Related papers: Introductory Causal Dynamical Triangulation
This is a Ph.D. thesis that presents the author's findings in the area of Causal Dynamical Triangulations. In compliance with Jagiellonian University of Krak\'ow regulations, the document consists of six publications and a general summary,…
With the rapid advancement of technology, 3D data acquisition and utilization have become increasingly prevalent across various fields, including computer vision, robotics, and geospatial analysis. 3D data, captured through methods such as…
In autonomous driving tasks, trajectory prediction in complex traffic environments requires adherence to real-world context conditions and behavior multimodalities. Existing methods predominantly rely on prior assumptions or generative…
We provide a pedagogical introduction to Regge theory as it pertains to the study of hadrons and their interactions. We clarify the fundamental concepts of analyticity in the complex angular momentum plane and their implications for…
Estimating dynamic treatment effects is a crucial endeavor in causal inference, particularly when confronted with high-dimensional confounders. Doubly robust (DR) approaches have emerged as promising tools for estimating treatment effects…
The discrete cosine transform (DCT) is a relevant tool in signal processing applications, mainly known for its good decorrelation properties. Current image and video coding standards -- such as JPEG and HEVC -- adopt the DCT as a…
Causal learning is the key to obtaining stable predictions and answering \textit{what if} problems in decision-makings. In causal learning, it is central to seek methods to estimate the average treatment effect (ATE) from observational…
In this paper, we introduce a decentralized digital twin (DDT) framework for dynamical systems and discuss the prospects of the DDT modeling paradigm in computational science and engineering applications. The DDT approach is built on a…
Recently, by using deep neural network based algorithms, object classification, detection and semantic segmentation solutions are significantly improved. However, one challenge for 2D image-based systems is that they cannot provide accurate…
Two-dimensional case in the theory of dynamical systems admitting the normal shift differs crucially from multidimensional case. Features of two-dimensional case are gathered and studied in this thesis.
Originating from Allen's Interval Algebra, composition-based reasoning has been widely acknowledged as the most popular reasoning technique in qualitative spatial and temporal reasoning. Given a qualitative calculus (i.e. a relation model),…
We report a high statistics simulation of Ising spins coupled to 2D quantum gravity in the Regge calculus approach using triangulated tori with up to $512^2$ vertices. For the constant area ensemble and the $dl/l$ functional measure we…
This review introduces Markov Chain Monte Carlo simulations in causal set theory, with a focus on the study of the 2d orders. It will first introduce the Benincasa-Dowker action on causal sets, and cover some musings on the philosophy of…
We define a new scaling limit of matrix models which can be related to the method of causal dynamical triangulations (CDT) used when investigating two-dimensional quantum gravity. Surprisingly, the new scaling limit of the matrix models is…
Regge calculus is a powerful method to approximate 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…
Generative AI models have made significant progress in automating the creation of 3D shapes, which has the potential to transform car design. In engineering design and optimization, evaluating engineering metrics is crucial. To make…
Causal representation learning promises to extend causal models to hidden causal variables from raw entangled measurements. However, most progress has focused on proving identifiability results in different settings, and we are not aware of…
Traditional clustering methods often perform clustering with low-level indiscriminative representations and ignore relationships between patterns, resulting in slight achievements in the era of deep learning. To handle this problem, we…
As an effective tool for two-dimensional data analysis, two-dimensional canonical correlation analysis (2DCCA) is not only capable of preserving the intrinsic structural information of original two-dimensional (2D) data, but also reduces…
The regression discontinuity design (RDD) is a quasi-experimental design that can be used to identify and estimate the causal effect of a treatment using observational data. In an RDD, a pre-specified rule is used for treatment assignment,…