Il presente volume raccoglie i long abstracts dei contributi presentati durante la quinta edizione della “Young Applied Mathematicians Conference” (YAMC, www.yamc.it). Ospitato dal Dipartimento di Ingegneria Civile, Edile e Ambientale (DICEA) dell’Università di Padova, in collaborazione con il Dipartimento di Matematica “Tullio Levi-Civita”, il convegno si è svolto dal 22 al 26 settembre 2025. L’edizione ha riunito 108 partecipanti provenienti da 52 università e centri di ricerca di 12 Paesi, coinvolgendo principalmente giovani ricercatori, tra dottorandi e post-doc.

Releasing capsules are widely employed in biomedical applications as smart carriers of therapeutic agents, including drugs and bioactive compounds. Such delivery vehicles typically consist of a loaded core, enclosed by one or multiple concentric coating strata. In this work, we extended existing mechanistic models to account for such multi-strata structures, including possible concurrent erosion of the capsule itself, and we characterized the release kinetics of the active substance into the surrounding medium. We presented a computational study of drug release from a spherical microcapsule, modeled through a non-linear diffusion equation incorporating radial asymmetric diffusion and space- and time-discontinuous coefficients, as suggested by the experimental data specifically collected for this study. The problem was solved numerically using a finite volume scheme on a grid with adaptive spatial and temporal resolution. Analytical expressions for concentration and cumulative release were derived for all strata, enabling the exploration of parameter sensitivity—such as coating permeability and internal diffusivity—on the overall release profile. The resulting release curves provide mechanistic insight into the transport processes and offer design criteria for achieving controlled release. Model predictions were benchmarked against in vitro experimental data obtained under physiologically relevant conditions, showing good agreement and validating the key features of the model. The proposed model thus serves as a practical tool for predicting the behavior of composite coated particles, supporting performance evaluation and the rational design of next-generation drug delivery systems with reduced experimental effort.

The increasing availability of traffic data from sensor networks has created new opportunities for understanding vehicular dynamics and identifying anomalies. In this study, we employ clustering techniques to analyse traffic flow data with the dual objective of uncovering meaningful traffic patterns and detecting anomalies, including sensor failures and irregular congestion events. We explore multiple clustering approaches, i.e. partitioning and hierarchical methods, combined with various time series representations and similarity measures. Our methodology is applied to real-world data from highway sensors, enabling us to assess the impact of different clustering frameworks on traffic pattern recognition. We also introduce a clustering-driven anomaly detection methodology that identifies deviations from expected traffic behaviour based on distance-based anomaly scores. Results indicate that hierarchical clustering with symbolic representations provides robust segmentation of traffic patterns, while partitioning methods such as k-means and fuzzy c-means yield meaningful results when paired with Dynamic Time Warping. The proposed anomaly detection strategy successfully identifies sensor malfunctions and abnormal traffic conditions with minimal false positives, demonstrating its practical utility for real-time monitoring. Real-world vehicular traffic data are provided by Autostrade Alto Adriatico S.p.A.

The study at the Peggy Guggenheim Collection in Venice highlights critical interactions between indoor air quality, visitor dynamics, and microclimatic conditions, offering insights into preventive conservation of modern artworks. By analyzing pollutants such as ammonia, formaldehyde, and organic acids, alongside visitor density and environmental data, the research identified key patterns and risks. Through three seasonal monitoring campaigns, the concentrations of SO2 (sulphur dioxide), NO (nitric oxide), NO2 (nitrogen dioxide), NOx (nitrogen oxides), HONO (nitrous acid), HNO3 (nitric acid), O3 (ozone), NH3 (ammonia), CH3COOH (acetic acid), HCOOH (formic acid), and HCHO (formaldehyde) were determined using passive samplers, as well as temperature and relative humidity data loggers. In addition, two specific short-term monitoring campaigns focused on NH3 were performed to evaluate the influence of visitor presence on indoor concentrations of the above compounds and environmental parameters. NH3 and HCHO concentrations spiked during high visitor occupancy, with NH3 levels doubling in crowded periods. Short-term NH3 campaigns confirmed a direct correlation between visitor numbers and the above indoor concentrations, likely due to human emissions (e.g., sweat, breath) and off-gassing from materials. The indoor/outdoor ratios indicated that several pollutants originated from indoor sources, with ammonia and acetic acid showing the highest indoor concentrations. By measuring the number of visitors and microclimate parameters (temperature and humidity) every 3 s, we were able to precisely estimate the causality and the temporal shift between these quantities, both at small time scale (a few minute delay between peaks) and at medium time scale (daily average conditions due to the continuous inflow and outflow of visitors).

