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 1288 prodotti
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39/2016 - 07/11/2016
Andrà, C.; Brunetto, D.; Parolini, N.; Verani, M.
Student interactions during class activities: a mathematical model | Abstract | | We propose a mathematical model describing the interactions among students during work group activities aimed at solving a math problem. The model, which hinges upon the pioneering work of Hegselmann and Krause, is able to incorporate: 1) the feelings of each student towards the classmates (building upon the “I can”-“You can” framework); 2) the influence of the correct solution to model the students’ preparation; 3) the presence of the teacher, who may or may not intervene to drive students towards the correct solution of the problem. Several numerical experiments are presented to assess the capability of the model in reproducing typical realistic scenarios. |
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38/2016 - 07/11/2016
Quarteroni, A.; Manzoni, A.; Vergara, C.
The Cardiovascular System: Mathematical Modeling, Numerical Algorithms, Clinical Applications | Abstract | | Mathematical and numerical modeling of the cardiovascular system is a research topic that
has attracted a remarkable interest from the mathematical community because of the intrinsic
mathematical difficulty and due to the increasing impact of cardiovascular diseases worldwide.
In this review article, we will address the two principle components of the cardiovascular
system, the arterial circulation and the heart function. We systematically go through the
complete pipeline from data imaging acquisition, setting the basic physical principles, analyzing
the associated mathematical models that comprise PDEs and ODEs systems, proposing
sound and efficient numerical methods for their approximation, simulating both benchmark
problems and clinically inspired (driven) problems. Mathematical modeling itself features
tremendous challenges, due to the amazing complexity of the cardiocirculatory system, the
multiscale nature of the involved physiological processes, and the need of devising computational
methods that are stable, reliable, and efficient. A critical issue is about filtering
the data, identifying the parameters of mathematical models, devising optimal treatments,
accounting for uncertainties. For this reason, we will devote the last part of the paper to
control and inverse problems, including parameter estimation, uncertainty quantification and
the development of reduced order models that are of paramount importance when solving
problems with high complexity, that would be out of reach otherwise. |
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37/2016 - 12/10/2016
Tugnoli, M; Abbà, A. ; Bonaventura, L.; Restelli, M.
A locally p-adaptive approach for Large Eddy Simulation of compressible flows in a DG framework | Abstract | | We investigate the possibility of reducing the computational burden of LES models by employing local polynomial degree adaptivity in the framework of a high order DG method. A novel degree adaptation technique especially featured to be effective for LES applications is proposed and its effectiveness is compared to that of other criteria already employed in the literature. The resulting locally adaptive approach allows to achieve significant reductions in computational cost of representative LES computations. |
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36/2016 - 12/10/2016
Mancini, L.; Paganoni, A.M.
Marked Point Process models for the admissions of heart failured patients | Abstract | | The aim of this paper is to model the stochastic process of hospitalizations with Marked Point Processes. We examine the longitudinal dataset including the admissions of heart failured patients to Lombardia hospitals on a follow-up period of six years since January 1st, 2006. We analyse four separate groups of patients, which we call HF groups, according to their diagnoses-codes contained in the SDO (dimission hospital discharge form) of their first hospitalizations.
The statistical model links the temporal trend of hospitalization (the ground process) with the length of stay (the mark) at each event. Instead of framing our application in the more theoretical context of the counting measures and processes, we make use of the conditional intensity function, a parametric approach which leads us to deal with Hawkes processes.
Hypotheses are made on the mark concerning its distribution as well as
its independence or dependence with the ground process. Independence is
better to model and give us significant results while dependence is harder
to be dealt with due to computational and modeling issues.
Finally, we provide a general framework for modeling longitudinal data with
a MPP as of methods for statistical inference and suggest a specific model
for our topic, validating it through a goodness of fit technique. |
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33/2016 - 06/10/2016
Antonietti, P. F.; Ferroni, A.; Mazzieri, I.; Quarteroni, A.
hp-version discontinuous Galerkin approximations of the elastodynamics equation | Abstract | | In this paper we extend the results contained in [Antonietti, Ayuso de Dios, Mazzieri, Quarteroni, J. Sci. Comput., 2016] and consider the problem of approximating the elastodynamics equation by means of hp-version discontinuous Galerkin methods. For the resulting semi-discretized schemes we derive stability bounds as well as hp error estimates in a suitable energy norm. Our theoretical estimates are verified through three dimensions numerical experiments. |
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35/2016 - 06/10/2016
Zonca, S.; Formaggia, L.; Vergara, C.
An unfitted formulation for the interaction of an incompressible fluid with a thick structure via an XFEM/DG approach | Abstract | | A numerical procedure that combines an Extended Finite Element (XFEM) formulation and a Discontinuous Galerkin technique is presented, with the final aim of providing an effective tool for the simulation of three-dimensional fluid-structure interaction problems where the structure undergoes large displacements. In this work we consider thick structures immersed in a fluid domain and we focus on the description of the numerical models and on the techniques used to deal with the issues related to the implementation of XFEM in this context. Numerical results are provided to show the effectiveness of the approach. |
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34/2016 - 06/10/2016
Menafoglio, A.; Secchi, P.
Statistical analysis of complex and spatially dependent data: a review of Object Oriented Spatial Statistics | Abstract | | We review recent advances in Object Oriented Spatial Statistics, a system of ideas, algorithms and methods that allows the analysis of high dimensional and complex data when their spatial dependence is an important issue. At the intersection of different disciplines -- including mathematics, statistics, computer science and engineering -- Object Oriented Spatial Statistics provides the right perspective to address key problems in varied contexts, from Earth and life sciences to urban planning. We illustrate a few paradigmatic methods applied to problems of prediction, classification and smoothing, giving emphasis to the key ideas Object Oriented Spatial Statistics relies upon. |
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32/2016 - 30/09/2016
Tarabelloni, N.; Schenone, E.; Collin, A.; Ieva, F.; Paganoni, A.M.; Gerbeau, J.-F.
Statistical Assessment and Calibration of Numerical ECG Models | Abstract | | Objective: Because of the inter-subject variability of ECGs in a healthy
population, it is not straightforward to assess the quality of synthetic ECGs
produced by deterministic mathematical models. We propose a statistical method
to address this question.
Methods: We use a dataset of 1588 healthy, real ECGs and we introduce a way to
calibrate the deterministic model so that its output fits the dataset. Our
approach is based on the concepts of spatial quantiles and spatial depths. These
notions are convenient to manipulate functional data since they provide a
non-parametric way to measure the discrepancy of the model output with a
distribution of data.
Results: The method is successfully applied to two very different models: a
phenomenological model based on ordinary differential equations, and a complex
biophysical model based on partial differential equations set on a
three-dimensional geometry of the heart and the torso. We show in particular
that the proposed calibration strategy allows us to improve the quality of the
ECG obtained with the biophysical model.
Significance: The proposed methodology is to our knowledge the first attempt to
assess the quality of synthetic ECGs with quantitative statistical arguments.
More generally it can be applied to other situations where a deterministic model
produces a functional output that has to be compared with a population of
measurements containing inter-subject variability. |
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