Andrea Vandin

Luca Cardelli, Mirco Tribastone, Max Tschaikowski et al.

It is well known that exact notions of model abstraction and reduction for dynamical systems may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. In this paper we consider this problem for nonlinear ordinary differential equations (ODEs) with polynomial derivatives. We introduce approximate differential equivalence as a more permissive variant of a recently developed exact counterpart, allowing ODE variables to be related even when they are governed by nearby derivatives. We develop algorithms to (i) compute the largest approximate differential equivalence; (ii) construct an approximate quotient model from the original one via an appropriate parameter perturbation; and (iii) provide a formal certificate on the quality of the approximation as an error bound, computed as an over-approximation of the reachable set of the perturbed model. Finally, we apply approximate differential equivalences to study the effect of parametric tolerances in models of symmetric electric circuits.

Riccardo Porcedda, Francesca Chiaromonte, Fabrizio Lillo et al.

Link prediction (inferring missing or future connections between nodes in a graph) is a fundamental problem in network science with widespread applications in, e.g., biological systems, recommender systems, finance and cybersecurity. The ability to accurately predict links has significant real-world applications, such as detecting fraudulent financial transactions or identifying drug-target interactions in biomedicine. Despite a rich literature, link prediction is still challenging, especially for graphs enriched with information on edges (direction) and nodes (attributes). In fact, research on link prediction, especially the one based on Graph Deep Learning (GDL), has mostly focused on undirected graphs, without fully leveraging node attributes. Here, we fill this gap by proposing Gravity-GraphSAGE (GG-SAGE), a modified version of GraphSAGE, a GDL model for node embeddings, composed of a gravity-inspired decoder. This implementation is the first example in the literature of a GraphSAGE backbone adopted for directed link prediction. Using the benchmark datasets Cora, Citeseer, PubMed and 16 real-world graphs from the online Netzschleuder repository, we show that our proposed model outperforms state-of-the-art GDL link prediction techniques. Using further experimental evidence, we relate the quality of the output of our model with various characteristics of the graph, suggesting that our framework scales well when applied to data of increasing complexity.

Riccardo Porcedda, Giuseppe Squillace, Bastian Epping et al.

While Graph Neural Networks (GNNs) have demonstrated significant efficacy in node classification tasks, where predictions rely on local neighborhood information, the performance of GNNs often drops when prediction tasks depend on long-range interactions. These limitations are attributed to phenomena such as oversquashing, where structural bottlenecks restrict signal propagation across the network topology. To address this challenge, we introduce RAwR, a computationally efficient rewiring framework that augments the input graph with a quotient graph derived from equitable partitions. This approach facilitates accelerated communication between nodes that share identical structural roles, as identified by the Weisfeiler-Leman graph coloring, and thereby reduces the total effective resistance of the system. Furthermore, by employing an approximate definition of the equitable partition, RAwR enables a controllable reduction of the quotient graph, which, in its most condensed state, recovers the conventional Master Node rewiring technique. Empirical evaluations across a diverse suite of benchmarks -- including homophilic, heterophilic, and synthetic long-range datasets -- demonstrate that RAwR achieves state-of-the-art results. Our contribution is further supported by an analytical investigation using a teacher-student model of linear GNNs, which elucidates the theoretical foundations of role-based rewiring. This analysis leads to the formulation of Spectral Role Lift (SRL), a metric designed to identify the optimal approximate equitable partition for maximizing predictive performance.

Giuseppe Squillace, Mirco Tribastone, Max Tschaikowski et al.

Structural network embedding is a crucial step in enabling effective downstream tasks for complex systems that aims to project a network into a lower-dimensional space while preserving similarities among nodes. We introduce a simple and efficient embedding technique based on approximate variants of equitable partitions. The approximation consists in introducing a user-tunable tolerance parameter relaxing the otherwise strict condition for exact equitable partitions that can be hardly found in real-world networks. We exploit a relationship between equitable partitions and equivalence relations for Markov chains and ordinary differential equations to develop a partition refinement algorithm for computing an approximate equitable partition in polynomial time. We compare our method against state-of-the-art embedding techniques on benchmark networks. We report comparable -- when not superior -- performance for visualization, classification, and regression tasks at a cost between one and three orders of magnitude smaller using a prototype implementation, enabling the embedding of large-scale networks which could not be efficiently handled by most of the competing techniques.