In this paper, we develop new methods to join machine learning techniques and macroscopic differential models, aimed at estimate and forecast vehicular traffic. This is done to complement respective advantages of data-driven and model-driven approaches. We consider here a dataset with flux and velocity data of vehicles moving on a highway, collected by fixed sensors and classified by lane and by class of vehicle. By means of a machine learning model based on an LSTM recursive neural network, we extrapolate two important pieces of information: (1) if congestion is appearing under the sensor, and (2) the total amount of vehicles which is going to pass under the sensor in the next future (30 min). These pieces of information are then used to improve the accuracy of an LWR-based first-order multi-class model describing the dynamics of traffic flow between sensors. The first piece of information is used to invert the (concave) fundamental diagram, thus recovering the density of vehicles from the flux data, and then inject directly the density datum in the model. This allows one to better approximate the dynamics between sensors, especially if an accident/bottleneck happens in a not monitored stretch of the road. The second piece of information is used instead as boundary conditions for the equations underlying the traffic model, to better predict the total amount of vehicles on the road at any future time. Some examples motivated by real scenarios will be discussed. Real data are provided by the Italian motorway company Autovie Venete S.p.A.

The volume collects the long abstracts of the 79 contributions presented during the fourth edition of the “Young Applied Mathematicians Conference” (YAMC, www.yamc.it). Organized in Rome under the sponsorship of the Institute for Applied Mathematics (IAC) of the CNR and the Department of Mathematics at Sapienza, University of Rome, the conference took place from September 16 to 20, 2024, and brought together primarily young researchers (students, PhD candidates, post-docs, etc.) from 37 universities and research centers across 8 countries. This volume is intended to promote the communication of the research presented in the field of applied mathematics, with a primary focus on numerical analysis, artificial intelligence, statistics, and mathematical modeling. Il volume raccoglie i long abstracts dei 79 contributi presentati durante la quarta edizione del convegno "Young Applied Mathematicians Conference" (YAMC, www.yamc.it). Organizzato a Roma sotto il patrocinato dell'Istituto per le Applicazioni del Calcolo (IAC) del CNR e del dipartimento di Matematica di Sapienza, Università di Roma, il convegno si è svolto nelle giornate 16--20 settembre 2024 ed ha riunito principalmente giovani ricercatori (studenti, dottorandi, post-doc, ...) provenienti da 37 fra università e centri di ricerca di 8 nazioni. Il presente volume è indirizzato a favorire la comunicazione delle ricerche presentate nel panorama della matematica applicata, con principale attenzione in analisi numerica, intelligenza artificiale, statistica e modellistica matematica.

Personalized medicine strategies are gaining momentum nowadays, enabling the introduction of targeted treatments based on individual differences that can lead to greater therapeutic efficacy by reducing adverse effects. Despite its crucial role, studying the contribution of the immune system (IS) in this context is difficult because of the intricate interplay between host, pathogen, therapy, and other external stimuli. To address this problem, a multidisciplinary approach involving in silico models can be of great help. In this perspective, we will discuss the use of a well-established agent-based model of the immune response, C-ImmSim, to study the relationship between long-lasting diseases and the combined effects of IS, drug therapies and exogenous factors such as physical activity and dietary habits.

We address the problem of user fast revocation in the lattice-based Ciphertext Policy Attribute-Based Encryption (CP-ABE) by extending the scheme originally introduced by Zhang and Zhang [Zhang J, Zhang Z. A ciphertext policy attribute-based encryption scheme without pairings. In: International Conference on Information Security and Cryptology. Springer; 2011. p. 324–40. doi: https://doi.org/10.1007/978-3-642-34704-7_23.]. While a lot of work exists on the construction of revocable schemes for CP-ABE based on pairings, works based on lattices are not so common, and – to the best of our knowledge – we introduce the first server-aided revocation scheme in a lattice-based CP-ABE scheme, hence being embedded in a post-quantum secure environment. In particular, we rely on semi-trusted “mediators” to provide a multi-step decryption capable of handling mediation without re-encryption. We comment on the scheme and its application, and we provide performance experiments on a prototype implementation in the Attribute-Based Encryption spin-off library of Palisade to evaluate the overhead compared with the original scheme.

