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 1238 products
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27/2017 - 06/10/2017
Bonaventura, L.; Ferretti, R.; Rocchi L.;
A fully semi-Lagrangian discretization for the 2D Navier--Stokes equations in the vorticity--streamfunction formulation | Abstract | | A numerical method for the two-dimensional, incompressible Navier--Stokes
equations in vorticity--streamfunction form is proposed, which employs semi-Lagrangian discretizations for both the advection and diffusion terms, thus achieving unconditional stability without the need to solve linear systems beyond that required by the Poisson solver for the reconstruction of the streamfunction. A description of the discretization of Dirichlet boundary conditions for the semi-Lagrangian approach to diffusion terms is also presented. Numerical experiments on classical benchmarks for incompressible flow in simple geometries validate the proposed method. |
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26/2017 - 06/05/2017
Masci, C.; Johnes, G.; Agasisti, T.
Student and School Performance in the OECD: a Machine Learning Approach. | Abstract | | In this paper, we develop and apply novel machine learning and statistical methods to analyse the determinants of students' PISA 2015 test scores in nine countries: Australia, Canada, France, Germany, Italy, Japan, Spain, UK and USA. The aim is to find out which student characteristics are associated with test scores and which school characteristics are associated to school value-added (measured at school level). A specific aim of our approach is to explore non-linearities in the associations between covariates and test scores, as well as to model interactions between school-level factors in affecting results. In order to address these issues, we apply a two-stage methodology using flexible tree-based methods. We first run multilevel regression trees in the first stage, to estimate school value-added. In the second stage, we relate the estimated school value-added to school level variables by means of regression trees and boosting. Results show that while several student and school level characteristics are significantly associated to students' achievements, there are marked differences across countries. The proposed approach allows an improved description of the structurally different educational production functions across countries. |
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25/2017 - 05/30/2017
Paulon, G.; De Iorio, M.; Guglielmi, A.; Ieva, F.
Joint modelling of recurrent events and survival: a Bayesian nonparametric approach | Abstract | | Heart failure (HF) is one of the main causes of morbidity, hospitalization
and death in the western world and the economic burden associated with HF
management is relevant and expected to increase in the future. We consider
hospitalization data for heart failure in the most populated Italian Region, Lombardia. Data were extracted from the administrative data warehouse of the regional healthcare system. The main clinical outcome of interest is time to death and research focus is on investigating how recurrent hospitalizations affect the time to event. The main contribution of the paper is to develop a joint model for gap times between two consecutive hospitalizations and survival time. The probability models for the gap times and for the survival outcome share a common patient specific frailty term. Using a Bayesian nonparametric prior as the random effects distribution accounts for patient heterogeneity in recurrent event trajectories. Moreover, the joint model allows for dependent censoring of gap times by death or administrative reasons and for the correlations between different gap times for the same individual. It is straightforward to include covariates in the survival and/or recurrence process through the specification of appropriate regression terms. Posterior inference is performed through Markov chain Monte Carlo methods. |
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24/2017 - 05/30/2017
Domanin, M.; Bissacco, D.; Le Van, D.; Vergara, C.
Computational fluid-dynamic comparison between patch-based and direct suture closure techniques after carotid endarterectomy | Abstract | | Objective: To describe and analyze hemodynamic modifications in patients submitted to carotid endarterectomy (CEA) with different carotid closure techniques, using a computational fluid-dynamic (CFD) strategy, in order to identify disturbed flow conditions potentially involved in the development of restenosis.
Methods: Data from 8 carotid geometries in 7 asymptomatic patients who underwent CEA were analyzed. In six cases (A-F), CEA was performed using patch graft (PG) closure, while in two cases (G and H) direct suture (DS) closure was performed. Three-dimensional carotid geometries, derived from postoperative Magnetic Resonance Angiography, were reconstructed using a level-set segmentation technique. Where PG was originally used it was virtually removed, creating a virtual DS scenario (PG vs virtual-DS) while, on the contrary, in cases submitted to DS closure, a virtual PG was inserted (DS vs virtual-PG). Modified geometries were designed using visualization-dedicated software. CFD analysis was performed using the finite elements library LifeV and velocity data obtained from Doppler Ultrasound waveforms.
To compare hemodynamic effects, wall shear stress-based quantities were considered indicators of disturbed flow and thus favorable conditions for the development of restenosis. In particular, oscillatory shear index (OSI) and relative residence time (RRT) were calculated both for original and virtual scenarios.
