arXiv subjects

Eleonora Andreotti

Publications and source records attributed to Eleonora Andreotti.

10 recordsLinked to original sources

arXiv2026

Collaboration, Integration, and Thematic Exploration in European Framework Programmes: A Longitudinal Network Analysis

Since their inception in 1984, the European Framework Programmes (FPs) have funded collaborative R&D to promote excellence, cohesion, and competitiveness in a growing European Union. However, their integrative impact and the evolution of the research landscape alongside its collaborative structures remain insufficiently understood. In this longitudinal study, we leverage CORDIS data from all nine FPs to reconstruct the evolution of country-level collaboration networks over time. We observe an increasing equity in project participation between FP1 and FP6, although newly included countries systematically tend to be marginal when first joining the programmes. However, we find that the collaborative nature of EU projects progressively integrates marginal countries in the network, even if this integration is still in progress. We also trace the evolution in time of research topics using semantic embeddings of project descriptions, identifying 117 topics grouped into 16 macro-topics. By computing the minimum spanning tree length of project embeddings within yearly time windows, we quantify how European research progressively explores a wider knowledge space. A comparison with a null model with points randomly distributed in the semantic space indicates that this exploration is more focused than a uniform coverage. Moreover, it appears uneven, with few topics mostly attracting industry and others academia. Our findings suggest that, while European funding promotes international cooperation, it has not yet fully resolved core-periphery asymmetries, and European research remains concentrated along established trajectories rather than broadly exploratory, with implications for future programme design and the excellence-cohesion debate.

physics.soc-ph↗

arXiv2025

Unifying points of interest taxonomies: mapping OpenStreetMap tags to the Foursquare category system

The heterogeneity of Point of Interest (POI) taxonomies is a persistent challenge for the integration of urban datasets and the development of location-based services. OpenStreetMap (OSM) adopts a flexible, community-driven tagging system, while Foursquare (FS) relies on a curated hierarchical structure. Here we present an openly available benchmark and mapping framework that aligns OSM tags with the FS taxonomy. This resource integrates the richness of community-driven OSM data with the hierarchical structure of FS, enabling reproducible and interoperable urban analytics. The dataset is complemented by an evaluation of embedding and LLM-based alignment strategies and a pipeline that supports scalable updates as OSM evolves. Together, these elements provide both a robust reference resource and a practical tool for the community. Our approach is structured around three components: the construction of a manually curated benchmark as a gold standard, the evaluation of pretrained text embedding models for semantic alignment between OSM tags and FS categories, and an LLM-based refinement stage that enhances robustness and adaptability. The proposed methodology provides a scalable and reproducible solution for taxonomy unification, with direct applications to urban analytics, mobility studies, and smart city services.

cs.SI↗

arXiv2025

Generalizing Lattice Structures to Hypergraphs: Spectra of Clique and Hyperedge-based Laplacians

Lattice structures play a central role in spectral graph theory, offering analytical insight into diffusion, synchronization, and transport processes on regular discrete spaces. While their spectral properties are completely characterized in the classical graph setting, an extension to hypergraphs, where interactions involve more than two nodes, remains largely unexplored in the matrix-based formulation. In this work, we generalize the notion of a lattice to the hypergraph framework and study its Laplacian spectra under two alternative definitions: the clique Laplacian, obtained through pairwise projection, and the hyperedge-based Laplacian, defined via normalized hyperedge incidences. For both definitions, we derive the corresponding Laplacian matrices, analyze their eigenvalue spectra, and discuss how they reflect the underlying topological and dynamical structure of the hyperlattice. Our main result is a theorem giving a full spectral characterization in the periodic case, together with a Toeplitz-type open analogue whose spectrum retains a separable trigonometric structure. The obtained eigenvalues are expressed explicitly in terms of the hyperedge size, the number of directional families, and the lattice side length, thereby capturing how the geometry of higher-order interactions shapes the spectral structure.

math.CO↗

arXiv2025

Scale-free Points-of-Interest Distribution in a City Emerging from Homogeneous Poissonian-point Processes

Urban systems often exhibit scale-invariant properties, with power-law distributions observed in various spatial and temporal patterns of human behavior. A prominent example is the distribution of commercial activities and other Points of Interest (POIs) across cities. However, the mechanisms by which such heavy-tailed behaviors emerge from local urban dynamics remain poorly understood. In this work, we demonstrate that global inhomogeneity in the spatial distribution of POIs can arise from the aggregation of locally homogeneous processes. Using Foursquare data from the city of Bologna, we show that POI distributions exhibit clear power-law scaling when analyzed at city scale. We develop a theoretical framework in which this behavior naturally emerges from spatial clusters defined by shared intensity levels across disjoint areas, rather than spatial contiguity. By analytically and empirically linking these local processes to the observed global distribution, we provide a generative explanation for the emergence of scale-free patterns in urban commercial structure. To further relax the assumptions underlying the purely spatial model, and to account for the empirical observation that areas with similar activity intensity can be spatially disjoint, we introduce a hybrid hierarchical approach that combines spatial clustering with statistical heterogeneity across regions of comparable density, modeled via Poisson mixtures. This enables us to capture real-world deviations from local regularity while preserving interpretability. Our findings highlight a key insight: complex global phenomena in cities can arise from the spatial superposition of simple, locally uniform dynamics. This connection between micro-level homogeneity and macro-scale complexity offers new tools for interpreting, modeling, and classifying urban space.

