Related papers: Causal Graph Dynamics and Kan Extensions
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
This thesis focuses on data that has complex spatio-temporal structure and on probabilistic graphical models that learn the structure in an interpretable and scalable manner. We target two research areas of interest: Gaussian graphical…
Graph transformations definable in logic can be described using the notion of transductions. By understanding transductions as a basic embedding mechanism, which captures the possibility of encoding one graph in another graph by means of…
The exploration of Graph Neural Networks (GNNs) for processing graph-structured data has expanded, particularly their potential for causal analysis due to their universal approximation capabilities. Anticipated to significantly enhance…
Covariate adjustment is a widely used approach to estimate total causal effects from observational data. Several graphical criteria have been developed in recent years to identify valid covariates for adjustment from graphical causal…
Many large-scale applications can be elegantly represented using graph structures. Their scalability, however, is often limited by the domain knowledge required to apply them. To address this problem, we propose a novel Causal Temporal…
Recently, there has been substantial interest in studying the dynamics of quantum theory beyond that of states, in particular, the dynamics of channels, measurements, and higher-order transformations. Ref. [Phys. Rev. X 8(1), 011047 (2018)]…
Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro-migration. Both continuous and stochastic dynamics are…
We study non-terminating graph rewriting models, whose local rules are applied non-deterministically -- and yet enjoy a strong form of determinism, namely space-time determinism. Of course in the case of terminating computation it is…
In recent years, diagrammatic languages have been shown to be a powerful and expressive tool for reasoning about physical, logical, and semantic processes represented as morphisms in a monoidal category. In particular, categorical quantum…
A major achievement in the study of complex networks is the observation that diverse systems, from sub-cellular biology to social networks, exhibit universal topological characteristics. Yet this universality does not naturally translate to…
We address the problem of defining graph transformations by the simultaneous application of direct transformations even when these cannot be applied independently of each other. An algebraic approach is adopted, with production rules of the…
We extend the notions of nonautonomous dynamics to arbitrary groups, through groupoid morphisms. This also presents a generalization of classic dynamical systems and group actions. We introduce the structure of cotranslations, as a specific…
The formalism of Causal Dynamical Triangulations (CDT) attempts to provide a non-perturbative regularization of quantum gravity, viewed as an ordinary quantum field theory. In two dimensions one can solve the lattice theory analytically and…
The applicability of computational and dynamical systems models to organisms is scrutinized, using examples from developmental biology and cognition. Developmental morphogenesis is dependent on the inherent material properties of developing…
In machine learning, exploring data correlations to predict outcomes is a fundamental task. Recognizing causal relationships embedded within data is pivotal for a comprehensive understanding of system dynamics, the significance of which is…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
Causal abstractions allow us to relate causal models on different levels of granularity. To ensure that the models agree on cause and effect, frameworks for causal abstractions define notions of consistency. Two distinct methods for causal…
Built upon the shoulders of graph theory, the field of complex networks has become a central tool for studying real systems across various fields of research. Represented as graphs, different systems can be studied using the same analysis…
We present a graph theory-based method to characterise flow defects and structural shifts in condensed matter. We explore the connection between dynamical properties, particularly the recently introduced concept of ''softness'', and…