Related papers: Computability of the causal boundary by using isoc…

Global hyperbolicity is a central concept in Mathematical Relativity. Here, we review the different approaches to this concept explaining both, classical approaches and recent results. The former includes Cauchy hypersurfaces, naked…

The b-boundary construction by B. Schmidt is a general way of providing a boundary to a manifold with connection. It has been shown to have undesirable topological properties however. C. J. S. Clarke gave a result showing that for…

We discuss recent work for causal inference and predictive robustness in a unifying way. The key idea relies on a notion of probabilistic invariance or stability: it opens up new insights for formulating causality as a certain risk…

In this study, we deal with the local structure of curves and surfaces immersed in a pseudo-isotropic space I_{p}^{3} that is a particular Cayley-Klein space. We provide the formulas of curvature, torsion and Frenet trihedron in order for…

It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical…

We employ a variational approach to study the Neumann boundary value problem for the $p$-Laplacian on bounded smooth-enough domains in the metric setting, and show that solutions exist and are bounded. The boundary data considered are Borel…

To a significant extent, the metrical and topological properties of spacetime can be described purely order-theoretically. The $K^+$ relation has proven to be useful for this purpose, and one could wonder whether it could serve as the…

The quantum theory of near horizon regions of spacetimes with classical spatially flat, homogeneous and isotropic Friedman-Robertson-Walker geometry can be approximately described by a two dimensional conformal field theory. The central…

Relationalism -- along the lines developed by Barbour and collaborators in the past 3 decades -- can be considered an advance with 1/4 of the facets of the canonical approach's Problem of Time as identified by Isham and Kuchar. Indeed,…

We focus on three distinct lines of recent developments: edge modes and boundary charges in gravitational physics, relational dynamics in classical and quantum gravity, and quantum reference frames. We argue that these research directions…

An outstanding issue in the treatment of boundaries in general relativity is the lack of a local geometric interpretation of the necessary boundary data. For the Cauchy problem, the initial data is supplied by the 3-metric and extrinsic…

In a bounded domain, we consider a variable range nonlocal operator, which is maximally isotropic in the sense that its radius of interaction equals the distance to the boundary. We establish $C^{1,\alpha}$ boundary regularity and existence…

Substatic Riemannian manifolds with minimal boundary arise naturally in General Relativity as spatial slices of static spacetimes satisfying the Null Energy Condition. Moreover, they constitute a vast generalization of nonnegative Ricci…

We present the set of axioms for topological space with the operation of boundary as primitive notion.

Causal discovery is the subfield of causal inference concerned with estimating the structure of cause-and-effect relationships in a system of interrelated variables, as opposed to quantifying the strength or describing the form of causal…

Cosmological correlators are very important objects in cosmology as they offer us a huge amount of information of the early universe. They reside on the future boundary of a de Sitter space and can be calculated by two methods. First method…

Learning the dynamic causal structure of time series is a challenging problem. Most existing approaches rely on distributional or structural invariance to uncover underlying causal dynamics, assuming stationary or partially stationary…

Computational analysis of time-course data with an underlying causal structure is needed in a variety of domains, including neural spike trains, stock price movements, and gene expression levels. However, it can be challenging to determine…

Deep learning has revolutionized the field of artificial intelligence. Based on the statistical correlations uncovered by deep learning-based methods, computer vision has contributed to tremendous growth in areas like autonomous driving and…

Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…