physics.soc-ph↗

arXiv2021

Signless Normalized Laplacian for Hypergraphs

The spectral theory of the normalized Laplacian for chemical hypergraphs is further investigated. The signless normalized Laplacian is introduced and it is shown that its spectrum for classical hypergraphs coincides with the spectrum of the normalized Laplacian for bipartite chemical hypergraphs. Furthermore, the spectra of special families of hypergraphs are established.

math.CO↗

arXiv2020

Measuring the stability of spectral clustering

As an indicator of the stability of spectral clustering of an undirected weighted graph into $k$ clusters, the $k$th spectral gap of the graph Laplacian is often considered. The $k$th spectral gap is characterized in this paper as an unstructured distance to ambiguity, namely as the minimal distance of the Laplacian to arbitrary symmetric matrices with vanishing $k$th spectral gap. As a conceptually more appropriate measure of stability, the structured distance to ambiguity of the $k$-clustering is introduced as the minimal distance of the Laplacian to Laplacians of graphs with the same vertices and edges but with weights that are perturbed such that the $k$th spectral gap vanishes. To compute a solution to this matrix nearness problem, a two-level iterative algorithm is proposed that uses a constrained gradient system of matrix differential equations in the inner iteration and a one-dimensional optimization of the perturbation size in the outer iteration. The structured and unstructured distances to ambiguity are compared on some example graphs. The numerical experiments show, in particular, that selecting the number $k$ of clusters according to the criterion of maximal stability can lead to different results for the structured and unstructured stability indicators.

math.NA↗

arXiv2020

Spectra of hyperstars on public transportation networks

The purpose of this paper is to introduce a model to study structures which are widely present in public transportation networks. We show that, through hypergraphs, one can describe these structures and investigate the relation between their spectra. To this aim, we extend the structure of $(m,k)$-stars on graphs to hypergraphs: the $(m,k)$-hyperstars on hypergraphs. Also, by giving suitable conditions on the hyperedge weights we prove the existence of matrix eigenvalues of computable values and multiplicities, where the matrices considered are Laplacian, adjacency and transition matrices. By considering separately the case of generic hypergraphs and uniform hypergraphs, we prove that two kinds of vertex set reductions on hypergraphs with $(m,k)$-hyperstar are feasible, keeping the same eigenvalues with reduced multiplicity. Finally, some useful eigenvectors properties are derived up to a product with a suitable matrix, and we relate these results to Fiedler spectral partitioning on the hypergraph.

math.CO↗

arXiv2018

Equivalence between spectral properties of graphs with and without loops

In this paper we introduce a spectra preserving relation between graphs with loops and graphs without loops. This relation is achieved in two steps. First, by generalizing spectra results got on (m, k)-stars to a wider class of graphs, the (m, k, s)-stars with or without loops. Second, by defining a covering space of graphs with loops that allows to remove the presence of loops by increasing the graph dimension. The equivalence of the two class of graphs allows to study graph with loops as simple graph without loosing information.

math.CO↗

arXiv2017

Graph partitioning using matrix differential equations

Given a connected undirected weighted graph, we are concerned with problems related to partitioning the graph. First of all we look for the closest disconnected graph (the minimum cut problem), here with respect to the Euclidean norm. We are interested in the case of constrained minimum cut problems, where constraints include cardinality or membership requirements, which leads to NP-hard combinatorial optimization problems. Furthermore, we are interested in ambiguity issues, that is in the robustness of clustering algorithms that are based on Fiedler spectral partitioning. The above-mentioned problems are restated as matrix nearness problems for the weight matrix of the graph. A key element in the solution of these matrix nearness problems is the use of a constrained gradient system of matrix differential equations.

math.NA↗

arXiv2017

On the multiplicity of Laplacian eigenvalues and Fiedler partitions

In this paper we study two classes of graphs, the (m,k)-stars and l-dependent graphs, investigating the relation between spectrum characteristics and graph structure: conditions on the topology and edge weights are given in order to get values and multiplicities of Laplacian matrix eigenvalues. We prove that a vertex set reduction on graphs with (m,k)-star subgraphs is feasible, keeping the same eigenvalues with reduced multiplicity. Moreover, some useful eigenvectors properties are derived up to a product with a suitable matrix. Finally, we relate these results with Fiedler spectral partitioning of the graph. The physical relevance of the results is shortly discussed.

math.NA↗