MOX Reports
The preprint collection of the Laboratory for Modeling and Scientific Computation MOX. It mainly contains works on numerical
analysis and mathematical modeling applied to engineering problems. MOX web site is mox.polimi.it
Found 1249 products
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45/2020 - 07/21/2020
Gatti, F.; Menafoglio, A.; Togni, N.; Bonaventura, L.; Brambilla, D.; Papini, M; Longoni, L.
A novel dowscaling procedure for compositional data in the Aitchison geometry with application to soil texture data | Abstract | | In this work, we present a novel downscaling procedure for compositional quantities based on the Aitchison geometry. The method is able to naturally consider compositional constraints, i.e. unit-sum and positivity. We show that the method can be used in a block sequential Gaussian simulation framework in order to assess the variability of downscaled quantities. Finally, to validate the method, we test it first in an idealized scenario and then apply it for the downscaling of digital soil maps on a more realistic case study. The digital soil maps for the realistic case study are obtained from SoilGrids, a system for automated soil mapping based on state-of-the-art spatial predictions methods. |
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44/2020 - 07/21/2020
Masci, C.; Ieva, F.; Paganoni A.M.
EM algorithm for semiparametric multinomial mixed-effects models | Abstract | | This paper proposes an EM algorithm for semiparametric mixed-effects
models dealing with a multinomial response. In multinomial mixed-effects models, in order to obtain the marginal distribution of the response, random effects need to be integrated out. In a full parametric context, where random effects follow a multivariate normal distribution, this is often computationally infeasible. We propose an alternative novel semiparametric approach in which random effects follow a multivariate discrete distribution with an a priori unknown number of support points, that is allowed to differ across categories.
The advantage of this modelling is twofold: the discrete distribution
on random effects allows, first, to express the marginal density as a weighted sum, avoiding numerical problems typical of the integration and, second, to identify a latent structure at the highest level of the hierarchy, where groups are clustered into subpopulations. The paper shows a simulation study to evaluate the method’s performance and applies the proposed algorithm to a real case study for predicting higher education student dropout, comparing the results with the ones of a full parametric method. |
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42/2020 - 06/25/2020
Miglio, E.; Parolini, N.; Quarteroni, A.; Verani, M.; Zonca, S.
A spatio-temporal model with multi-city mobility for COVID-19 epidemic | Abstract | | The COVID-19 epidemic is the last of a long list of pandemics that have affected human kind in the last century. The virus spread very quickly all over the world due to the structure of modern society where mobility is very high.
In this paper we aim at a critical study of a multi-city model consisting of 8 compartments for describing the spreading of a disease. A convenient parameter calibration is implemented with the aim of reproducing the past history of the epidemic and of exploring its predicting capabilities. |
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43/2020 - 06/23/2020
Dede’, L.; Regazzoni, F.; Vergara, C.; Zunino, P.; Guglielmo, M.; Scrofani, R.; Fusini, L.;Cogliati, C.; Pontone, G.; Quarteroni, A.
Modeling the effect of COVID-19 on the cardiac function: A computational study
| Abstract | | Emerging studies address how COVID-19 infection can impact the cardiovascular system. This relates particularly to the development of myocardial injury, acute coronary syndrome, myocarditis, arrhythmia, and heart failure. Prospective treatment approach is advised for these patients. To study the interplay between local changes (reduced contractility), global variables (peripheral resistances, heart rate) and the cardiac function, we considered a lumped parameters computational model of the cardiovascular system. Our mathematical model allows to simulate the systemic and pulmonary circulations, the four cardiac valves and the four heart chambers, through equations describing the underlying physical processes. By the assessment of conventionally relevant parameters of cardiac function obtained through our numerical simulations, we propose our computational model as an effective method to evaluate short-term prognosis both in patients with normal and impaired cardiac function at baseline affected by mild or severe COVID-19. |
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41/2020 - 06/07/2020
Cannistrà,M.; Masci, C.; Ieva, F.; Agasisti, T.; Paganoni, A.M.
Not the magic algorithm: modelling and early-predicting students dropout through machine learning and multilevel approach | Abstract | | According to OECD, almost 30 per cent of students leave tertiary education programs without obtaining
a degree. This number measures a dead loss of human capital and a waste of public and private
resources. This paper contributes to the existing knowledge about students dropout by combining a
theoretical-based model with a data-driven approach to detect students who are more likely to leave
university in the first year. We propose the use of multilevel statistical models and machine learning
methods, applied to administrative data from a leading Italian university. The findings are encouraging,
as the methodology is able to predict at-risk students very precisely. We provide evidence of
the essential role of data relative to early performance (i.e. grades obtained in the first semester).
