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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02/2021 - 01/23/2021
Calissano, A.; Feragen, A; Vantini, S.
Graph-Valued Regression: Prediction of unlabelled networks in a Non-Euclidean Graph-Space | Abstract | | Understanding how unlabeled graphs depend on input values or vectors is of extreme interest in a range of applications. In this paper, we propose a regression model taking values in Graph Space, representing unlabeled graphs which can be weighted or unweighted, one or multi-layer, and have same or different numbers of nodes, as a function of real valued regressor. As Graph Space is not a manifold, well-known manifold regression models are not applicable. We provide flexible parameterized regression models for Graph Space, along with precise and computationally efficient estimation procedures given by the introduced Align All and Compute regression algorithm. We show the potential of the proposed model for two real datasets: a time dependent cryptocurrency correlation matrices and a set of bus mobility usage network in Copenhagen (DK) during the Covid-19 pandemic. |
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01/2021 - 01/17/2021
Pegoraro, M.; Beraha, M.
Projected Statistical Methods for Distributional Data on the Real Line with the Wasserstein Metric | Abstract | | We present a novel class of projected methods, to perform statistical analysis on a data set of probability distributions on the real line, with the 2-Wasserstein metric. We focus in particular on Principal Component Analysis (PCA) and regression. To define these models, we exploit a representation of the Wasserstein space closely related to its weak
Riemannian structure, by mapping the data to a suitable linear space and using a metric projection operator to constrain the results in the Wasserstein space. By carefully choosing the tangent point, we are able to derive fast empirical methods, exploiting a constrained B-spline approximation. As a byproduct of our approach, we are also able to derive faster routines for previous work on PCA for distributions. By means of simulation studies, we compare our approaches to previously proposed methods, showing that our projected PCA has similar performance for a fraction of the computational cost and that the projected regression is extremely flexible even under misspecification. Several theoretical properties of the models are investigated and asymptotic consistency is proven. Two real world applications to Covid-19 mortality in the US and wind speed forecasting are discussed.
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85/2020 - 12/23/2020
Cavinato, L.; Sollini, M.; Kirienko, M.; Biroli, M.; Ricci, 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.; Ieva, F.;
PET radiomics-based lesions representation in Hodgkin lymphoma patients | Abstract | | As medical image analysis has been proven to entail tumor-specific in- formation, the so-called radiomics paradigm holds the promise to characterize the disease and infer long term outcomes of chemotherapy. In this work, we propose an insightful framework for disease characterization in Hodgkin lymphoma which could inform future research. Particularly, an intra-patient similarity index (ISI) was built to represent the homogeneity of the patients’ disease, while a radiomics-based fingerprint was create for local lesion description. Through descriptive statistics and classification algorithms, ISI-weighted fingerprint has been showed to be discriminatory between responders and relapsing patients. |
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84/2020 - 12/23/2020
Vergara, C.; Stella, S.; Maines, M.; Catanzariti, D.; Demattè, C.; Centonze, M.; Nobile, F.; Quarteroni, A.; Del Greco, M.
Computational electrophysiology to support the mapping of coronary sinus branches for cardiac resynchronization therapy | Abstract | | BACKGROUND
This work dealt with the assessment of a computational tool to estimate the latest electrically activated segment (LEAS) of the left ventricle during cardiac resynchronization therapy (CRT). OBJECTIVE
The aim of the work was to show that for patients with left bundle branch block (LBBB), possibly in presence of fibrosis, the proposed computational tool was able to accurately reproduce the epicardial activation maps and in particular LEAS location in the epicardial veins, often used as a target site for the left lead placement.
METHODS
We considered a computational tool based on Finite Elements used to recover the activation maps in all the myocardium. The model was calibrated by using activation times acquired in the epicardial veins with an electroanatomic mapping system (EAMS).
RESULTS
We applied our computational tool to predict LEAS in the epicardial veins of ten patients. We found an excellent accordance with LEAS measured by EAMS, the discrepancy being less than 4mm. We also calibrated our model using only the activation maps of the coronary sinus (CS), still obtaining an excellent agreement with the measured LEAS.
