Related papers: Order-invariant measures on causal sets

Following on from the notion of (first-order) causality, which generalises the notion of being tracepreserving from CP-maps to abstract processes, we give a characterization for the most general kind of map which sends causal processes to…

Requiring that the causal structure between different parties is well-defined imposes constraints on the correlations they can establish, which define so-called causal correlations. Some of these are known to have a "dynamical" causal order…

We describe the interface between measure theoretic probability and causal inference by constructing causal models on probability spaces within the potential outcomes framework. We find that measure theory provides a precise and instructive…

Prior work has shown that causal structure can be uniquely identified from observational data when these follow a structural equation model whose error terms have equal variances. We show that this fact is implied by an ordering among…

For two causal structures with the same set of visible variables, one is said to observationally dominate the other if the set of distributions over the visible variables realizable by the first contains the set of distributions over the…

We present a sample path dependent measure of causal influence between two time series. The proposed measure is a random variable whose expected sum is the directed information. A realization of the proposed measure may be used to identify…

We introduce a class of variational principles on measure spaces which are causal in the sense that they generate a relation on pairs of points, giving rise to a distinction between spacelike and timelike separation. General existence…

It is often desirable to summarise a probability measure on a space $X$ in terms of a mode, or MAP estimator, i.e.\ a point of maximum probability. Such points can be rigorously defined using masses of metric balls in the small-radius…

An indefinite causal order, where the causes of events are not necessarily in past events, is predicted by the process matrix framework. A fundamental question is how these non-separable causal structures can be related to the thermodynamic…

Quantum mechanics allows for coherent control over the order in which different processes take place on a target system, giving rise to a new feature known as indefinite causal order. Indefinite causal order provides a resource for quantum…

The moments of random variables are fundamental statistical measures for characterizing the shape of a probability distribution, encompassing metrics such as mean, variance, skewness, and kurtosis. Additionally, the product moments,…

Causal emergence is the theory that macroscales can reduce the noise in causal relationships, leading to stronger causes at the macroscale. First identified using the effective information and later the integrated information in model…

Causal inference studies whether the presence of a variable influences an observed outcome. As measured by quantities such as the "average treatment effect," this paradigm is employed across numerous biological fields, from vaccine and drug…

In general relativity, the causal structure between events is dynamical, but it is definite and observer-independent; events are point-like and the membership of an event A in the future or past light-cone of an event B is an…

We show a method of describing processes with indefinite causal order (ICO) by a definite causal order. We do so by relabeling the processes that take place in the circuit in accordance with the basis of measurement of control qubit. Causal…

We generalize standard credal set models for imprecise probabilities to include higher order credal sets -- confidences about confidences. In doing so, we specify how an agent's higher order confidences (credal sets) update upon observing…

We study a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. For such random dynamical systems, we consider estimates of absolutely continuous…

Causal spaces have recently been introduced as a measure-theoretic framework to encode the notion of causality. While it has some advantages over established frameworks, such as structural causal models, the theory is so far only developed…

We consider a deterministic system with two conserved quantities and infinity many invariant measures. However the systems possess a unique invariant measure when enough stochastic forcing and balancing dissipation are added. We then show…

In the past decade, the toolkit of quantum information has been expanded to include processes in which the basic operations do not have definite causal relations. Originally considered in the context of the unification of quantum mechanics…