Related papers: Directed diagrammatic reducibility
Let $K$ be an algebraically closed field of arbitrary characteristic, $X$ an irreducible variety and $Y$ an irreducible projective variety over $K$, both are not necessarily smooth. Let $f:X\rightarrow X$ and $g:Y\rightarrow Y$ be dominant…
We study random graph models for directed acyclic graphs, an important class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models, roughly analogous to the…
Butterfly minors are a generalisation of the minor containment relation for undirected graphs to directed graphs. Many results in directed structural graph theory use this notion as a central tool next to directed treewidth, a…
We present a new method for completing higher derivative corrections for theories that exhibit duality symmetries under reduction. This proposal is based on the observation that duality symmetry in the reduced theory highly constrains the…
We define a graph Laplacian with vertex weights in addition to the more classical edge weights, which unifies the combinatorial Laplacian and the normalised Laplacian. Moreover, we give a combinatorial interpretation for the coefficients of…
We study a class of Riemannian manifolds with respect to the covariant derivative of their curvature tensors. We introduce geometrically the class of directed Riemannian manifolds of pointwise constant relative sectional curvature and give…
We study the controllability of a Partial Differential Equation of transport type, that arises in crowd models. We are interested in controlling it with a control being a vector field, representing a perturbation of the velocity, localized…
Decision trees (DTs) embody interpretable classifiers. DTs have been advocated for deployment in high-risk applications, but also for explaining other complex classifiers. Nevertheless, recent work has demonstrated that predictions in DTs…
Directed graphs have long been used to gain understanding of the structure of semigroups, and recently the structure of directed graph semigroups has been investigated resulting in a characterization theorem and an analog of Fruct's…
This short note introduces a notion of directed homotopy equivalence and of "directed" topological complexity (which elaborates on the notion that can be found in e.g. Farber's book) which have a number of desirable joint properties. In…
A powerful data transformation method named guided projections is proposed creating new possibilities to reveal the group structure of high-dimensional data in the presence of noise variables. Utilising projections onto a space spanned by a…
We study adaptive data-dependent dimensionality reduction in the context of supervised learning in general metric spaces. Our main statistical contribution is a generalization bound for Lipschitz functions in metric spaces that are…
In this paper, we define and study the concept of traceable regressions. These are sequences of regressions in joint or single responses for which a corresponding regression graph captures not only an independence structure but represents,…
A new approach to find all the transitive orientations for a comparability graph (finite or infinite) is presented. This approach is based on the link between the notion of ``strong'' partitive set and the forcing theory (notions of…
In general the problem of finding a miminum spanning tree for a weighted directed graph is difficult but solvable. There are a lot of differences between problems for directed and undirected graphs, therefore the algorithms for undirected…
This article is concerned with automating the decreasing diagrams technique of van Oostrom for establishing confluence of term rewrite systems. We study abstract criteria that allow to lexicographically combine labelings to show local…
In a former paper the first and third authors introduced the notion of direction set for a subset of R^n, and showed that the dimension of the common direction set of two subanalytic subsets, called directional dimension, is preserved by a…
We apply the techniques of computable model theory to the distance function of a graph. This task leads us to adapt the definitions of several truth-table reducibilities so that they apply to functions as well as to sets, and we prove…
In this article, we introduce a notion of reducibility for partial functions on the natural numbers, which we call subTuring reducibility. One important aspect is that the subTuring degrees correspond to the structure of the realizability…
The main purpose of this paper is to define dynamical degrees for rational maps over an algebraic closed field of characteristic zero and prove some basic properties (such as log-concavity) and give some applications. We also define…