CONCLUSION
We showed that our computational tool is able to accurately predict the location of LEAS, even when information only at CS were used for calibration. This could be of utmost importance in view of CRT implantation, since LEAS could be determined by mapping only CS, saving time and avoiding the exposition of the patient to a deeper invasive procedure. |
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83/2020 - 12/23/2020
Hron, K.; Machalova, J.; Menafoglio, A.
Bivariate densities in Bayes spaces: orthogonal decomposition and spline representation | Abstract | | A new orthogonal decomposition for bivariate probability densities embedded in Bayes Hilbert spaces is derived. It allows one to represent a density into independent and interactive parts, the former being built as the product of revised definitions of marginal densities and the latter capturing the dependence between the two random variables being studied. The developed framework opens new perspectives for dependence modelling (which is commonly performed through copulas),
and allows for the analysis of dataset of bivariate densities, in a Functional Data Analysis perspective. A spline representation for bivariate densities is also proposed, providing a computational cornerstone for the developed theory.
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82/2020 - 12/11/2020
Vismara, F; Benacchio, T.; Bonaventura, L.
A seamless, extended DG approach for hyperbolic-parabolic problems on unbounded domains | Abstract | | We propose and analyze a seamless extended Discontinuous Galerkin (DG) discretization of hyperbolic-parabolic equations on semi-infinite domains. The semi-infinite half line is split into a finite subdomain where the model uses a standard polynomial basis, and a semi-unbounded subdomain where scaled Laguerre functions are employed as basis and test functions. Numerical fluxes enable the coupling at the interface between the two subdomains in the same way as standard single domain DG interelement fluxes. A novel linear analysis on the extended DG model yields stability constraints on the finite subdomain grid size that get tighter for increasing values of the P'eclet number.
Errors due to the use of different sets of basis functions on different portions of the domain are negligible, as highlighted in numerical experiments with the linear advection-diffusion and viscous Burgers' equations. With an added damping term on the semi-infinite subdomain, the extended framework is able to efficiently simulate absorbing boundary conditions without additional conditions at the interface. A few modes in the semi-infinite subdomain are found to suffice to deal with outgoing single wave and wave train signals, thus providing an appealing model for fluid flow simulations in unbounded regions. |
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81/2020 - 12/02/2020
Antonietti, P. F.; Mascotto, L.; Verani, M.; Zonca, S.
Stability analysis of polytopic Discontinuous Galerkin approximations of the Stokes problem with applications to fluid-structure interaction problems | Abstract | | We present a stability analysis of the Discontinuous Galerkin method on polygonal and polyhedral meshes (PolyDG) for the Stokes problem. In particular, we analyze the discrete inf-sup condition for different choices of the polynomial approximation order of the velocity and pressure approximation spaces. To this aim, we employ a generalized inf-sup condition with a pressure stabilization term. We also prove a priori hp-version error estimates in suitable norms. We numerically check the behaviour of the inf-sup constant and the order of convergence with respect to the mesh configuration, the mesh-size, and the polynomial degree. Finally, as a relevant application of our analysis, we consider the PolyDG approximation for a fluid-structure interaction problem and we numerically explore the stability properties of the method. |
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80/2020 - 11/30/2020
Zingaro, A.; Dede', L.; Menghini, F.; Quarteroni, A.
Hemodynamics of the heart's left atrium based on a Variational Multiscale-LES numerical model | Abstract | | In this paper, we investigate the hemodynamics of a left atrium (LA) by proposing a computational model suitable to provide physically meaningful fluid dynamics indications and detailed blood flow characterization. In particular, we consider the incompressible Navier-Stokes equations in Arbitrary Lagrangian Eulerian (ALE) formulation to deal with the LA domain under prescribed motion. A Variational Multiscale (VMS) model is adopted to obtain a stable formulation of the Navier-Stokes equations discretized by means of the Finite Element method and to account for turbulence modeling based on Large Eddy Simulation (LES). The aim of this paper is twofold: on one hand to improve the general understanding of blood flow in the human LA in normal conditions; on the other, to analyse the effects of VMS-LES models on a situation of blood flow which is neither laminar, nor fully turbulent, but rather transitional as in LA. Our conclusion is that the VMS-LES model is better suited to capture transitional effects than the standard SUPG stabilization method. |
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