Related papers: Matrix and graph representations of vine copula st…
Matchings and coverings are central topics in graph theory. The close relationship between these two has been key to many fundamental algorithmic and polyhedral results. For mixed graphs, the notion of matching forest was proposed as a…
The original development of Shapley values for prediction explanation relied on the assumption that the features being described were independent. If the features in reality are dependent this may lead to incorrect explanations. Hence,…
We present an interface between PineAPPL and Matrix, which allows fully differential cross sections to be calculated in the form of interpolation grids, accurate at next-to-next-to-leading order (NNLO) in QCD and next-to-leading order in…
Current applications have produced graphs on the order of hundreds of thousands of nodes and millions of edges. To take advantage of such graphs, one must be able to find patterns, outliers and communities. These tasks are better performed…
In an attempt to prove the Graceful Tree Conjecture, we present two propagation of graphs. The first is to propagate graceful graphs, and the second is to propagate trees from a gracefully labeled tree. The motivation in propagating such…
A shelling of a graph, viewed as an abstract simplicial complex that is pure of dimension 1, is an ordering of its edges such that every edge is adjacent to some other edges appeared previously. In this paper, we focus on complete bipartite…
In this chapter we show that chordal structure can be used to devise efficient optimization methods for many common model predictive control problems. The chordal structure is used both for computing search directions efficiently as well as…
Phylogenetic networks are used to represent evolutionary scenarios in biology and linguistics. To find the most probable scenario, it may be necessary to compare candidate networks, to distinguish different networks, and to see when one…
This study introduces a new method of visualizing complex tree structured objects. The usefulness of this method is illustrated in the context of detecting unexpected features in a data set of very large trees. The major contribution is a…
Most algorithms for computing persistent homology do so by tracking cycles that represent homology classes. There are many choices of such cycles, and specific choices have found different uses in applications. Although it is known that…
A new framework is proposed to study rank-structured matrices arising from discretizations of 2D and 3D elliptic operators. In particular, we introduce the notion of a graph-induced rank structure (GIRS) which aims to capture the fine low…
It is known that any chordal graph on $n$ vertices can be represented as the intersection of $n$ subtrees in a tree on $n$ nodes. This fact is recently used in [2] to generate random chordal graphs on $n$ vertices by generating $n$ subtrees…
Vine copula models have become highly popular and practical tools for modelling multivariate probability distributions due to their flexibility in modelling different kinds of dependences between the random variables involved. However,…
Discrete statistical models supported on labelled event trees can be specified using so-called interpolating polynomials which are generalizations of generating functions. These admit a nested representation. A new algorithm exploits the…
Vine copulas are a flexible tool for multivariate non-Gaussian distributions. For data from an observational study where the explanatory variables and response variables are measured together, a proposed vine copula regression method uses…
We show that there exist linear-time algorithms that compute the strong chromatic index and a maximum induced matching of tree-cographs when the decomposition tree is a part of the input. We also show that there exist efficient algorithms…
For an arbitrary tree we investigate the problems of constructing a maximum matching which minimizes or maximizes the cardinality of a maximum matching of the graph obtained from original one by its removal and present corresponding…
We construct tree-decompositions of graphs that distinguish all their k-blocks and tangles of order k, for any fixed integer k. We describe a family of algorithms to construct such decompositions, seeking to maximize their diversity subject…
In this paper, we prove that the self-dual morphological hierarchical structure computed on a n-D gray-level wellcomposed image u by the algorithm of G{\'e}raud et al. [1] is exactly the mathematical structure defined to be the tree of…
We introduce a novel representation of structured polynomial ideals, which we refer to as chordal networks. The sparsity structure of a polynomial system is often described by a graph that captures the interactions among the variables.…