Results: For the six original PG cases, we measured the following: Mean of averaged-in-space OSI of 0.07 ± 0.01 for PG and 0.03 ± 0.02 for virtual-DS (difference 0.04 ± 0.01; P=.0016). Mean of the percentage of area with OSI > 0.2 (%A-OSI > 0.2) 10.08% ± 3.38% (PG) and 3.80% ± 3.22% (virtual-DS) (difference 6.28 ± 1.91; P= .008). Mean of the averaged-in-space RRT 5.48 ± 3.40 1/Pa (PG) and 2.62 ± 1.12 1/Pa (virtual-DS) (difference 2.87 ± 1.46; P =.097). Mean %A RRT > 4 1/Pa of 26.53% ± 12.98% (PG) and 9.95% ± 6.53% (virtual-DS) (difference 16.58 ± 5.93; P= .025).
For the two original DS cases we measured the following: Averaged-in-space OSI 0.02 and 0.04 (DS) and 0.03 and 0.02 (virtual-PG), %A-OSI > 0.2, 0.9% and 7.6% (DS) and 3.0% and 2.2% (virtual-PG), averaged-in-space RRT 1.8 and 2.0 1/Pa (DS) and 2.9 and 1.9 1/Pa (virtual-PG), %A-RRT > 4.0 1/Pa: 6.8% and 9.8% (DS) 9.4% and 6.2% (virtual-PG). These results revealed generally higher disturbed flows in the PG configurations with respect to the DS ones.
Conclusions: OSI and RRT values were higher in PG cases with respect to virtual-DS ones, while, in direct contrast, the virtual insertion of PG gave conflicting results that were primarily determined by the original carotid geometries. |
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23/2017 - 05/30/2017
Quarteroni, A.; Vergara, C.
Computational models for hemodynamics | Abstract | | Mathematical foundation and numerical approximation of the cardiocirculatory
system are addressed |
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22/2017 - 04/14/2017
Bartezzaghi, A.; Dede', L.; Quarteroni, A.
Biomembrane modeling with Isogeometric Analysis | Abstract | | We consider the numerical approximation of lipid biomembranes, including red blood cells, described through the Canham{Helfrich model, according to which the shape minimizes the bending energy under area and volume constraints. Energy minimization is performed via L2-gradient flow of the Canham-Helfrich energy using two Lagrange multipliers to weakly enforce the
constraints. This yields a highly nonlinear, high order, time dependent geometric Partial Differential Equation (PDE). We represent the biomembranes as single-patch NURBS closed surfaces. We discretize the geometric PDEs in space with NURBS-based Isogeometric Analysis and in time with Backward Differentiation Formulas. We tackle the nonlinearity in our formulation through a semi-implicit approach by extrapolating, at each time level, the geometric quantities of interest from previous time steps. We report the numerical results of the approximation of the Canham-Helfrich
problem on ellipsoids of different aspect ratio, which lead to the classical biconcave shape of lipid vesicles at equilibrium. We show that this framework permits an accurate approximation of the Canham-Helfrich problem, while being computationally efficient. |
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21/2017 - 04/14/2017
Talska, R.; Menafoglio, A.; Machalova, J.; Hron, K.; Fiserova, E.
Compositional regression with functional response | Abstract | | This work addresses the problem of performing functional linear regression when the response variable is represented as a probability density function (PDF). PDFs are interpreted as functional compositions, that are objects carrying primarily relative information. In this context, the unit integral constraint allows to single out one of the possible representations of a class of equivalent measures. On these bases, a function-on-scalar regression model with distributional response is proposed, by relying on the theory of Bayes Hilbert spaces. The geometry of Bayes spaces allows capturing all the key inherent feature of distributional data (e.g., scale invariance, relative scale). A B-spline basis expansion combined with a functional version of the centred log-ratio transformation is employed for actual computations. For this purpose, a new key result is proved to characterize B-spline representations in Bayes spaces. We show the potential of the methodological developments on a real case study, dealing with metabolomics data. Here, a bootstrap-based study is also performed for the uncertainty quantification of the obtained estimates.
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20/2017 - 03/14/2017
Albrecht G.; Caliò F.; Miglio E.
Fair surface reconstruction through rational triangular cubic Bézier patches | Abstract | | We consider the problem from reverse engineering to
construct a G^1 continuous interpolant to a triangulated set of 3D
points and corresponding normals by fitting a composite surface
consisting of rational triangular Bézier patches by using the
so--called rational blend technique. The solution depends on free
shape parameters which are fixed by minimizing different functionals
depending on suitable surface metrics. |
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