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 1349 prodotti
-
48/2018 - 25/09/2018
Arnone, E.; Azzimonti, L.; Nobile, F.; Sangalli, L.M.
Modeling spatially dependent functional data via regression with differential regularization | Abstract | | We propose a method for modeling spatially dependent functional data, based on regression with differential regularization. The regularizing term enables to include problem-specific information about the spatio-temporal variation of the phenomenon under study, formalized in terms of a time-dependent partial differential equation. The method is implemented using a discretization based on finite elements in space and finite differences in time. This non-tensor product basis allows to handle e fficiently data distributed over complex domains and where the shape of the domain infl uences the phenomenon's behavior. Moreover, the method can comply with speci fic conditions at the boundary of the domain of interest. Simulation studies compare the proposed model to available techniques for spatio-temporal data. The method is also illustrated via an application to the study of blood- flow velocity fi eld in a carotid artery affected by atherosclerosis, starting from echo-color doppler and magnetic resonance imaging data. |
-
47/2018 - 25/09/2018
Stefanucci, M.; Sangalli, L.M.; Brutti, P.
PCA-based discrimination of partially observed functional data, with an application to Aneurisk65 dataset | Abstract | | Functional data are usually assumed to be observed on a common domain. However, it is often the case that some portion of the functional data is missing for some statistical units, invalidating most of the existing techniques for functional data analysis. The developments of methods able to handle partially observed or incomplete functional data is currently attracting an increasing interest. We here briefly review this literature. We then focus on discrimination based on principal component analysis, and illustrate a few possible methods via simulation studies and an application to the AneuRisk65 dataset. We show that carrying out the analysis over the full domain, where at least one of the functional data is observed, may not be the optimal choice for classi fication purposes. |
-
46/2018 - 25/09/2018
Riccobelli, D.; Ciarletta, P.
Morpho-elastic model of the tortuous tumour vessels | Abstract | | Solid tumours have the ability to assemble their own vascular network for optimizing their access to the vital nutrients. These new capillaries are morphologically different from normal physiological vessels. In particular, they have a much higher spatial tortuosity forcing an impaired flow within the peritumoral area. This is a major obstacle for the efficient delivery of antitumoral drugs.
This work proposes a morpho-elastic model of the tumour vessels. A tumour capillary is considered as a growing hyperelastic tube that is spatially constrained by a linear elastic environment, representing the interstitial matter. We assume that the capillary is an incompressible neo-Hookean material, whose growth is modeled using a multiplicative decomposition of the deformation gradient.
We study the morphological stability of the capillary by means of the method of incremental deformations superposed on finite strains, solving the corresponding incremental problem using the Stroh formulation and the impedance matrix method. The incompatible axial growth of the straight capillary is found to control the onset of a bifurcation towards a tortuous shape. The post-buckling morphology is studied using a mixed finite element formulation in the fully nonlinear regime. The proposed model highlights how the geometrical and the elastic properties of the capillary and the surrounding medium concur to trigger the loss of marginal stability of the straight capillary and the nonlinear development of its spatial tortuosity. |
-
45/2018 - 13/08/2018
Bernardi, M.S.; Carey, M.; Ramsay, J.O.; Sangalli, L.M.
Modeling spatial anisotropy via regression with partial di fferential regularization | Abstract | | We consider the problem of analyzing spatially distributed data characterized by spatial anisotropy. Following a functional data analysis approach, we propose a method based on regression with partial di fferential regularization, where the diff erential operator in the regularizing term is anisotropic and is derived from data. We show that the method correctly identifi es the direction and intensity of anisotropy and returns an accurate estimate of the spatial eld. The method compares favorably to both isotropic and anisotropic kriging, as tested in simulation studies under various scenarios. The method is then applied to the analysis of Switzerland rainfall data. |
-
44/2018 - 13/08/2018
Bernardi, M.S.; Sangalli, L.M.
