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 1152 products
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95/2023 - 11/28/2023
Barnafi, N. A.; Regazzoni, F.; Riccobelli, D.
Reconstructing relaxed configurations in elastic bodies: mathematical formulation and numerical methods for cardiac modeling | Abstract | | Modeling the behavior of biological tissues and organs often necessitates the knowledge of their shape in the absence of external loads. However, when their geometry is acquired in-vivo through imaging techniques, bodies are typically subject to mechanical deformation due to the presence of external forces, and the load-free configuration needs to be reconstructed. This paper addresses this crucial and frequently overlooked topic, known as the inverse elasticity problem (IEP), by delving into both theoretical and numerical aspects, with a particular focus on cardiac mechanics. In this work, we extend Shield's seminal work to determine the structure of the IEP with arbitrary material inhomogeneities and in the presence of both body and active forces. These aspects are fundamental in computational cardiology, and we show that they may break the variational structure of the inverse problem. In addition, we show that the inverse problem might be ill-posed, even in the presence of constant Neumann boundary conditions and a polyconvex strain energy functional. We then present the results of extensive numerical tests to validate our theoretical framework, and to characterize the computational challenges associated with a direct numerical approximation of the IEP. Specifically, we show that this framework outperforms existing approaches both in terms of robustness and optimality, such as Sellier's iterative procedure, even when the latter is improved with acceleration techniques. A notable discovery is that multigrid preconditioners are, in contrast to standard elasticity, not efficient, and domain decomposition methods provide a much more reliable alternative. Finally, we successfully address the IEP for a full-heart geometry, demonstrating that the IEP formulation can compute the stress-free configuration in real-life scenarios where Sellier's algorithm proves inadequate. |
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93/2023 - 11/25/2023
Andrini, D.; Magri, M.; Ciarletta, P.
Optimal surface clothing with elastic nets | Abstract | | The clothing problem aims at identifying the shape of a planar fabric for covering a target surface in the three-dimensional space. It poses significant challenges in various applications, ranging from fashion industry to digital manufacturing. Here, we propose a novel inverse design approach to the elastic clothing problem that is formulated as a constrained optimization problem. We assume that the textile behaves as an orthotropic, nonlinear elastic surface with fibers distributed along its warp and weft threads, and we enforce mechanical equilibrium as a variational problem. The target surface is frictionless, except at its boundary where the textile is pinned, imposing a unilateral obstacle condition for the reactive forces at the target surface. The constrained optimization problem also accounts for an elongation condition of the warp and weft fibers, possibly with bounded shearing angle. We numerically solve the resulting constrained optimization problem by means of a gradient descent algorithm. The numerical results are first validated against known clothing solutions for Chebyshev nets, taking the limit of inextensible fibers. We later unravel the interplay between thread and shear stiffness for driving the optimal cloth shape covering the hemisphere and the hemicatenoid. We show how the metric of these target surfaces strongly affects the resulting distribution of the reaction forces. When considering the limit of covering the full sphere, we show how clothing with elastic nets allows to avoid the onset of singularities in the corresponding Chebyshev net, by developing corners at the cloth boundary. |
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92/2023 - 11/16/2023
Burzacchi, A.; Rossi, L.; Agasisti, T.; Paganoni, A. M.; Vantini, S.
Commuting time as a determinant of higher education students' performance: the case of Politecnico di Milano | Abstract | | Despite its crucial role in students' daily lives, commuting time remains an underexplored dimension in higher education research. To address this gap, this study focuses on challenges that students face in urban environments and investigates the impact of commuting time on the academic performance of first-year bachelor students of Politecnico di Milano, Italy.
This research employs an innovative two-step methodology. In the initial phase, machine learning algorithms trained on GPS data from anonymous users are used to construct accessibility maps to the university and to obtain an estimate of students' commuting times. In the subsequent phase, authors utilize polynomial linear mixed-effects models and investigate the factors influencing students' academic performance, with a particular emphasis on commuting time. Notably, this investigation incorporates a causal framework, which enables the establishment of causal relationships between commuting time and academic outcomes.
The findings underscore the significant impact of travel time on students' performance and may support policies and implications aiming at improving students' educational experience in metropolitan areas.
The study's innovation lies both in its exploration of a relatively uncharted factor and the novel methodologies applied in both phases. |
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90/2023 - 11/10/2023
Gregorio, C.; Baj, G.; Barbati, G.; Ieva, F.