Moreover, the selection of major strongly influences the probability of dropping out. |
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40/2020 - 06/07/2020
Fresca, S.; Manzoni, A.; Dedè, L.; Quarteroni, A.
Deep learning-based reduced order models in cardiac electrophysiology | Abstract | | Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the formulation and numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential, that is the polarization/depolarization cycle occurring at every heart beat that models the time evolution of the electrical potential across the cell membrane, as well as a set of ionic variables. Multiple solutions of these systems, corresponding to different model inputs, are required to evaluate outputs of clinical interest, such as activation maps and action potential duration. More importantly, these models feature coherent structures that propagate over time, such as wavefronts. These systems can hardly be reduced to lower dimensional problems by conventional reduced order models (ROMs) such as, e.g., the reduced basis (RB) method. This is primarily due to the low regularity of the solution manifold (with respect to the problem parameters) as well as to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To overcome this difficulty, in this paper we propose a new, nonlinear approach which exploits deep learning (DL) algorithms to obtain accurate and efficient ROMs, whose dimensionality matches the number of system parameters. Our DL approach combines deep feedforward neural networks (NNs) and convolutional autoencoders (AEs). We show that the proposed DL-ROM framework can efficiently provide solutions to parametrized electrophysiology problems, thus enabling multi-scenario analysis in pathological cases. We investigate three challenging test cases in cardiac electrophysiology and prove that DL-ROM outperforms classical projection-based ROMs. |
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39/2020 - 06/07/2020
Martinolli, M.; Biasetti, J.; Zonca, S.; Polverelli, L.; Vergara, C.
Extended Finite Element Method for Fluid-Structure Interaction in Wave Membrane Blood Pumps | Abstract | | Numerical simulations of cardiac blood pump systems are integral to the optimization of device design, hydraulic performance and hemocompatibility. In wave membrane blood pumps, blood propulsion arises from the wave propagation along an oscillating immersed membrane, which generates small pockets of fluid that are pushed towards the outlet against an adverse pressure gradient.
We studied the Fluid-Structure Interaction between the oscillating membrane and the blood flow via three-dimensional simulations using the Extended Finite Element Method, an unfitted numerical technique that avoids remeshing by using a fluid fixed mesh.
Our three-dimensional numerical simulations in a realistic pump geometry highlighted the role of the membrane deformation in promoting a blood flow towards the outlet despite of a resistive pressure gradient. We also simulated the pump system at different pressure conditions and we validated the numerical results against textit{in-vitro} experimental data. |
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38/2020 - 06/03/2020
Sollini, M.; Kirienko, M.; Cavinato, L.; Ricci, F.; Biroli, M.; Ieva, F.; Calderoni, L.; Tabacchi, E.; Nanni, C.; Zinzani, P.L.; Fanti, S.; Guidetti, A; Alessi, A.; Corradini, P.; Seregni, E.; Carlo-Stella, C.; Chiti, A.
Methodological framework for radiomics applications in Hodgkin’s lymphoma | Abstract | | Background: According to published data, radiomics features differ between lesions of refractory/relapsing HL patients from those of long-term responders. However,several methodological aspects have not been elucidated yet.
Purpose: The study aimed at setting up a methodological framework in radiomics applications in Hodgkin’s lymphoma (HL), especially at (a) developing a novel feature selection approach, (b) evaluating radiomic intra-patient lesions’ similarity, and (c) classifying relapsing refractory (R/R) vs non-(R/R) patients.
Methods: We retrospectively included 85 patients (male:female = 52:33; median age 35 years, range 19–74). LIFEx (www.lifexsoft.org) was used for [18F]FDG-PET/CT segmentation and feature extraction. Features were a-priori selected if they were highly correlated or uncorrelated to the volume. Principal component analysis transformed features were used to build the fingerprints that were tested to assess lesions’ similarity, using the silhouette. For intra-patient similarity analysis, we used patients having multiple lesions only. To classify patients as non-R/R and R/R, the fingerprint considering one single lesion (fingerprint_One) and all lesions (fingerprint_All) was tested using Random Undersampling Boosting of Tree Ensemble (RUBTE).
Results: HL fingerprints included up to 15 features. Intra-patient lesion similarity analysis resulted in mean/median silhouette values below 0.5 (low similarity especially in the non-R/R group). In the test set, the fingerprint_One classification accuracy was 62% (78% sensitivity and 53% specificity); the classification by RUBTE using fingerprint_All resulted in 82% accuracy (70% sensitivity and 88% specificity).
Conclusions: Lesion similarity analysis was developed, and it allowed to demonstrate that HL lesions were not homogeneous within patients in terms of radiomics signature. Therefore, a random target lesion selection should not be adopted for radiomics applications. Moreover, the classifier to predict R/R vs non-R/R performed the best when all the lesions were used. |
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