Related papers: Directed diagrammatic reducibility
In Riemannian computing applications, it is crucial to map manifold data to a Euclidean domain, where vector space arithmetic is available, and back. Classical manifold theory guarantees the existence of such mappings, called charts and…
We develop the representation theory for reductive linear differential algebraic groups (LDAGs). In particular, we exhibit an explicit sharp upper bound for orders of derivatives in differential representations of reductive LDAGs, extending…
Decomposable graphs are known for their tedious and complicated Markov update steps. Instead of modelling them directly, this work introduces a class of tree-dependent bipartite graphs that span the projective space of decomposable graphs.…
We generate new mathematical tools with which to quantify the macroscopic topological structure of large directed networks. This is achieved via a statistical mechanical analysis of constrained maximum entropy ensembles of directed random…
We study a model of random $\mathcal{R}$-enriched trees that is based on weights on the $\mathcal{R}$-structures and allows for a unified treatment of a large family of random discrete structures. We establish distributional limits…
In recent years, a variety of novel measures of dependence have been introduced being capable of characterizing diverse types of directed dependence, hence diverse types of how a number of predictor variables $\mathbf{X} = (X_1, \dots,…
We introduce a dynamic data structure for the compact representation of binary relations $\mathcal{R} \subseteq A \times B$. The data structure is a dynamic variant of the k$^2$-tree, a static compact representation that takes advantage of…
The relationship according to which one physical theory encompasses the domain of empirical validity of another is widely known as "reduction." Here it is argued that one popular methodology for showing that one theory reduces to another,…
This paper investigates properties of realizations of linear or group codes on general graphs that lead to local reducibility. Trimness and properness are dual properties of constraint codes. A linear or group realization with a constraint…
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…
Hyperbolicity is a property of a graph that may be viewed as being a "soft" version of a tree, and recent empirical and theoretical work has suggested that many graphs arising in Internet and related data applications have hyperbolic…
The large size of multiscale, distribution and transmission, power grids hinder fast system-wide estimation and real-time control and optimization of operations. This paper studies graph reduction methods of power grids that are favorable…
We develop a complete theory for the combinatorics of walk-counting on a directed graph in the case where each backtracking step is downweighted by a given factor. By deriving expressions for the associated generating functions, we also…
Optimal transport (\OT) theory defines a powerful set of tools to compare probability distributions. \OT~suffers however from a few drawbacks, computational and statistical, which have encouraged the proposal of several regularized variants…
Tree-graded spaces are a generalization of $\mathbb{R}$-trees and play an important role in describing the large-scale geometry of relatively hyperbolic groups. We consider a subclass of tree-graded spaces that we call "disjointly…
This article expands our work in [Ca16]. By its reliance on Turing computability, the classical theory of effectivity, along with effective reducibility and Weihrauch reducibility, is only applicable to objects that are either countable or…
We prove local convergence results for the uniformly random, labelled or unlabelled, graphs from subcritical families. As an example special case, we prove Benjamini-Schramm convergence for the uniform random unlabelled tree. We introduce a…
We derive computationally tractable methods to select a small subset of experiment settings from a large pool of given design points. The primary focus is on linear regression models, while the technique extends to generalized linear models…
We introduce the notion of weak reduciblity for Dupin submanifolds with arbitrary codimension. We give a complete characterization of all weakly reducible Dupin submanifolds, as a consequence of a general result on a broader class of…
We introduce a general framework of low regularity integrators which allows us to approximate the time dynamics of a large class of equations, including parabolic and hyperbolic problems, as well as dispersive equations, up to arbitrary…