Quaderni MOX
Pubblicazioni
del Laboratorio di Modellistica e Calcolo Scientifico MOX. I lavori riguardano prevalentemente il campo dell'analisi numerica, della statistica e della modellistica matematica applicata a problemi di interesse ingegneristico. Il sito del Laboratorio MOX è raggiungibile
all'indirizzo mox.polimi.it
Trovati 1152 prodotti
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37/2024 - 30/04/2024
Begu, B.; Panzeri, S.; Arnone, E.; Carey, M.; Sangalli, L.M.
A nonparametric penalized likelihood approach to density estimation of space-time point patterns | Abstract | |
In this work, we consider space-time point processes and study their continuous space-time evolution. We propose an innovative nonparametric methodology to estimate the unknown space-time density of the point pattern, or, equivalently, to estimate the intensity of an inhomogeneous space-time Poisson point process. The presented approach combines maximum likelihood estimation with roughness penalties, based on differential operators, defined over the spatial and temporal domains of interest. We first establish some important theoretical properties of the considered estimator, including its consistency. We then develop an efficient and flexible estimation procedure that leverages advanced numerical and computation techniques. Thanks to a discretization based on finite elements in space and B–splines in time, the proposed method can effectively capture complex multi-modal and strongly anisotropic spatio-temporal point patterns; moreover, these point patterns may be observed over planar or curved domains with non-trivial geometries, due to geographic constraints, such as coastal regions with complicated shorelines, or curved regions with complex orography. In addition to providing estimates, the method’s functionalities also include the introduction of appropriate uncertainty quantification tools. We thoroughly validate the proposed method, by means of simulation studies and applications to real-world data. The obtained results highlight significant advantages over state-of-the-art competing approaches.
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36/2024 - 29/04/2024
Torri, V.; Ercolanoni, M.; Bortolan, F.; Leoni, O.; Ieva, F.
A NLP-based semi-automatic identification system for delays in follow-up examinations: an Italian case study on clinical referrals | Abstract | | Background: This study aims to propose a semi-automatic method for monitoring the waiting times of follow-up examinations within the National Health System (NHS) in Italy, which is currently not possible to due the absence of the necessary structured information in the official databases.
Methods: A Natural Language Processing (NLP) based pipeline has been developed to extract the waiting time information from the text of referrals for follow-up examinations in the Lombardy Region. A manually annotated dataset of 10 000 referrals has been used to develop the pipeline and another manually annotated dataset of 10 000 referrals has been used to test its performance. Subsequently, the pipeline has been used to analyze all 12 million referrals prescribed in 2021 and performed by May 2022 in the Lombardy Region.
Results: The NLP-based pipeline exhibited high precision (0.999) and recall (0.973) in identifying waiting time information from referrals’ texts, with high accuracy in normalization (0.948-0.998). The overall reporting of timing indications in referrals’ texts for follow-up examinations was low (2%), showing notable variations across medical disciplines and types of prescribing physicians. Among the referrals reporting waiting times, 16% experienced delays (average delay = 19 days, standard deviation = 34 days), with significant differences observed across medical disciplines and geographical areas.
Conclusions: The use of NLP proved to be a valuable tool for assessing waiting times in follow-up examinations, which are particularly critical for the NHS due to the significant impact of chronic diseases, where follow-up exams are pivotal. Health authorities can exploit this tool to monitor the quality of NHS services and optimize resource allocation. |
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35/2024 - 22/04/2024
Botti, L.; Botti, M.; Di Pietro, D.A.; Massa; F.C.
Stability, convergence, and pressure-robustness of numerical schemes for incompressible flows with hybrid velocity and pressure | Abstract | | In this work we study the stability, convergence, and pressure-robustness of discretization methods for incompressible flows with hybrid velocity and pressure. Specifically, focusing on the Stokes problem, we identify a set of assumptions that yield inf-sup stability as well as error estimates which distinguish the velocity- and pressure-related contributions to the error. We additionally identify the key properties under which the pressure-related contributions vanish in the estimate of the velocity,
thus leading to pressure-robustness. Several examples of existing and new schemes that fit into the framework are provided, and extensive numerical validation of the theoretical properties is provided. |
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34/2024 - 22/04/2024
Corti, M.
Exploring tau protein and amyloid-beta propagation: a sensitivity analysis of mathematical models based on biological data | Abstract | | Alzheimer's disease is the most common dementia worldwide. Its pathological development is well known to be connected with the accumulation of two toxic proteins: tau protein and amyloid-beta. Mathematical models and numerical simulations can predict the spreading patterns of misfolded proteins in this context. However, the calibration of the model parameters plays a crucial role in the final solution. In this work, we perform a sensitivity analysis of heterodimer and Fisher-Kolmogorov models to evaluate the impact of the equilibrium values of protein concentration on the solution patterns. We adopt advanced numerical methods such as the IMEX-DG method to accurately describe the propagating fronts in the propagation phenomena in a polygonal mesh of sagittal patient-specific brain geometry derived from magnetic resonance images. We calibrate the model parameters using biological measurements in the brain cortex for the tau protein and the amyloid-beta in Alzheimer's patients and controls. Finally, using the sensitivity analysis results, we discuss the applicability of both models in the correct simulation of the spreading of the two proteins. |
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32/2024 - 17/04/2024
Ziarelli, G.; Parolini, N.; Verani, M.
