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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50/2018 - 10/10/2018
Gervasio, P.; Quarteroni, A.
The INTERNODES method for non-conforming discretizations of PDEs | Abstract | | INTERNODES is a general purpose method to deal with non-conforming discretizations of partial differential equations on regions partitioned into two or several disjoint subdomains. It exploits two intergrid interpolation operators, one for transfering the Dirichlet trace across the interfaces, the others for the Neumann trace. In this paper, in every subdomain the original problem is discretized by either the finite element method (FEM) or the spectral element method (SEM or hp-fem), using a priori non-matching grids and piece-wise polynomials of different degree. Other discretization methods however can be used. INTERNODES can also be applied to heterogeneous or multiphysics problems, that is problems that feature different differential operators inside adjacent subdomains. For instance, in this paper we apply the INTERNODES method to a Stokes-Darcy coupled problem that models the filtration of fluids in porous media. Our results highlight the flexibility of the method as well as its optimal rate of convergence with respect to the grid size and the polynomial degree. |
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49/2018 - 25/09/2018
Massi, M.C.; Ieva, F.; Lettieri, E.
Data Mining Application to Healthcare Fraud Detection: A Two-Step Unsupervised Clustering Model for Outlier Detection with Administrative Databases | Abstract | | Being the recipient for huge public and private investments, the healthcare sector results to be an interesting target for fraudsters. Nowadays, the availability of a great amount of data makes it possible to tackle this issue with the adoption of data mining techniques. This approach can provide more efficient control of processes in terms of costs and time compared to manual audits. This research has the objective of developing a novel data mining model devoted to fraud detection among hospitals. In particular, it is focused on the DRG upcoding practice, i.e. the tendency of coding within Hospital Discharge Charts (HDC) in Administrative Databases, codes for provided services and inpatients health status so to make the hospitalization fall within a more remunerative DRG class. The model here proposed is constituted by two steps: one first step entails the clustering of providers according to their characteristics and behavior in the treatment of a specific disease, in order to spot outliers within this groups of peers; in the second step, a cross-validation is performed. This second phase is useful for controllers to verify whether within the list of suspects identified in the first step, any hospital exists, which may be justified in its outlierness by its particular characteristics, or by the treatment of a more complex patients' base. The proposed model was tested on a database relative to HDC collected by Regione Lombardia (Italy) in a time period of three years (2013-2015), focusing on the treatment of heart failure. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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