Simone Tonini, Andrea Vandin, Francesca Chiaromonte et al.

We present a novel, simple and widely applicable semi-supervised procedure for anomaly detection in industrial and IoT environments, SAnD (Simple Anomaly Detection). SAnD comprises 5 steps, each leveraging well-known statistical tools, namely; smoothing filters, variance inflation factors, the Mahalanobis distance, threshold selection algorithms and feature importance techniques. To our knowledge, SAnD is the first procedure that integrates these tools to identify anomalies and help decipher their putative causes. We show how each step contributes to tackling technical challenges that practitioners face when detecting anomalies in industrial contexts, where signals can be highly multicollinear, have unknown distributions, and intertwine short-lived noise with the long(er)-lived actual anomalies. The development of SAnD was motivated by a concrete case study from our industrial partner, which we use here to show its effectiveness. We also evaluate the performance of SAnD by comparing it with a selection of semi-supervised methods on public datasets from the literature on anomaly detection. We conclude that SAnD is effective, broadly applicable, and outperforms existing approaches in both anomaly detection and runtime.

Maurice H. ter Beek, Axel Legay, Alberto Lluch Lafuente et al.

Domain-specific quantitative modeling and analysis approaches are fundamental in scenarios in which qualitative approaches are inappropriate or unfeasible. In this paper, we present a tool-supported approach to quantitative graph-based security risk modeling and analysis based on attack-defense trees. Our approach is based on QFLan, a successful domain-specific approach to support quantitative modeling and analysis of highly configurable systems, whose domain-specific components have been decoupled to facilitate the instantiation of the QFLan approach in the domain of graph-based security risk modeling and analysis. Our approach incorporates distinctive features from three popular kinds of attack trees, namely enhanced attack trees, capabilities-based attack trees and attack countermeasure trees, into the domain-specific modeling language. The result is a new framework, called RisQFLan, to support quantitative security risk modeling and analysis based on attack-defense diagrams. By offering either exact or statistical verification of probabilistic attack scenarios, RisQFLan constitutes a significant novel contribution to the existing toolsets in that domain. We validate our approach by highlighting the additional features offered by RisQFLan in three illustrative case studies from seminal approaches to graph-based security risk modeling analysis based on attack trees.

Maurice H. ter Beek, Axel Legay, Alberto Lluch Lafuente et al.

This paper presents our approach to the quantitative modeling and analysis of highly (re)configurable systems, such as software product lines. Different combinations of the optional features of such a system give rise to combinatorially many individual system variants. We use a formal modeling language that allows us to model systems with probabilistic behavior, possibly subject to quantitative feature constraints, and able to dynamically install, remove or replace features. More precisely, our models are defined in the probabilistic feature-oriented language QFLAN, a rich domain specific language (DSL) for systems with variability defined in terms of features. QFLAN specifications are automatically encoded in terms of a process algebra whose operational behavior interacts with a store of constraints, and hence allows to separate system configuration from system behavior. The resulting probabilistic configurations and behavior converge seamlessly in a semantics based on discrete-time Markov chains, thus enabling quantitative analysis. Our analysis is based on statistical model checking techniques, which allow us to scale to larger models with respect to precise probabilistic analysis techniques. The analyses we can conduct range from the likelihood of specific behavior to the expected average cost, in terms of feature attributes, of specific system variants. Our approach is supported by a novel Eclipse-based tool which includes state-of-the-art DSL utilities for QFLAN based on the Xtext framework as well as analysis plug-ins to seamlessly run statistical model checking analyses. We provide a number of case studies that have driven and validated the development of our framework.

Maurice H. ter Beek, Axel Legay, Alberto Lluch Lafuente et al.

We investigate the suitability of statistical model checking techniques for analysing quantitative properties of software product line models with probabilistic aspects. For this purpose, we enrich the feature-oriented language FLan with action rates, which specify the likelihood of exhibiting particular behaviour or of installing features at a specific moment or in a specific order. The enriched language (called PFLan) allows us to specify models of software product lines with probabilistic configurations and behaviour, e.g. by considering a PFLan semantics based on discrete-time Markov chains. The Maude implementation of PFLan is combined with the distributed statistical model checker MultiVeStA to perform quantitative analyses of a simple product line case study. The presented analyses include the likelihood of certain behaviour of interest (e.g. product malfunctioning) and the expected average cost of products.