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 1239 prodotti
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88/2021 - 16/12/2021
Kuchta, M.; Laurino, F.; Mardal, K.A.; Zunino, P.
Analysis and approximation of mixed-dimensional PDEs on 3D-1D domains coupled with Lagrange multipliers | Abstract | | Coupled partial differential equations defined on domains with different dimensionality are usually called mixed dimensional PDEs. We address mixed dimensional PDEs on three-dimensional (3D) and one-dimensional domains, giving rise to a 3D-1D coupled problem.
Such problem poses several challenges from the standpoint of existence of solutions and numerical approximation. For the coupling conditions across dimensions, we consider the combination of essential and natural conditions, basically the combination of Dirichlet and Neumann conditions. To ensure a meaningful formulation of such conditions, we use the Lagrange multiplier method, suitably adapted to the mixed dimensional case. The well posedness of the resulting saddle point problem is analyzed. Then, we address the numerical approximation of the problem in the framework of the finite element method. The discretization of the Lagrange multiplier space is the main challenge. Several options are proposed, analyzed and compared, with the purpose to determine a good balance between the mathematical properties of the discrete problem and flexibility of implementation of the numerical scheme. The results are supported by evidence based on numerical experiments. |
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87/2021 - 16/12/2021
Both, J.W.; Barnafi, N.A.; Radu, F.A.; Zunino, P.; Quarteroni, A.
Iterative splitting schemes for a soft material poromechanics model | Abstract | | We address numerical solvers for a poromechanics model particularly adapted for soft materials, as it generally respects thermodynamics principles and energy balance. Considering the multi-physics nature of the problem, which involves solid and fluid species, interacting on the basis of mass balance and momentum conservation, we decide to adopt a solution strategy of the discrete problem based on iterative splitting schemes. As the model is similar (but not equivalent to) the Biot poromechanics problem, we follow the abundant literature for solvers of the latter equations, developing two approaches that resemble the well known undrained and fixed-stress splits for the Biot model. A thorough convergence analysis of the proposed schemes is performed. In particular, the undrained-like split is developed and analyzed in the framework of generalized gradient flows, whereas the fixed-stress-like split is understood as block-diagonal $L^2$-type stabilization and analyzed by means of a relative stability analysis. In addition, the application of Anderson acceleration is suggested, improving the robustness of the split schemes. Finally, we test these methods on different benchmark tests, and we also compare their performance with respect to a monolithic approach. Together with the theoretical analysis, the numerical examples provide guidelines to appropriately choose what split scheme shall be used to address realistic applications of the soft material poromechanics model. |
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86/2021 - 16/12/2021
Possenti, L.; Cicchetti, A.; Rosati, R.; Cerroni, D.; Costantino, M.L.; Rancati, T.; Zunino, P.
A Mesoscale Computational Model for Microvascular Oxygen Transfer | Abstract | | We address a mathematical model for oxygen transfer in the microcirculation. The model includes blood flow and hematocrit transport coupled with the interstitial flow, oxygen transport in the blood and the tissue, including capillary-tissue exchange effects. Moreover, the model is suited to handle arbitrarily complex vascular geometries. The purpose of this study is the validation of the model with respect to classical solutions and the further demonstration of its adequacy to describe the heterogeneity of oxygenation in the tissue microenvironment. Finally, we discuss the importance of these effects in the treatment of cancer using radiotherapy. |
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85/2021 - 16/12/2021
Cavinato, L., Gozzi, N., Sollini, M., Carlo-Stella, C., Chiti, A., & Ieva, F.
Recurrence-specific supervised graph clustering for subtyping Hodgkin Lymphoma radiomic phenotypes | Abstract | | Abstract— The prediction at baseline of patients at high risk for therapy failure or recurrence would significantly impact on Hodgkin Lymphoma patients treatment, informing clinical practice. Current literature is extensively searching insights in radiomics, a promising framework for high-throughput imaging feature extraction, to derive biomarkers and quantitative prognostic factors from images. However, existing studies are limited by intrinsic radiomic limitations, high dimensionality among others. We propose an exhaustive patient representation and a recurrence-specific multi-view supervised clustering algorithm for estimating patient-to-patient similarity graph and learning recurrence probability. We stratified patients in two risk classes and characterize each group in terms of clinical variables. |
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84/2021 - 16/12/2021
Torti, A.; Galvani, M.; Urbano, V.; Arena, M.; Azzone, G.; Secchi, P.; Vantini, S.
