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Causal reasoning is a crucial part of science and human intelligence. In order to discover causal relationships from data, we need structure discovery methods. We provide a review of background theory and a survey of methods for structure…
The Kibble-Zurek mechanism describes the evolution of topological defect structures like domain walls, strings, and monopoles when a system is driven through a second order phase transition. The model is used on very different scales like…
It is well-known that if one assumes quantum theory to hold locally, then processes with indefinite causal order and cyclic causal structures become feasible. Here, we study qualitative limitations on causal structures and correlations…
A well known argument in cosmology gives that the power spectrum (or structure function) $P(k)$ of mass density fluctuations produced from a uniform initial state by physics which is causal (i.e. moves matter and momentum only up to a…
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…
Developing predictive models that perform reliably across diverse patient populations and heterogeneous environments is a core aim of medical research. However, generalization is only possible if the learned model is robust to statistical…
The control of complex systems is an ongoing challenge of complexity research. Recent advances using concepts of structural control deduce a wide range of control related properties from the network representation of complex systems. Here,…
This study investigates how the interaction between gene expression time delay and domain size governs spatio-temporal pattern formation in a reaction-diffusion system. To investigate these phenomena, we utilize a modified version of the…
Growing networks have a causal structure. We show that the causality strongly influences the scaling and geometrical properties of the network. In particular the average distance between nodes is smaller for causal networks than for…
"What-if" questions are intuitively generated and commonly asked during the design process. Engineers and architects need to inherently conduct design decisions, progressing from one phase to another. They either use empirical domain…
We present results of numerical studies of the Landau-Ginzburg dynamics of the order parameter in one-dimensional models inspired by the condensed matter analogues of cosmological phase transitions. The main goal of our work is to show…
We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…
Schema-guided reasoning pipelines ask LLMs to produce explicit intermediate structures -- rubrics, checklists, verification queries -- before committing to a final decision. But do these structures causally determine the output, or merely…
We extend the theory of symmetry breaking dynamics in non-equilibrium second order phase transitions known as the Kibble-Zurek mechanism (KZM) to transitions where the change of phase occurs not in time, but in space. This can be due to a…
Modern systems (e.g., deep neural networks, big data analytics, and compilers) are highly configurable, which means they expose different performance behavior under different configurations. The fundamental challenge is that one cannot…
This paper addresses the problem of estimating causal effects when adjustment variables in the back-door or front-door criterion are partially observed. For such scenarios, we derive bounds on the causal effects by solving two non-linear…
This paper focuses on the problem of semi-supervised domain adaptation for time-series forecasting, which is underexplored in literatures, despite being often encountered in practice. Existing methods on time-series domain adaptation mainly…
Field dynamics in a rapidly expanding system is investigated by transforming from space-time to the rapidity - proper-time frame. The proper-time dependence of different contributions to the total energy is established. For systems…
Causal precedence between biochemical interactions is crucial in the biomedical domain, because it transforms collections of individual interactions, e.g., bindings and phosphorylations, into the causal mechanisms needed to inform…
The relation between domain wall motion and intensity of driven current is examined in a phenomenological theory where the kinetic energy is expanded as a series of polynomial function of current density just as the Landau phase transition…