Related papers: Evidence for a continuum limit in causal set dynam…
Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the…
Most work on causality in machine learning assumes that causal relationships are driven by a constant underlying process. However, the flexibility of agents' actions or tipping points in the environmental process can change the qualitative…
Causal decomposition depicts a cause-effect relationship that is not based on the concept of prediction, but based on the phase dependence of time series. It has been validated in both stochastic and deterministic systems and is now…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
We study models of correlated percolation where there are constraints on the occupation of sites that mimic force-balance, i.e. for a site to be stable requires occupied neighboring sites in all four compass directions in two dimensions. We…
The theoretical basis of continuum percolation has changed greatly since its beginning as little more than an analogy with lattice systems. Nevertheless, there is yet no comprehensive theory of this field. A basis for such a theory is…
Structural causal models postulate noisy functional relations among a set of interacting variables. The causal structure underlying each such model is naturally represented by a directed graph whose edges indicate for each variable which…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
In this paper, we study convergence of coupled dynamical systems on convergent sequences of graphs to a continuum limit. We show that the solutions of the initial value problem for the dynamical system on a convergent graph sequence tend to…
Instrumental variables have proven useful, in particular within the social sciences and economics, for making inference about the causal effect of a random variable, B, on another random variable, C, in the presence of unobserved…
Motivated by a number of recent experimental and computational studies of the dynamics of fluids plunged in quenched-disordered external fields, we report on a theoretical investigation of this topic within the framework of the…
In an intelligent transportation system, the effects and relations of traffic flow at different points in a network are valuable features which can be exploited for control system design and traffic forecasting. In this paper, we define the…
This paper concerns the probabilistic evaluation of the effects of actions in the presence of unmeasured variables. We show that the identification of causal effect between a singleton variable X and a set of variables Y can be accomplished…
We study oriented percolation on random causal triangulations, those are random planar graphs obtained roughly speaking by adding horizontal connections between vertices of an infinite tree. When the underlying tree is a geometric…
Causal discovery outputs a causal structure, represented by a graph, from observed data. For time series data, there is a variety of methods, however, it is difficult to evaluate these on real data as realistic use cases very rarely come…
We study a lattice model where the coupling stochastically switches between repulsive (subtractive) and attractive (additive) at each site with probability p at every time instance. We observe that such kind of coupling stabilizes the local…
Computation models such as circuits describe sequences of computation steps that are carried out one after the other. In other words, algorithm design is traditionally subject to the restriction imposed by a fixed causal order. We address a…
We prove a functional central limit theorem for subgraph counts in a dynamic version of the random connection model. To establish tightness, we develop a dynamic extension of the cumulant method.
We consider the supercritical finite-range random connection model where the points $x,y$ of a homogeneous planar Poisson process are connected with probability $f(|y-x|)$ for a given $f$. Performing percolation on the resulting graph, we…