The growth potential of a crypto project, typically sustained by an associated cryptocurrency, can be measured by the use cases spurred by the underlying technology. However, these projects are implemented through decentralized applications, with a weak (if any) feedback scheme. Hence, a metric that is widely used as a proxy for the healthiness of such projects is the number of transactions and related volumes. Nevertheless, such a metric can be subject to manipulation - the crypto market being an unregulated one, magnifies such a risk. To address the cited gap, in this paper, we design a comprehensive methodology to process large cryptocurrency transaction graphs that, after clustering user addresses of interest, derives a compact representation of the network that highlights interactions among clusters. The analysis of these interactions provides insights into/over/on the strength of the project.To show the quality and viability of our solution, we bring forward a use case centered on Polkadot. The Polkadot network, a cutting-edge cryptocurrency platform, has gained significant attention in the digital currency landscape due to its pioneering approach to interoperability and scalability. However, little is known about how many and to what extent its wide range of enabled use cases have been adopted by end-users so far. The answer to this type of question means mapping Polkadot (or any analyzed crypto project) on a palette that ranges from a thriving ecosystem to a speculative coin without compelling use cases.Our findings, rooted on extensive experimental results - we have parsed 12.5+ million blocks - , demonstrate that crypto exchanges exert considerable influence on the Polkadot network, owning nearly 40% of all addresses in the ledger and absorbing at least 80% of all transactions. In addition, the high volume of inter-exchange transactions (more than 20%) underscores the strong interconnections among just a couple of prominent exchanges, prompting further investigations into the behavior of these actors to uncover potential unethical activities, such as wash trading.These results are a testament to the quality and viability of the proposed solution that, while characterized by a high level of scalability and adaptability, is at the same time immune from the drawbacks of currently used metrics.

The importance of the immune system (IS) in tuberculosis (TB) drug development is often underestimated because of the intricate nature of experiments and the specialized knowledge needed. In vitro and animal studies fall short in replicating the intricate reactions of the human IS to drugs and infections. In this study, we present our initial efforts in employing an in silico approach to comprehend how an individual’s IS impacts the efficacy of therapy, particularly in managing mycobacterium tuberculosis (Mtb) infection and minimizing the risk of relapse. We employed a well-established agent-based IS simulator called C-IMMSIM. We conducted simulations to investigate the long-term outcomes of TB disease in a virtual cohort infected with Mtb over a 50-year period. Our simulations revealed that individuals with competent IS showed a high success rate in containing Mtb infection. Furthermore, to better understand the dynamic interactions between Mtb and the IS, we deliberately introduced specific IS deficiencies, thus successfully inducing short-term relapses and mortality. These results confirm the model’s ability to elucidate the mechanisms underlying the interactions between Mtb and the IS.

Algebraic Cryptanalysis is a widely used technique that tackles the problem of breaking ciphers mainly relying on the ability to express a cryptosystem as a solvable polynomial system. Each output bit/word can be expressed as a polynomial equation in the cipher’s inputs—namely the key and the plaintext or the initialisation vector bits/words. A part of research in this area consists in finding suitable algebraic structures where polynomial systems can be effectively solved, e.g., by computing Gröbner bases. In 2009, Dinur and Shamir proposed the cube attack, a chosen plaintext algebraic cryptanalysis technique for the offline acquisition of an equivalent system by means of monomial reduction; interpolation on cubes in the space of variables enables retrieving a linear polynomial system, hence making it exploitable in the online phase to recover the secret key. Since its introduction, this attack has received both many criticisms and endorsements from the crypto community; this work aims at providing, under a unified notation, a complete state-of-the-art review of recent developments by categorising contributions in five classes. We conclude the work with an in-depth description of the kite attack framework, a cipher-independent tool that implements cube attacks on GPUs. Mickey2.0 is adopted as a showcase.

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Drug repurposing is a highly active research area, aiming at finding novel uses for drugs that have been previously developed for other therapeutic purposes. Despite the flourishing of methodologies, success is still partial, and different approaches offer, each, peculiar advantages. In this composite landscape, we present a novel methodology focusing on an efficient mathematical procedure based on gene similarity scores and biased random walks which rely on robust drug-gene-disease association data sets. The recommendation mechanism is further unveiled by means of the Markov chain underlying the random walk process, hence providing explainability about how findings are suggested. Performances evaluation and the analysis of a case study on rheumatoid arthritis show that our approach is accurate in providing useful recommendations and is computationally efficient, compared to the state of the art of drug repurposing approaches.

Networks are pervasive in computer science and in real world applications. It is often useful to leverage distinctive node features to regroup such data in clusters, by making use of a single representative node per cluster. Such contracted graphs can help identify features of the original networks that were not visible before. As an example, we can identify contiguous nodes having the same discrete property in a social network. Contracting a graph allows a more scalable analysis of the interactions and structure of the network nodes. This paper delves into the problem of contracting possibly large colored networks into smaller and more easily manageable representatives. It also describes a simple but effective algorithm to perform this task. Extended performance plots are given for a range of graphs and results are detailed and discussed with the aim of providing useful use cases and application scenarios for the approach.

