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This paper uncovers the fundamental relationship between total and partial computation in the form of an equivalence of certain categories. This equivalence involves on the one hand effectuses, which are categories for total computation,…
Statistical inference about the average effect in random-effects meta-analysis has been considered insufficient in the presence of substantial between-study heterogeneity. Predictive distributions are well-suited for quantifying…
We study cosmology in a class of minimally modified gravity (MMG) with two local gravitational degrees of freedom. We classify modified gravity theories into type-I and type-II: theories of type-I have an Einstein frame and can be recast by…
This thesis concerns embeddings and self-embeddings of foundational structures in both set theory and category theory. The first part of the work on models of set theory consists in establishing a refined version of Friedman's theorem on…
This paper considers the identification of dynamic treatment effects with panel data, in complex designs where the treatment may not be binary and may not be absorbing. We first show that under no-anticipation and parallel-trends…
Gauge-invariant perturbation theory is an extension of ordinary perturbation theory which describes strictly gauge-invariant states in theories with a Brout-Englert-Higgs effect. Such gauge-invariant states are composite operators which…
Unitarity is a cornerstone of quantum theory, ensuring the conservation of probability and information. Although non-Hermitian Hamiltonians are typically associated with open or dissipative systems, pseudo-Hermitian quantum mechanics shows…
Many segmentation tasks, such as medical image segmentation or future state prediction, are inherently ambiguous, meaning that multiple predictions are equally correct. Current methods typically rely on generative models to capture this…
In this paper we give a brief review of semiparametric theory, using as a running example the common problem of estimating an average causal effect. Semiparametric models allow at least part of the data-generating process to be unspecified…
A differential category is an additive symmetric monoidal category, that is, a symmetric monoidal category enriched over commutative monoids, with an algebra modality, axiomatizing smooth functions, and a deriving transformation on this…
Symmetry is ubiquitous in many real-world phenomena and tasks, such as physics, images, and molecular simulations. Empirical studies have demonstrated that incorporating symmetries into generative models can provide better generalization…
In this paper, the relationship between probabilistic graphical models, in particular Bayesian networks, and causal diagrams, also called structural causal models, is studied. Structural causal models are deterministic models, based on…
A higher-derivative, interacting, scalar field theory in curved spacetime with the most general action of sigma-model type is studied. The one-loop counterterms of the general theory are found. The renormalization group equations…
The analysis of contingency tables is a powerful statistical tool used in experiments with categorical variables. This study improves parts of the theory underlying the use of contingency tables. Specifically, the linkage disequilibrium…
The Standard Model of particle physics is standardly formulated in terms of principal fibre bundles and their associated representations -- what may be called a symmetry-first approach. This paper develops an alternative geometry-first…
Effectful categories have two classes of morphisms: pure morphisms, which form a monoidal category; and effectful morphisms, which can only be combined monoidally with central morphisms (such as the pure ones), forming a premonoidal…
We exhibit a functor from the category OUS of order unit spaces and positive, unit-preserving mappings into the category $\Prob$ of probabilistic models (test spaces with designated state spaces) and morphisms thereof. Restricted to any…
The image of physics is connected with simple "mechanical" deterministic events: that an apple always falls down, that force equals mass times acceleleration. Indeed, applications of such concept to social or historical problems go back two…
Researchers increasingly leverage movement across multiple treatments to estimate causal effects. While these "mover regressions" are often motivated by a linear constant-effects model, it is not clear what they capture under weaker…
We investigate the influence of diffraction on the statistics of energy levels in quantum systems with a chaotic classical limit. By applying the geometrical theory of diffraction we show that diffraction on singularities of the potential…