相关论文: Causal Structures in Linear Spaces
We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. We define causaltopes, our chosen portmanteau of "causal polytopes", for…
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 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…
We introduce a two-dimensional metric (interval) temporal logic whose internal and external time flows are dense linear orderings. We provide a suitable semantics and a sequent calculus with axioms for equality and extralogical axioms. Then…
Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…
Causality among events is widely recognized as a most fundamental structure of spacetime, and causal sets have been proposed as discrete models of the latter in the context of quantum gravity theories, notably in the Causal Set Programme.…
More often than not, recently popular structuralist interpretations of physical theories leave the central concept of a structure insufficiently precisified. The incipient causal sets approach to quantum gravity offers a paradigmatic case…
A space curve is determined by conformal arc-length, conformal curvature, and conformal torsion, up to M\"obius transformations. We use the spaces of osculating circles and spheres to give a conformally defined moving frame of a curve in…
It is demonstrated how a convenient choice of the mathematical structure of the quantum cosmology superspace, precisely the definition of a convenient regular state superspace and the restriction of the dynamics to this space, yields…
Informally, the 'linear representation hypothesis' is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does "linear…
Topology and nonlinearity are deeply connected. However, whether topological effects can arise solely from the structure of nonlinear interaction terms, and the nature of the resulting topological phases, remain to large extent open…
Starting from the observation that distinct notions of copying have arisen in different categorical fields (logic and computation, contrasted with quantum mechanics) this paper addresses the question of when, or whether, they may coincide.…
Recent results on causality in noncommutative space-time are reviewed. We study, in particular, quantum causal structures in 1+1 dimensional kappa Minkowski space-time. This later is described by a twisted Lorentzian Spectral Triple build…
In this work, a possible description for quantum dynamics of the cuscuton within the sigma-model approach is presented. Lower order perturbative corrections and the structure of divergences are found. Motivated by the results generated by…
Topological techniques have become a popular tool for studying information flows in neural networks. In particular, simplicial homology theory is used to analyze how cognitive representations of space emerge from large conglomerates of…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
The subject of limit curve theorems in Lorentzian geometry is reviewed. A general limit curve theorem is formulated which includes the case of converging curves with endpoints and the case in which the limit points assigned since the…
A physical theory of experiments carried out in a space-time region can accommodate a detector localized in another space-like separated region, in three, not necessarily exclusive, ways: 1) the detector formally collapses physical states…
Among plenty of applications, low-dimensional homogeneous spaces appear in cosmological models as both, classical factor spaces of multidimensional geometry and minisuperspaces in canonical quantization. Here a new tool to restrict their…