Individual tracking of museum visitors based on portable radio beacons, an asset for behavioural analyses and comfort/performance improvements, is seeing increasing diffusion. Conceptually, this approach enables room-level localisation based on a network of small antennas (thus, without invasive modification of the existent structures). The antennas measure the intensity (RSSi) of self-advertising signals broadcasted by beacons individually assigned to the visitors. The signal intensity provides a proxy for the distance to the antennas and thus indicative positioning. However, RSSi signals are well-known to be noisy, even in ideal conditions (high antenna density, absence of obstacles, absence of crowd, ...). In this contribution, we present a method to perform accurate RSSi-based visitor tracking when the density of antennas is relatively low, e.g. due to technical constraints imposed by historic buildings. We combine an ensemble of "simple" localisers, trained based on ground-truth, with an encoding of the museum topology in terms of a total-coloured graph. This turns the localisation problem into a cascade process, from large to small scales, in space and in time. Our use case is visitors tracking in Galleria Borghese, Rome (Italy), for which our method manages >96% localisation accuracy, significantly improving on our previous work (J. Comput. Sci. 101357, 2021).

An early research in solid modeling led by Herbert Voelcker at the University of Rochester and later at Cornell suggested that every solid representation scheme corresponds to an algebra, where the elements of the algebra are solid representations constructed and edited using operations in the algebra. For example, every CSG representation describes an element in a finite Boolean algebra of closed regular sets, whereas every boundary representation describes an element of a vector space of 2-chains in an algebraic topological chain complex. In this paper, we elucidate the precise relationships (functors) between all algebras used for CSG and boundary representations of solids. Based on these properties, we show that many solid modeling operations, including boundary evaluation, reduce to straightforward algebraic operations or application of identified functors that are efficiently implemented using point membership tests and sparse matrix operations. To fully exploit the efficacy of the new algebraic approach to solid modeling, all algorithms are fully implemented in Julia, the modern language of choice for numerical and scientific computing.

The development of Boolean algebra based algorithms lied the foundation for a wide variety of cryptanalysis techniques based on the reformulation of a cryptosystem as a polynomial function over F2. Widely used approaches to solve multivariate system of equations include Gröbner bases (see [11]) and linearisation techniques like XL [4] and XSL [5]). Performances of these methodologies were however completely unfeasible for real problems’ size, making it impossible to directly find useful relations between cryptographic schemes’ input and output. At Eurocrypt’09 a new methodology settled in this environment, providing a feasible family of attacks able to retrieve useful in- put/output relations within feasible time: Dinur and Shamir Cube Attack [7]. The attack relied on the new concept of tweakable poly- nomials, polynomials in variables the attacker can set at will during the attack through which a black-box representation of the cipher is analysed. The resonance of this approach was unexpected, making it the forefather of many other approaches ranging from generic finite fields [1, 15] and non-linear [14] approaches to Meet-in-the- Middle [2, 13] and side channels [8] attacks. The idea of tweakable polynomials was also exploited to provide property (cube) testers which generated Conditional [12] and Dynamic [9] cube attacks. All of these approaches come with their own nomenclature, often making it unclear about their real contribute to the state of the art. The aim of this work is to introduce a novel notation to provide a global representation of the cube attacks family.

We present an all-around study of the visitors flow in crowded museums: a combination of Lagrangian field measurements and statistical analyses enable us to create stochastic digital-twins of the guest dynamics, unlocking comfort- and safety-driven optimizations. Our case study is the Galleria Borghese museum in Rome (Italy), in which we performed a real-life data acquisition campaign. We specifically employ a Lagrangian IoT-based visitor tracking system based on Raspberry Pi receivers, displaced in fixed positions throughout the museum rooms, and on portable Bluetooth Low Energy beacons handed over to the visitors. Thanks to two algorithms: a sliding window-based statistical analysis and an MLP neural network, we filter the beacons RSSI and accurately reconstruct visitor trajectories at room-scale. Via a clustering analysis, hinged on an original Wasserstein-like trajectory-space metric, we analyze the visitors paths to get behavioral insights, including the most common flow patterns. On these bases, we build the transition matrix describing, in probability, the room-scale visitor flows. Such a matrix is the cornerstone of a stochastic model capable of generating visitor trajectories in silico. We conclude by employing the simulator to enhance the museum fruition while respecting numerous logistic and safety constraints. This is possible thanks to optimized ticketing and new entrance/exit management.

We tackle the issue of measuring and analyzing the visitors’ dynamics in crowded museums. We propose an IoT-based system – supported by artificial intelligence models – to reconstruct the visitors’ trajectories throughout the museum spaces. Thanks to this tool, we are able to gather wide ensembles of visitors’ trajectories, allowing useful insights for the facility management and the preservation of the art pieces. Our contribution comes with one successful use case: the Galleria Borghese in Rome, Italy.