Michele Bellomo

Michele Bellomo

Mathematical Engineer,
Ph.D. in Electrical Engineering.

Publications

A list of selected publications. For the full record, visit my Google Scholar profile.

Journal Articles

Can We Do Without the Hairdresser? A Mathematical Solution

Published in The College Mathematics Journal, 2025

The Germanic folk tale “Rapunzel,” popularized by the Brothers Grimm in 1812, tells the story of a young woman who lets down her hair from a tower window, allowing a prince to climb up and visit her. But is such a situation realistic? Could someone’s hair actually grow that long? This article investigates, using mathematics, what would happen if a person decided to stop cutting their hair. Specifically, we introduce a stochastic model for hair growth and examine how the average length evolves as time tends to infinity. Besides offering curious insights about our hair, the proposed model provides an engaging and unconventional exercise in probability. It can also serve as an innovative way to introduce students and young researchers to the fascinating world of stochastic processes, particularly the Poisson process and renewal theory.

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Hawkes Processes in Finance: An Application in Modeling Transactions in EUA Futures

Published in Contemporary Mathematics, 2025

Hawkes processes are stochastic point processes with self-exciting behavior, where the occurrence of an event increases the probability of subsequent events. In this paper, we provide a concise yet comprehensive introduction to Hawkes processes, focused on applications. We then employ marked Hawkes processes to model the occurrences of transactions in European Union Allowances (EUA) futures. The models are trained using an innovative and efficient Maximum Likelihood Estimation (MLE) implementation, that leverages PyTorch library to parallelize computations and exploit automatic differentiation. We evaluate and compare different excitation functions using Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Quantile-Quantile (Q-Q) plots based on the Random Time Change theorem. Additionally, we analyze the distribution of the calibrated parameters across different trading hours, finding a consistent relationship, to our knowledge never described before, between the self-exciting intensity parameter α and the decay parameter β . Furthermore, we identify two clusters: one characterized by transactions with a strong self-exciting effect, but that decays very quickly, and another with a less intense effect, that persists over longer time. Using logistic regression, we analyze the characteristics of the clusters and provide possible interpretations. We consider Hawkes processes very promising yet underutilized techniques for studying financial markets, and we believe this work can encourage researchers and practitioners to dive further into these models.

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Conference Papers

An Innovative Transformer-Based Approach for State of Health Trajectory Prediction and Remaining Useful Life Estimation in Lithium-Ion Batteries

Published in 2025 International Conference on Clean Electrical Power (ICCEP), 2025

In this article, we introduce an innovative approach based on the Transformer neural network architecture for future state of health (SoH) trajectory prediction and remaining useful life (RUL) estimation in lithium-ion batteries. In this methodology, the same model handles predictions for both early and late cycles, thanks to intelligent management of variable-length input and output sequences. Additionally, the future SoH curve is obtained through a one-shot multistep (OSMS) prediction, which enables faster predictions and fewer accumulated errors compared to the standard autoregressive approach. We tested this model on the PoliMi-TUB battery dataset, achieving better results than previous models based on Long Short-Term Memory (LSTM) networks.

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Generalized Additive Mixed Models in medicine: a case study on LDL cholesterol in people living with HIV under different antiretroviral regimens

Published in Methodological and Applied Statistics and Demography III, 2025

Generalized Additive Models (GAMs) are statistical methods that enable the modeling of variables through smooth effects. GAMs are powerful and flexible models, well-consolidated among statisticians. However, their application in medicine, especially in infectious diseases, is still limited. In this study, we applied GAMs to evaluate the dynamic of low-density lipoprotein (LDL) cholesterol in people living with HIV (PLHIV) who have switched to an antiretroviral regimen based on doravirine, rilpivirine, dolutegravir or bictegravir. Data were collected at IRCCS San Raffaele Scientific Institute and involve 2742 individuals and 54552 observations. A Generalized Additive Mixed Model (GAMM) and a quasi-Poisson GAMM were trained considering several risk factors and accounting for temporal dynamics through random effects and autoregressive covariance structures. Doravirine exhibited the most favorable effect on LDL cholesterol, with an associated average reduction in the first two years of use of −5.43 mg/L per year according to the GAMM and of −5.41% per year in the quasi-Poisson GAMM.

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