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Recent years have seen rapid progress at the intersection between causality and machine learning. Motivated by scientific applications involving high-dimensional data, in particular in biomedicine, we propose a deep neural architecture for…
We analyse the causal structure of the ambient boundary, the conformal infinity of the ambient (Poincar\'e) metric. Using topological tools we show that the only causal relation compatible with the global topology of the boundary spacetime…
Emergence and causality are two fundamental concepts for understanding complex systems. They are interconnected. On one hand, emergence refers to the phenomenon where macroscopic properties cannot be solely attributed to the cause of…
Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike…
A notion of delegated causality is introduced. This subtle kind of causality is dual to interventional causality. Delegated causality elucidates the causal role of dynamical systems at the "edge of chaos", explicates evident cases of…
The causal character of singularities is often studied in relation to the existence of naked singularities and the subsequent possible violation of the cosmic censorship conjecture. Generally one constructs a model in the framework of…
We present a general class of spatio-temporal stochastic processes describing the causal evolution of a positive-valued field in space and time. The field construction is based on independently scattered random measures of Levy type whose…
Causal inference is widely used in various fields, such as biology, psychology and economics, etc. In observational studies, we need to balance the covariates before estimating causal effect. This study extends the one-dimensional entropy…
A theory governing the metric and matter fields in spacetime is {\it locally causal} if the probability distribution for the fields in any region is determined solely by physical data in the region's past, i.e. it is independent of events…
This paper reviews work, largely due to W. Simon and the author, on multipole theory of static spacetimes. The main purpose is to make this work, which lies at the interface of potential theory, conformal geometry and general relativity,…
We investigate three causality-violating spacetimes: Misner space (including Kip Thorne's "moving wall" model), the pseudo-Schwarzschild spacetime, and a new model introduced here, the pseudo-Reissner-Nordstr\"{o}m spacetime. Despite their…
Some results related to the causality of compact Lorentzian manifolds are proven: (1) any compact Lorentzian manifold which admits a timelike conformal vector field is totally vicious, and (2) a compact Lorentzian manifold covered regularly…
It is widely held that plane wave spacetimes are causally well behaved which means that they are free from causal pathologies such as closed timelike curves or closed null geodesics. In this paper, we show that one can get closed null…
There is a by now well-established isomorphism between stationary 4-dimensional spacetimes and 3-dimensional purely spatial Randers geometries - these Randers geometries being a particular case of the more general class of 3-dimensional…
Abstractions of causal models allow for the coarsening of models such that relations of cause and effect are preserved. Whereas abstractions focus on the relation between two models, in this paper we study a framework for causal embeddings…
We derive a formula for the spacetime volume of a small causal cone. We use this formula within the context of causal set theory to construct causal set expressions for certain geometric quantities relating to a spacetime with a spacelike…
We review recent theoretical progress and observational constraints on multifractional spacetimes, geometries that change with the probed scale. On the theoretical side, the basic structure of the Standard Model and of the gravitational…
We investigate structure that describes physical data in gravitational systems that is, to one degree or another, independent of the metric and affine structure. We dub such structure surplus structure and seek to incorporate it into our…
Much of scientific data is collected as randomized experiments intervening on some and observing other variables of interest. Quite often, a given phenomenon is investigated in several studies, and different sets of variables are involved…
Causality plays an important role in daily processes, human reasoning, and artificial intelligence. There has however not been much research on causality in multi-agent strategic settings. In this work, we introduce a systematic way to…