arXiv subjects

Michela Ascolese

Publications and source records attributed to Michela Ascolese.

4 recordsLinked to original sources

arXiv2026

A graph reconstruction problem involving common neighbors

Given a simple graph $G = (V, E)$ on $v$ vertices and two distinct vertices $x, y \in V$, the co-degree $c_{x,y}$ associated to the pair $\{x, y\}$ is the number of their common neighbors in the graph $G$. The co-degree sequence of $G$, denoted by $γ(G)$, is the list of all the co-degrees associated to all the possible pairs of distinct vertices, arranged in non-increasing order. In this paper we consider the following problem, which can be viewed as a generalization of a result by Erdős and Gallai as well as of the Erdős, Rényi and Sós' friendship theorem: given an integer $v\geqslant 2$ and a sequence $γ$ of nonnegative integers arranged in non-increasing order, establish if there exists a simple graph on $v$ vertices having $γ$ as its co-degree sequence and, in case of positive answer, provide such a graph. We provide a full answer to this problem for the class of planar $C_4$-free graphs.

math.CO↗

arXiv2026

Weakly supervised neural network: segmentation of complex structures in X-ray microCT

Segmentation of complex structures in X-ray tomographic data is a fundamental task in biomedical research, but it often requires large amounts of precisely annotated data, making fully supervised approaches costly and difficult to scale. In this study, weakly supervised deep learning is investigated as a strategy to reduce annotation effort while maintaining accurate segmentation. A two-dimensional convolutional neural network based on the nnU-Net framework was adapted to a weak supervision setting using sparse dot-based annotations, complemented by a limited number of fully segmented images. The approach was evaluated on high-resolution microCT slices of rat kidneys, targeting the segmentation of renal glomeruli, which are small, low-contrast anatomical structures. Results indicate that weak supervision provides a meaningful learning signal, enabling reliable localization of glomeruli even in the absence of dense labels. Incorporating a small set of high-quality annotations substantially improves segmentation performance, approaching that of a fully supervised model. These findings highlight the potential of weakly supervised learning as an annotation-efficient strategy for the analysis of complex structures in X-ray tomographic data, and suggest that alternative loss formulations tailored to sparse annotations may further enhance performance.

cs.AI↗

arXiv2024

Randomized algorithms to generate hypergraphs with given degree sequences

The question whether there exists a hypergraph whose degrees are equal to a given sequence of integers is a well-known reconstruction problem in graph theory, which is motivated by discrete tomography. In this paper we approach the problem by randomized algorithms which generate the required hypergraph with positive probability if the sequence satisfies certain constraints.

math.CO↗

arXiv2023

On a conjecture on prime double square tiles

In [2], while studying a relevant class of polyominoes that tile the plane by translation, i.e., double square polyominoes, the authors found that their boundary words, encoded by the Freeman chain coding on a four letters alphabet, have specific interesting properties that involve notions of combinatorics on words such as palindromicity, periodicity and symmetry. Furthermore, they defined a notion of reducibility on double squares using homologous morphisms, so leading to a set of irreducible tile elements called prime double squares. The authors, by inspecting the boundary words of the smallest prime double squares, conjectured the strong property that no runs of two (or more) consecutive equal letters are present there. In this paper, we prove such a conjecture using combinatorics on words tools, and setting the path to the definition of a fast generation algorithm and to the possibility of enumerating the elements of this class w.r.t. standard parameters, as perimeter and area.

math.CO↗