1 citations · 2 across the 15 of their papers we have counts for
17 papers
From Raw Segmentations to Simulation-Ready Cardiac Meshes: An Automated Framework for Anatomical Reconstruction and Virtual Cohort Generation
Francesco Fabbri, Martino Andrea Scarpolini, Paolo Ciancarella +4
Computational models of the human heart are widely used to study electromechanical and fluid-dynamical cardiac function and to support applications such as in silico clinical trial…
Neural-HSS: Hierarchical Semi-Separable Neural PDE Solver
Pietro Sittoni, Emanuele Zangrando, Angelo A. Casulli +2
Deep learning-based methods have shown remarkable effectiveness in solving PDEs, largely due to their ability to enable fast simulations once trained. However, despite the availabi…
Stuart-Landau Oscillatory Graph Neural Network
Kaicheng Zhang, David N. Reynolds, Piero Deidda +1
Oscillatory Graph Neural Networks (OGNNs) are an emerging class of physics-inspired architectures designed to mitigate oversmoothing and vanishing gradient problems in deep GNNs. I…
Nonlinear Joint Spectral Radius
Piero Deidda, Nicola Guglielmi, Francesco Tudisco
We introduce a nonlinear extension of the joint spectral radius (JSR) for switched discrete-time dynamical systems governed by sub-homogeneous and order-preserving maps acting on c…
Graph-Convolutional-Beta-VAE for Synthetic Abdominal Aorta Aneurysm Generation
Francesco Fabbri, Martino Andrea Scarpolini, Angelo Iollo +2
Synthetic data generation plays a crucial role in medical research by mitigating privacy concerns and enabling large-scale patient data analysis. This study presents a beta-Variati…
Nonlinear spectral graph theory
Piero Deidda, Francesco Tudisco, Dong Zhang
Nonlinear spectral graph theory is an extension of the traditional (linear) spectral graph theory and studies relationships between spectral properties of nonlinear operators defin…
Approximation properties of neural ODEs
Arturo De Marinis, Davide Murari, Elena Celledoni +3
We study the approximation properties of neural ordinary differential equations (neural ODEs) in the space of continuous functions. Since a neural ODE requires input and output dim…
Efficient Sparsification of Simplicial Complexes via Local Densities of States
Anton Savostianov, Michael T. Schaub, Nicola Guglielmi +1
Simplicial complexes (SCs) have become a popular abstraction for analyzing complex data using tools from topological data analysis or topological signal processing. However, the an…
Are We Measuring Oversmoothing in Graph Neural Networks Correctly?
Kaicheng Zhang, Piero Deidda, Desmond Higham +1
Oversmoothing is a fundamental challenge in graph neural networks (GNNs): as the number of layers increases, node embeddings become increasingly similar, and model performance drop…
Improving the robustness of neural ODEs with minimal weight perturbation
Arturo De Marinis, Nicola Guglielmi, Stefano Sicilia +1
We propose a method to enhance the stability of a neural ordinary differential equation (neural ODE) by reducing the maximum error growth subsequent to a perturbation of the initia…
The graph -Laplacian eigenvalue problem
Piero Deidda, Martin Burger, Mario Putti +1
We analyze various formulations of the -Laplacian eigenvalue problem on graphs, comparing their properties and highlighting their respective advantages and limitations. Fir…
Contractivity of neural ODEs: an eigenvalue optimization problem
Nicola Guglielmi, Arturo De Marinis, Anton Savostianov +1
We propose a novel methodology to solve a key eigenvalue optimization problem which arises in the contractivity analysis of neural ODEs. When looking at contractivity properties of…
Provable Emergence of Deep Neural Collapse and Low-Rank Bias in -Regularized Nonlinear Networks
Emanuele Zangrando, Piero Deidda, Simone Brugiapaglia +2
We present a unified theoretical framework connecting the first property of Deep Neural Collapse (DNC1) to the emergence of implicit low-rank bias in nonlinear networks trained wit…
Cholesky-like Preconditioner for Hodge Laplacians via Heavy Collapsible Subcomplex
Anton Savostianov, Francesco Tudisco, Nicola Guglielmi
Techniques based on -th order Hodge Laplacian operators are widely used to describe the topology as well as the governing dynamics of high-order systems modeled as simplic…
Learning the effective order of a hypergraph dynamical system
Leonie Neuhäuser, Michael Scholkemper, Francesco Tudisco +1
Dynamical systems on hypergraphs can display a rich set of behaviours not observable for systems with pairwise interactions. Given a distributed dynamical system with a putative hy…
Optimizing network robustness via Krylov subspaces
Stefano Massei, Francesco Tudisco
We consider the problem of attaining either the maximal increase or reduction of the robustness of a complex network by means of a bounded modification of a subset of the edge weig…
Nodal domain count for the generalized graph -Laplacian
Piero Deidda, Mario Putti, Francesco Tudisco
Inspired by the linear Schrödinger operator, we consider a generalized -Laplacian operator on discrete graphs and present new results that characterize several spectral properti…