Modelling spatially dependent functional data by spatial regression with differential regularization | Abstract | | In this chapter we describe the modelling of spatially dependent functional data by
regression with differential regularization. |
-
43/2018 - 29/07/2018
Fontana, L.; Masci, C.; Ieva, F.; Paganoni, A.M.
Performing Learning Analytics via Generalized Mixed-Effects Trees | Abstract | | Nowadays, the importance of Educational Data Mining and Learning Analytics in higher education institutions is increasingly recognized. The analysis of university careers and of student dropout prediction is one of the most studied topics in the area of Learning Analytics. In the perspective of modeling the student dropout, we propose an innovative statistical method, that is a generalization of mixed-effects trees for a response variable in the exponential family: Generalized Mixed-Effects Trees (GMET). We perform a simulation study in order to validate the performance of our proposed method and to compare GMET to classical models. In the case study, we apply GMET to model Bachelor student dropout in different degree programmes of Politecnico di Milano. The model is able to identify discriminating student characteristics and estimate the degree programme effect on the probability of student dropout. |
-
42/2018 - 29/07/2018
Antonietti, P.F.; Melas, L.
Algebraic multigrid schemes for high-order discontinuous Galerkin methods | Abstract | | We present algebraic multigrid (AMG) methods for the efficient solution of the linear system of equations stemming from high-order discontinuous Galerkin discretizations of second-order elliptic problems.
For discontinuous Galerkin methods standard multigrid approaches cannot be employed because of redundancy of the degrees of freedom associated to the same grid point. We present new aggregation procedures and test them on extensive two-dimensional numerical experiments that demonstrate that the proposed AMG method is uniformly convergent with respect to all the discretization parameters, namely the mesh-size and the polynomial approximation degree. |
-
41/2018 - 24/07/2018
Mazzieri, I.; Melas, L.; Smerzini, C.; Stupazzini, M.
The role of near-field ground motion on seismic risk assessment in large urban areas | Abstract | | During the last ten years a long series of events like Wenchuan (2008, China), l’Aquila (Italy, 2009), Christchurch (New Zealand, 2010-2011), Emilia-Romagna (Italy, 2012), Meinong (Taiwan, 2016), Kumamoto (Japan, 2016) and Norcia (Italy, 2016) once more proved that the near-field of an earthquake poses a serious threat and even buildings considered earthquake-resistant might be severely affected. As a matter of fact, during the so-called “Christchurch sequence” around 70% of the central business district's (CBD) buildings turned out to be severely damaged and required to be demolished, in spite of the state-of-the-art New Zealand seismic building code and the stringent adoption and enforcement of this latter.
In this study we examine a large and representative set of numerical scenarios generated by means of physics-based simulations (PBS), in order to constrain the ground motion at short distances (within few kilometers range) by taking into account the rupture process, the seismic wave propagation and three-dimensional (3D) complex configurations. The experience gathered in the past years regarding 3D modelling of seismic wave propagation in complex alluvial basin (Guidotti et al., 2011; Smerzini and Villani, 2012) allowed us to enhance the choice of simulated scenarios in order to exhaustively explore the variability of ground motion and overcoming certain deficiency of the GMPEs and especially the insufficient number of records located close to the causative faults. All PBS presented in this study are carried out through the spectral element code SPEED (http://speed.mox.polimi.it).
The large metropolitan area of Beijing (China) is considered because of the (i) proximity with a well-known mapped fault system capable to trigger a severe earthquake, a (ii) relatively good description of the geotechnical characterization of the soil and a (iii) reliable reconstruction of the deep alluvial structure.
Focusing on the class of high-rise buildings and taking into account on one hand suitable fragility curves and on the other hand the aforementioned PBSs, seismic damage scenarios in the Beijing area will be produced and the variability of different damage states, as induced by a wide set of fault rupture scenarios with magnitude in the range 6.5-7.3, will be explored. |
|
