18 citations · 46 across the 10 of their papers we have counts for
19 papers
Persistent Homology and Equivariance in Data Analysis: A Topological Introduction
Patrizio Frosini, Ulderico Fugacci, Nicola Quercioli +1
This new book is intended as a first elementary introduction to Topological Data Analysis for mathematics students seeking a rigorous account of the foundations of persistent homol…
LARAG: Link-Aware Retrieval Strategy for RAG Systems in Hyperlinked Technical Documentation
Giorgia Bolognesi, Claudio Estatico, Ulderico Fugacci +3
Retrieval-Augmented Generation (RAG) enhances the factual grounding of Large Language Models by conditioning their outputs on external documents. However, standard embedding-based…
Hook-decomposable modules and their resolutions
Isabella Mastroianni, Marco Guerra, Ulderico Fugacci +1
We compare several classes of biparameter persistence modules: -products of monoparameter modules, hook-decomposable modules, modules admitting a Smith-type structure theorem, a…
The Convex Matching Distance in Multiparameter Persistence
Francesco Conti, Patrizio Frosini, Ulderico Fugacci +4
We introduce the convex matching distance, a novel metric for comparing functions with values in the real plane. This metric measures the maximal bottleneck distance between the pe…
SHREC 2025: Protein surface shape retrieval including electrostatic potential
Taher Yacoub, Camille Depenveiller, Atsushi Tatsuma +25
This SHREC 2025 track dedicated to protein surface shape retrieval involved 9 participating teams. We evaluated the performance in retrieval of 15 proposed methods on a large datas…
Topological Correlation
Isabella Mastroianni, Ulderico Fugacci
We introduce two novel concepts, topological difference and topological correlation, that offer a new perspective on the discriminative power of multiparameter persistence. The for…
Retrieving biparameter persistence modules from monoparameter ones: a characterization of hook-decomposable persistence modules
Isabella Mastroianni, Marco Guerra, Ulderico Fugacci +1
Motivated by the need to relate the biparameter persistence module induced by a pair of scalar functions with the monoparameter persistence modules induced by each function separat…
GEO-Nav: a geometric dataset of voltage-gated sodium channels
Andrea Raffo, Ulderico Fugacci, Silvia Biasotti
Voltage-gated sodium (Nav) channels constitute a prime target for drug design and discovery, given their implication in various diseases such as epilepsy, migraine and ataxia to na…
SHREC 2022: Protein-ligand binding site recognition
Luca Gagliardi, Andrea Raffo, Ulderico Fugacci +12
This paper presents the methods that have participated in the SHREC 2022 contest on protein-ligand binding site recognition. The prediction of protein-ligand binding regions is an…
Compression for 2-Parameter Persistent Homology
Ulderico Fugacci, Michael Kerber, Alexander Rolle
Compression aims to reduce the size of an input, while maintaining its relevant properties. For multi-parameter persistent homology, compression is a necessary step in any computat…
SHREC 2021: Retrieval and classification of protein surfaces equipped with physical and chemical properties
Andrea Raffo, Ulderico Fugacci, Silvia Biasotti +21
This paper presents the methods that have participated in the SHREC 2021 contest on retrieval and classification of protein surfaces on the basis of their geometry and physicochemi…
On the notion of weak isometry for finite metric spaces
Alessandro De Gregorio, Ulderico Fugacci, Facundo Memoli +1
Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of…
Homological Scaffold via Minimal Homology Bases
Marco Guerra, Alessandro De Gregorio, Ulderico Fugacci +2
The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representa…
Critical Sets of PL and Discrete Morse Theory: a Correspondence
Ulderico Fugacci, Claudia Landi, Hanife Varlı
Piecewise-linear (PL) Morse theory and discrete Morse theory are used in shape analysis tasks to investigate the topological features of discretized spaces. In spite of their commo…
Topology-Preserving Terrain Simplification
Ulderico Fugacci, Michael Kerber, Hugo Manet
We give necessary and sufficient criteria for elementary operations in a two-dimensional terrain to preserve the persistent homology induced by the height function. These operation…
Chunk Reduction for Multi-Parameter Persistent Homology
Ulderico Fugacci, Michael Kerber
The extension of persistent homology to multi-parameter setups is an algorithmic challenge. Since most computation tasks scale badly with the size of the input complex, an importan…
Computing discrete Morse complexes from simplicial complexes
Ulderico Fugacci, Federico Iuricich, Leila De Floriani
We consider the problem of efficiently computing a discrete Morse complex on simplicial complexes of arbitrary dimension and very large size. Based on a common graph-based formalis…
A Kernel for Multi-Parameter Persistent Homology
René Corbet, Ulderico Fugacci, Michael Kerber +2
Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one…
Betti splitting from a topological point of view
Davide Bolognini, Ulderico Fugacci
A Betti splitting of a monomial ideal ensures the recovery of the graded Betti numbers of starting from those of and . In this paper, we introduce t…