Learning epidemic trajectories through Kernel Operator Learning: from modelling to optimal control | Abstract | | Since infectious pathogens start spreading into a susceptible population, mathematical models can provide policy makers with reliable forecasts and scenario analyses, which can be concretely implemented or solely consulted. In these complex epidemiological scenarios, machine learning architectures can play an important role, since they directly reconstruct data-driven models circumventing the specific modelling choices and the parameter calibration, typical of classical compartmental models. In this work, we discuss the efficacy of Kernel Operator Learning (KOL) to reconstruct population dynamics during epidemic outbreaks, where the transmission rate is ruled by an input strategy. In particular, we introduce two surrogate models, named KOL-m and KOL-$partial$, which reconstruct in two different ways the evolution of the epidemics. Moreover, we evaluate the generalization performances of the two approaches with different kernels, including the Neural Tangent Kernels, and compare them with a classical neural network model learning method. Employing synthetic but semi-realistic data, we show how the two introduced approaches are suitable for realizing fast and robust forecasts and scenario analyses, and how these approaches are competitive for determining optimal intervention strategies with respect to specific performance measures. |
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31/2024 - 27/03/2024
Gambarini, M.; Agate, G.; Ciaramella, G.; Miglio, E.; Maran, S.
Modeling and optimization for arrays of water turbine OWC devices | Abstract | | The large-scale implementation of wave energy conversion requires the installation of parks of devices.
We study the problem of optimizing park layout and control for wave energy converters of the oscillating water column type. As a test case, we consider a device with a Wells turbine working in water. First, a novel model based on a nonlinear ordinary differential equation is derived to describe the behavior of the water column and used to estimate the power matrix. Then, its linearization is derived in order to enable the fast simulation of large parks of devices.
The choice of the hydrodynamic model allows obtaining the gradient of the power with respect to the positions through an adjoint approach, making it especially convenient for optimization. We consider in particular the case of interaction with the piles of a floating wind energy plant.
The results from the developed computational framework allow us to draw interesting conclusions about park layout design. In particular, we observe that mutual interaction effects can be significant even in parks made up of devices of small size, and that wave reflection from the piles of an offshore structure can improve energy production. |
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30/2024 - 25/03/2024
Gregorio, C.; Rea, F.; Ieva, F.; Scagnetto, A.; Indennidade, C.; Cappelletto, C.; Di Lenarda, A.; Barbati, G.
Flexible approaches based on multi-state models and microsimulation to perform real-world cost-effectiveness analyses: an application to PCSK9-inhibitors | Abstract | | Objectives: This study aims to show the application of flexible statistical methods in real-world cost-effectiveness analyses applied in the cardiovascular field, focusing specifically on the use of PCSK9
inhibitors for hyperlipidaemia.
Methods: The proposed method allowed us to use an electronic health database to emulate a target trial for cost-effectiveness analysis using multi-state modelling and microsimulation. We formally
established the study design and provided precise definitions of the causal measures of interest, while also outlining the assumptions necessary for accurately estimating these measures using the available
data. Additionally, we thoroughly considered goodness-of-fit assessments and sensitivity analyses of the decision model, which are crucial to capture the complexity of individuals' healthcare pathway
and to enhance the validity of this type of health economic models.
Results: In the disease model, the Markov assumption was found to be inadequate, and a "time-reset" timescale was implemented together with the use of a time-dependent variable to incorporate past hospitalization history. Furthermore, the microsimulation decision model demonstrated a satisfying goodness-of-fit, as evidenced by the consistent results obtained in the short-term horizon
compared to a non-model-based approach. Notably, only in the long-term follow-up PCSK9 inhibitors revealed their favourable cost-effectiveness, with a minimum willingness-to-pay of 39,000
Euro/LY gained.
Conclusions: The approach demonstrated its significant utility in several ways. Unlike non-model based or alternative model-based methods, it enabled to 1) investigate long-term cost-effectiveness
comprehensively, 2) employ an appropriate disease model that aligns with the specific problem under study, and 3) conduct subgroup-specific cost-effectiveness analyses to gain more targeted insights.
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29/2024 - 19/03/2024
Palummo, A.;, Arnone, E.; Formaggia, L.; Sangalli, L.M.
Functional principal component analysis for incomplete space-time data | Abstract | | Environmental signals, acquired, e.g., by remote sensing, often present large gaps of missing observations in space and time. In this work, we present an innovative approach to identify the main variability patterns, in space-time data, when data may be affected by complex missing data structures. We formalise the problem in the framework of Functional Data Analysis, proposing an innovative method of functional Principal Component Analysis (fPCA) for incomplete space-time data. The functional nature of the proposed method permits to borrow information from measurements observed at nearby spatio-temporal locations. The resulting functional principal components are smooth fields over the considered spatio-temporal domain, and can lead to interesting insights in the spatio-temporal dynamic of the phenomenon under study. Moreover, they can be used to provide a reconstruction of the missing entries, also under severe missing data patterns. The proposed model combines a weighted rank-one approximation of the data matrix with a roughness penalty. We show that the estimation problem can be solved using a Majorize-Minimization approach, and we provide a numerically efficient algorithm for its solution. Thanks to a discretization based on finite elements in space and B-splines in time, the proposed method can handle multidimensional spatial domains with complex shapes, such as water bodies with complicated shorelines, or curved spatial regions with complex orography. As shown by simulation studies, the proposed space-time fPCA is superior to alternative techniques for Principal Component Analysis with missing data. We further highlight the potentiality of the proposed method for environmental problems, by applying space-time fPCA to the study of the Lake Water Surface Temperature (LWST) of Lake Victoria, in Central Africa, starting from satellite measurements with large gaps. LWST is considered one of the fundamental indicators of how climate change is affecting the environment, and is recognized as an Essential Climate Variable. |
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