arXiv subjects

Emanuele Verri

Publications and source records attributed to Emanuele Verri.

4 recordsLinked to original sources

arXiv2025

Global Permutation Entropy

Permutation Entropy, introduced by Bandt and Pompe, is a widely used complexity measure for real-valued time series that is based on the relative order of values within consecutive segments of fixed length. After standardizing each segment to a permutation and computing the frequency distribution of these permutations, Shannon Entropy is then applied to quantify the series' complexity. We introduce Global Permutation Entropy (GPE), a novel index that considers all possible patterns of a given length, including non-consecutive ones. Its computation relies on recently developed algorithms that enable the efficient extraction of full permutation profiles. We illustrate some properties of GPE and demonstrate its effectiveness through experiments on synthetic datasets, showing that it reveals structural information not accessible through standard permutation entropy. We provide a Julia package for the calculation of GPE at `https://github.com/AThreeH1/Global-Permutation-Entropy'.

cs.LG↗

arXiv2025

Efficient counting of permutation patterns via double posets

Corner trees, introduced in "Even-Zohar and Leng, 2021, Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms", allow for the efficient counting of certain permutation patterns. Here we identify corner trees as a subset of finite (strict) double posets, which we term twin-tree double posets. They are contained in both twin double posets and tree double posets, giving candidate sets for generalizations of corner tree countings. We provide the generalization of an algorithm proposed by Even-Zohar/Leng to a class of tree double posets, thereby enlarging the space of permutations that can be counted in O(n^{5/3}).

math.CO↗

arXiv2023

Hopf Algebra on Vincular Permutation Patterns

We introduce a new Hopf algebra that operates on pairs of finite interval partitions and permutations of equal length. This algebra captures vincular patterns, which involve specifying both the permutation patterns and the consecutive occurrence of values. Our motivation stems from linear functionals that encode the number of occurrences of these patterns, and we show that they behave well with respect to the operations of this Hopf algebra.

math.RA↗

arXiv2023

Signatures of graphs for bicommutative Hopf algebras

This article approaches the counting of subgraphs, in terms of signature-type functionals defined over combinatorial Hopf algebras of graphs. Well-known algebraic identities that arise in the context of counting subgraphs are then captured by their character property and a type of "Chen's identity". While different notions of subgraphs (and homomorphisms) correspond to different combinatorial Hopf algebras on graphs, we will show that they are all isomorphic to a polynomial Hopf algebra. In addition, the isomorphy between the Hopf algebras can be realized by maps that respect the counting operations.

math.RA↗