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Neural Architecture Representation Learning aims to transform network models into feature representations for predicting network attributes, playing a crucial role in deploying and designing networks for real-world applications. Recently,…

Causal DAGs(Directed Acyclic Graphs) are usually considered in a 2D plane. Edges indicate causal effects' directions and imply their corresponding time-passings. Due to the natural restriction of statistical models, effect estimation is…

We show that any twisted Dijkgraaf-Witten representation of a mapping class group of an orientable, compact surface with boundary has finite image. This generalizes work of Etingof, Rowell and Witherspoon showing that the braid group images…

Laplacian matrices of graphs arise in large-scale computational applications such as semi-supervised machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits;…

Describing a scene in terms of primitives -- geometrically simple shapes that offer a parsimonious but accurate abstraction of structure -- is an established and difficult fitting problem. Different scenes require different numbers of…

This paper proposes a new approach to deriving a finite particle content, suitable for the construction of a gauge theory. Specifically, the outlined construction generates a finite set of irreducible gauge representations, which are…

Deformable registration is a fundamental task in medical image processing, aiming to achieve precise alignment by establishing nonlinear correspondences between images. Traditional methods offer good adaptability and interpretability but…

Supervised deep learning models for automated CTG analysis are typically constrained by narrowly curated labelled datasets and limited patient cohorts, leaving substantial volumes of physiologically informative clinical recordings untapped.…

Due to the inherent flexibility of prompting, foundation models have emerged as the predominant force in the fields of natural language processing and computer vision. The recent introduction of the Segment Anything Model (SAM) signifies a…

Invariant theory provides more efficient tools, such as Molien generating functions and integrity bases, than basic group theory, that relies on projector techniques for the construction of symmetry--adapted polynomials in the symmetry…

Chain graphs (CG) use undirected and directed edges to represent both structural and associative dependences. Like acyclic directed graphs (ADGs), the CG associated with a statistical Markov model may not be unique, so CGs fall into Markov…

Foundation models, pre-trained on large image datasets and capable of capturing rich feature representations, have recently shown potential for zero-shot image registration. However, their performance has mostly been tested in the context…

We present Advancing Front Mapping (AFM), a provably robust algorithm for the computation of surface mappings to simple base domains. Given an input mesh and a convex or star-shaped target domain, AFM installs a (possibly refined) version…

Functional connectivity (FC) has become a primary means of understanding brain functions by identifying brain network interactions and, ultimately, how those interactions produce cognitions. A popular definition of FC is by statistical…

Strong untestable assumptions are almost universal in causal point estimation. In particular settings, bounds can be derived to narrow the possible range of a causal effect. Symbolic bounds apply to all settings that can be depicted using…

Directed acyclic graph (DAG) models, also called Bayesian networks, impose conditional independence constraints on a multivariate probability distribution, and are widely used in probabilistic reasoning, machine learning and causal…

Medical image registration is a fundamental task in medical image analysis, aiming to establish spatial correspondences between paired images. However, existing unsupervised deformable registration methods rely solely on intensity-based…

This paper presents an algebraic theory of linear signal processing. At the core of algebraic signal processing is the concept of a linear signal model defined as a triple (A, M, phi), where familiar concepts like the filter space and the…

We analyze the identifiability of directed acyclic graphs in the case of partial excitation and measurement. We consider an additive model where the nonlinear functions located in the edges depend only on a past input, and we analyze the…

The numerical approximation of partial differential equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and…