degrees of the vertices are i.i.d.\ random…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…