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
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44/2019 - 20/11/2019
Formaggia, L.; Gatti, F.; Zonca, S.
An XFEM/DG approach for fluid-structure interaction problems with contact | Abstract | | In this work, we address the problem of fluid-structure interaction with moving structures that may come into contact. We propose a penalization contact algorithm implemented in an unfitted numerical framework designed to treat large displacements. In the proposed method, the fluid mesh is fixed and the structure meshes are superimposed to it without any constraint on the conformity. Thanks to the Extended Finite Element Method (XFEM), we can treat discontinuities of the fluid solution on the mesh elements intersecting the structure; the coupling conditions at the fluid structure interface are enforced via a discontinuous Galerkin mortaring technique, which is a penalization method that ensures the consistency of the scheme with the underlining problem. Concerning the contact problem, we consider a frictionless contact model in a master/slave approach. Finally, we perform some numerical tests in the case of contact between a flexible body and a rigid wall and between two deformable structures. |
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43/2019 - 09/11/2019
Antonietti, P.F.; Mazzieri, I.; Migliorini, F.
A space-time discontinuous Galerkin method for the elastic wave equation | Abstract | | In this work we present a new high order space-time discretization method based on a discontinuos Galerkin paradigm for the second order visco-elastodynamics equation. After introducing the method, we show that the resulting space-time discontinuous Galerkin formulation is well-posed, stable and retains optimal rate of
convergence with respect to the discretization parameters, namely the mesh size and the polynomial approximation degree. A set of three-dimensional numerical experiments confirms the theoretical bounds. |
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42/2019 - 09/11/2019
Martino, A.; Guatteri, G.; Paganoni, A.M.
hmmhdd Package: Hidden Markov Model for High Dimensional Data | Abstract | | The R package "hmmhdd" provides some tools to study times series and longitudinal datasets. In particular, the package is based on Hidden Markov Models, i.e. it considers an underlying structure defined by a Markov Model with non-observable states generating a certain type of data, in the multivariate or functional framework. In the former setting, a Gaussian copula models the correlation structure between the components of the observations while, in the latter setting, the data are multivariate functional data and the methods are based on distances between curves. The package is able to estimate all the parameters corresponding to the states of the underlying Markov model, while also computing the optimal state sequence and providing some further helpful tools. |
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41/2019 - 09/11/2019
Abbà, A.; Bonaventura, L.; Recanati, A.; Tugnoli, M.;
Dynamical p-adaptivity for LES of compressible flows in a high order DG framework | Abstract | | We investigate the possibility of reducing the computational burden of LES models by employing locally and dynamically adaptive polynomial degrees in the framework of a high order DG method. A degree adaptation technique especially featured to be effective for LES applications, that was previously developed by the authors and tested in the statically adaptive case, is applied here in a dynamically adaptive fashion.
Two significant benchmarks are considered, comparing the results of adaptive and non adaptive simulations.
The proposed dynamically adaptive approach allows for a significant reduction of the computational cost of representative LES computation, while allowing to maintain the level of accuracy guaranteed by LES carried out with constant, maximum polynomial degree values. |
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38/2019 - 16/10/2019
Massi, M.C.; Ieva, F.; Gasperoni, F.; Paganoni, A.M.
Minority Class Feature Selection through Semi-Supervised Deep Sparse Autoencoders | 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 examples
with respect to majority class ones. To solve classification problems in imbalanced settings, and improve accuracy specifically on the minority class, we propose a feature selection algorithm based on the
application of a Deep Sparse AutoEncoder (DSAE) as a semi-supervised outlier detection method, where minority class examples are considered outliers of the normal population of majority class observations. We use a DSAE trained only on normal observations to reconstruct both inliers and outliers. From the analysis of the Reconstruction Error (RE) on both classes, we determine in which features the minority class has a significantly different distribution of values with respect to the majority class, thus identifying the most relevant features to discriminate between the two classes. We proved the efficacy of our algorithm in improving minority class classification accuracy (evaluated on specificity and AUROC metrics) on different datasets of high dimensionality and varying sample size, outperforming other benchmark feature selection methods. |
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40/2019 - 16/10/2019
Lovato, I.; Pini, A.; Stamm, A.; Vantini, S.
Model-free two-sample test for network-valued data | Abstract | | In the framework of Object Oriented Data Analysis, a permutation approach to the two-sample testing problem for network-valued data is proposed. In details, the present framework proceeds in four steps: (i) matrix representation of the networks, (ii) computation of the matrix of pairwise (inter-point) distances, (iii) computation of test statistics based on inter-point distances and (iv) embedding of the test statistics within a permutation test. The proposed testing procedures are proven to be exact for every finite sample size and consistent. Two new test statistics based on inter-point distances (i.e., IP-Student and IP-Fisher) are defined and a method to combine them to get a further inferential tool (i.e., IP-StudentFisher) is introduced. Simulated data shows that tests with our statistic exhibit a statistical power that is either the best or second-best but very close to the best on a variety of possible alternatives hypotheses and other statistics. A second simulation study that aims at better understanding which features are captured by specific combinations of matrix representations and distances is presented. Finally, a case study on mobility networks in the city of Milan is carried out. The proposed framework is fully implemented in the {R} package texttt{nevada} (NEtwork-VAlued Data Analysis). |
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39/2019 - 16/10/2019
Lovato, I.; Pini, A.; Stamm, A.; Taquet, M.; Vantini, S.
Multiscale null hypothesis testing for network-valued data: analysis of brain networks of patients with autism | Abstract | | Networks are a natural way of representing the human brain for studying its structure and function and, as such, have been extensively used. In this view, case-control studies for understanding autism pertain to comparing samples of healthy and autistic brain networks. In order to understand the biological mechanisms involved in the pathology, it is key to localize the differences on the brain network. Motivated by this question, we hereby propose a general non-parametric finite-sample exact statistical framework that allows to test for differences in connectivity within and between pre-specified areas inside the brain network, with strong control of the family-wise error rate. We demonstrate unprecedented ability to differentiate children with non-syndromic autism from children with both autism and tuberous sclerosis complex using EEG data. The implementation of the method is available in the R package nevada. |
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37/2019 - 30/09/2019
Menafoglio, A.; Secchi, P.
O2S2: a new venue for computational geostatistics | Abstract | | Applied sciences have witnessed an explosion of georeferenced data. Object oriented spatial statistics (O2S2) is a recent system of ideas that provides a solid framework where the new challenges posed by the GeoData revolution can be faced, by grounding the analysis on a powerful geometrical and topological approach. We shall present a perspective on O2S2, as a fruitful ground where novel computational approaches to geosciences can be developed, at the very interface among varied fields of applied sciences – including mathematics, statistics, computer science and engineering.
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