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A natural generalization of the recognition problem for a geometric graph class is the problem of extending a representation of a subgraph to a representation of the whole graph. A related problem is to find representations for multiple…
Graphical Transformation Models (GTMs) are introduced as a novel approach to effectively model multivariate data with intricate marginals and complex dependency structures semiparametrically, while maintaining interpretability through the…
We study geodesics in generalized Wallach spaces which are expressed as orbits of products of three exponential terms. These are homogeneous spaces $M=G/K$ whose isotropy representation decomposes into a direct sum of three submodules…
In this paper, we present a method to compute the minimal form factors (MFFs) of diagonal integrable field theories perturbed by generalized $T\bar{T}$ perturbations. Building on existing results by the same authors, these MFFs are…
Kernelization algorithms, usually a preprocessing step before other more traditional algorithms, are very special in the sense that they return (reduced) instances, instead of final results. This characteristic excludes the freedom of…
Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and…
We introduce a simple procedure to integrate differential forms with arbitrary holomorphic poles on Riemann surfaces. It gives rise to an intrinsic regularization of such singular integrals in terms of the underlying conformal geometry.…
The two most popular types of graphical model are directed models (Bayesian networks) and undirected models (Markov random fields, or MRFs). Directed and undirected models offer complementary properties in model construction, expressing…
The aim of this article is to provide space level maps between configuration spaces of graphs that are predicted by algebraic manipulations of cellular chains. More explicitly, we consider edge contraction and half-edge deletion, and…
Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…
We study generating series of torus integrals that contain all so-called modular graph forms relevant for massless one-loop closed-string amplitudes. By analysing the differential equation of the generating series we construct a solution…
In recent years, knowledge graphs (KGs) - in particular in the form of labeled property graphs (LPGs) - have become essential components in a broad range of applications. Although the absence of strict schemas for KGs facilitates structural…
Modular symbols for the congruence subgroup $\Gamma_0(\mathfrak{n})$ of $GL_{2}(\mathbf{F}_q[T])$ have been defined by Teitelbaum. They have a presentation given by a finite number of generators and relations, in a formalism similar to…
Transformation coefficients between standard bases for irreducible representations of the Brauer centralizer algebra $\mathfrak{B}_f(x)$ and split bases adapted to the $\mathfrak{B}_{f_1} (x) \times \mathfrak{B}_{f_2} (x) \subset…
Nonnegative matrix factorization (NMF) is a popular method used to reduce dimensionality in data sets whose elements are nonnegative. It does so by decomposing the data set of interest, $\mathbf{X}$, into two lower rank nonnegative matrices…
Molecular graph generation (MGG) is essentially a multi-class generative task, aimed at predicting categories of atoms and bonds under strict chemical and structural constraints. However, many prevailing diffusion paradigms learn to regress…
Exploring sample relationships within each mini-batch has shown great potential for learning image representations. Existing works generally adopt the regular Transformer to model the visual content relationships, ignoring the cues of…
The aim of this paper is to introduce and study a large class of $\mathfrak{g}$-module algebras which we call factorizable by generalizing the Gauss factorization of (square or rectangular) matrices. This class includes coordinate algebras…
Grain boundaries (GBs) are ubiquitous in large-scale graphene samples, playing a crucial role in their overall performance. Due to their complexity, they are usually investigated as model structures, under the assumption of a fully relaxed…
We introduce a taxonomy of interaction types and show that graphs are focal hypergraphs: every graph is canonically a focal hypergraph via its closed neighbourhood structure, and every graph dynamical model is a special case of the general…