Related papers: Introductory Causal Dynamical Triangulation
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
We review some recent results from the causal dynamical triangulation (CDT) approach to quantum gravity. We review recent observations of dimensional reduction at a number of previously undetermined points in the parameter space of CDT, and…
To solve the path integral for quantum gravity, one needs to regularise the space-times that are summed over. This regularisation usually is a discretisation, which makes it necessary to give up some paradigms or symmetries of continuum…
Recent years have seen a surge of interest in learning high-level causal representations from low-level image pairs under interventions. Yet, existing efforts are largely limited to simple synthetic settings that are far away from…
We introduce a dually-weighted multi-matrix model that for a suitable choice of weights reproduce two-dimensional Causal Dynamical Triangulations (CDT) coupled to the Ising model. When Ising degrees of freedom are removed, this model…
The Regge Calculus approximates a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The Discrete Regge model employed in this work…
This paper proposes an efficient approach to learning disentangled representations with causal mechanisms based on the difference of conditional probabilities in original and new distributions. We approximate the difference with models'…
The Causal Dynamical Triangulation model of quantum gravity (CDT) has a transfer matrix, relating spatial geometries at adjacent (discrete lattice) times. The transfer matrix uniquely determines the theory. We show that the measurements of…
The proper handling of 3D orientations is a central element in many optimization problems in engineering. Unfortunately many researchers and engineers struggle with the formulation of such problems and often fall back to suboptimal…
Causal reasoning can be considered a cornerstone of intelligent systems. Having access to an underlying causal graph comes with the promise of cause-effect estimation and the identification of efficient and safe interventions. However,…
In Regge calculus space time is usually approximated by a triangulation with flat simplices. We present a formulation using simplices with constant sectional curvature adjusted to the presence of a cosmological constant. As we will show…
A fast Discrete Cosine Transform (DCT) algorithm is introduced that can be of particular interest in image processing. The main features of the algorithm are regularity of the graph and very low arithmetic complexity. The 16-point version…
This thesis develops methods for causal inference and causal representation learning (CRL) in high-dimensional, time-varying data. The first contribution introduces the Causal Dynamic Variational Autoencoder (CDVAE), a model for estimating…
The article proposes formulating and codifying a set of applied numerical methods, coined as Deep Learning Discrete Calculus (DLDC), that uses the knowledge from discrete numerical methods to interpret the deep learning algorithms through…
Why does a phenomenon occur? Addressing this question is central to most scientific inquiries and often relies on simulations of scientific models. As models become more intricate, deciphering the causes behind phenomena in high-dimensional…
Integrating expert knowledge, e.g. from large language models, into causal discovery algorithms can be challenging when the knowledge is not guaranteed to be correct. Expert recommendations may contradict data-driven results, and their…
Automatic chest X-ray report generation is an important area of research aimed at improving diagnostic accuracy and helping doctors make faster decisions. Current AI models are good at finding correlations (or patterns) in medical images.…
Early detection and diagnosis of coronary artery disease (CAD) could save lives and reduce healthcare costs. The current clinical practice is to perform CAD diagnosis through analysing medical images from computed tomography coronary…
We analyze the matrix model characterizing the Ising model coupled to Causal Dynamical Triangulations (CDT) from the point of view of the Functional Renormalization Group Equation (FRGE). This model is a dually weighted matrix model, whose…
Dynamic Uncertain Causality Graph(DUCG) is a recently proposed model for diagnoses of complex systems. It performs well for industry system such as nuclear power plants, chemical system and spacecrafts. However, the variable state…