Analysing transportation system reliability: the case study of the metro system of Milan | Abstract | | This paper introduces a methodology to monitor the passenger flow in a subway transport system and analyse the system
reliability under different offer and demand scenarios.
Motivated by a collaboration with ATM - the company responsible for the management of the public transport in Milan - we focus on the subway system of Milan with the aim of helping operation managers to handle the daily access of travellers to the train stations during Covid-19 pandemic. In details, we first apply a calibration procedure to estimate a reliable OD matrices; then, a model able to monitor the passenger flow by estimating, for each train, the number of passengers getting on and off at each station, along with the load factor of the train along the line.
Results highlight the subway sections and the stations most at risk of congestion under different offer and demand scenarios; moreover, eventual queues at each station are estimated.
The proposed approach develops a flexible and scalable method to analyse and monitor any urban railway system in any city. |
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83/2021 - 15/12/2021
Colasuonno, F.; Ferrari F.; Gervasio, P.; Quarteroni, A.
Some evaluations of the fractional p-Laplace operator on radial functions | Abstract | | We face a rigidity problem for the fractional p-Laplace operator to extend to this new framework some tools useful for the linear case. It is known that (-Delta)^s (1-bar xbar ^2)^s_+ and -Delta_p (1-bar x bar^(p/(p-1))) are constant functions in (-1,1) for fixed p and s. We evaluated (-Delta_p)^s(1-bar x bar^(p/(p-1)))^s proving that it is not constant in (-1,1) for some p in (1,+infty) and s in (0,1). This conclusion is obtained numerically thanks to the use of very accurate Gaussian numerical quadrature formulas. |
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82/2021 - 02/12/2021
Massi, M.C.; Ieva, F.
Learning Signal Representations for EEG Cross-Subject Channel Selection and Trial Classification | Abstract | | EEG is a non-invasive powerful system that finds applications in several domains and research areas. Most EEG systems are multi-channel in nature, but multiple channels might include noisy and redundant information and increase computational times of automated EEG decoding algorithms. To reduce the signal-to-noise ratio, improve accuracy and reduce computational time, one may combine channel selection with feature extraction and dimensionality reduction. However, as EEG signals present high inter-subject variability, we introduce a novel algorithm for subject-independent channel selection through representation learning of EEG recordings. The algorithm exploits channel-specific 1D-CNNs as supervised feature extractors to maximize class separability and reduces a high dimensional multi-channel signal into a unique 1-Dimensional representation from which it selects the most relevant channels for classification. The algorithm can be transferred to new signals from new subjects and obtain novel highly informative trial vectors of controlled dimensionality to be fed to any kind of classifier. |
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81/2021 - 02/12/2021
Massi, M.C.; Gasperoni, F.; Ieva, F.; Paganoni, A.
Feature Selection for Imbalanced Data with Deep Sparse Autoencoders Ensemble | Abstract | | Class imbalance is a common issue in many domain applications of learning algorithms. Oftentimes, in the same domains it is much more relevant to correctly classify and profile minority class observations. This need can be addressed by Feature Selection (FS), that offers several further advantages, s.a. decreasing computational costs, aiding inference and interpretability. However, traditional FS techniques may become sub-optimal in the presence of strongly imbalanced data. To achieve FS advantages in this setting, we propose a filtering FS algorithm ranking feature importance on the basis of the Reconstruction Error of a Deep Sparse AutoEncoders Ensemble (DSAEE). We use each DSAE trained only on majority class to reconstruct both classes. From the analysis of the aggregated Reconstruction Error, we determine the
features where the minority class presents a different distribution of values w.r.t. the overrepresented one, thus identifying the most relevant features to discriminate between the two. We empirically demonstrate the efficacy of our algorithm in several experiments, both simulated and on high-dimensional datasets of varying sample size, showcasing its capability to select relevant and generalizable features to profile and classify minority class, outperforming other benchmark FS methods. We also briefly present a real application in radiogenomics, where the methodology was applied successfully. |
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