Dynamic treatment effect phenotyping through functional survival analysis | Abstract | | In recent years, research interest in personalised treatments has been growing. However, treatment effect heterogeneity and possibly time-varying treatment effects are still often overlooked in clinical studies. Statistical tools are needed for the identification of treatment response patterns, taking into account that treatment response is not constant over time. We aim to provide an innovative method to obtain dynamic treatment effect phenotypes on a time-to-event outcome, conditioned
on a set of relevant effect modifiers. The proposed method does not require the assumption of proportional hazards for the treatment effect, which is rarely realistic. We propose a spline-based survival neural network, inspired by the Royston-Parmar survival model, to estimate time-varying conditional treatment effects. We then exploit the functional nature of the resulting estimates to apply a functional clustering of the treatment effect curves in order to identify different patterns of treatment effects. The application that motivated this work is the discontinuation of treatment with Mineralocorticoid receptor Antagonists (MRAs) in patients with heart failure, where there is no clear evidence as to which patients it is the safest choice to discontinue treatment and, conversely, when it leads to a higher risk of adverse events. The data come from an electronic health record database. A simulation study was performed to assess the performance of the spline-based neural network and the stability of the treatment response phenotyping procedure. In light of the results, the suggested approach has the potential to support personalized medical choices by assessing treatment responses in various medical contexts over a period of time. |
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89/2023 - 11/08/2023
Savaré, L.; Ieva, F.; Corrao, G.; Lora, A.
Capturing the variety of clinical pathways in patients with schizophrenic disorders through state sequences analysis | Abstract | | Background Care pathways are increasingly being used to enhance the quality of care and optimize the use
of resources for health care. Nevertheless, recommendations regarding the sequence of care are mostly based
on consensus-based decisions as there is a lack of evidence on effective treatment sequences. In a real-world setting,
classical statistical tools were insufficient to consider a phenomenon with such high variability adequately and have
to be integrated with novel data mining techniques suitable for identifying patterns in complex data structures.
Data-driven techniques can potentially support empirically identifying effective care sequences by extracting them
from data collected routinely. The purpose of this study is to perform a state sequence analysis (SSA) to identify different
patterns of treatment and to asses whether sequence analysis may be a useful tool for profiling patients according
to the treatment pattern.
Methods The clinical application that motivated the study of this method concerns the mental health field. In fact,
the care pathways of patients affected by severe mental disorders often do not correspond to the standards required
by the guidelines in this field. In particular, we analyzed patients with schizophrenic disorders (i.e., schizophrenia,
schizotypal or delusional disorders) using administrative data from 2015 to 2018 from Lombardy Region. This methodology
considers the patient’s therapeutic path as a conceptual unit, composed of a succession of different states,
and we show how SSA can be used to describe longitudinal patient status.
Results We define the states to be the weekly coverage of different treatments (psychiatric visits, psychosocial interventions,
and anti-psychotic drugs), and we use the longest common subsequences (dis)similarity measure to compare
and cluster the sequences. We obtained three different clusters with very different patterns of treatments.
Conclusions This kind of information, such as common patterns of care that allowed us to risk profile patients, can
provide health policymakers an opportunity to plan optimum and individualized patient care by allocating appropriate
resources, analyzing trends in the health status of a population, and finding the risk factors that can be leveraged
to prevent the decline of mental health status at the population level.
Keywords State sequence analysis, Care pathways, Schizophrenic disorder |
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88/2023 - 11/08/2023
Masci, C.; Spreafico, M.; Ieva, F.
Joint modelling of recurrent and terminal events with discretely-distributed non-parametric frailty: application on re-hospitalizations and death in heart failure patients | Abstract | | In the context of clinical and biomedical studies, joint frailty models have been developed to study the
joint temporal evolution of recurrent and terminal events, capturing both the heterogeneous susceptibility
to experiencing a new episode and the dependence between the two processes. While discretely-distributed
frailty is usually more exploitable by clinicians and healthcare providers, existing literature on joint frailty
models predominantly assumes continuous distributions for the random effects. In this article, we present a
novel joint frailty model that assumes bivariate discretely-distributed non-parametric frailties, with an unknown
finite number of mass points. This approach facilitates the identification of latent structures among subjects,
grouping them into sub-populations defined by a shared frailty value. We propose an estimation routine via
Expectation-Maximization algorithm, which not only estimates the number of subgroups but also serves as an
unsupervised classification tool. This work is motivated by a study of patients with Heart Failure (HF) receiving
ACE inhibitors treatment in the Lombardia region of Italy. Recurrent events of interest are hospitalizations
due to HF and terminal event is death for any cause. |
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86/2023 - 11/04/2023
Ferraccioli, F.; Sangalli, L.M.; Finos, L.
Nonparametric tests for semiparametric regression models | Abstract | | Semiparametric regression models have received considerable attention over the last decades, because of their flexibility and their good finite sample performances. Here we propose an innovative nonparametric test for the linear part of the models, based on random sign-flipping of an appropriate transformation of the residuals, that exploits a spectral decomposition of the residualizing matrix associated with the nonparametric part of the model. The test can be applied to a vast class of extensively used semiparametric regression models with roughness penalties, with nonparametric components defined over one-dimensional, as well as over multi-dimensional domains, including for instance models based on univariate or multivariate splines. We prove the good asymptotic properties of the proposed test. Moreover, by means of extensive simulation studies, we show the superiority of the proposed test with respect to current parametric alternatives, demonstrating its excellent control of the Type I error, accompanied by a good power, even in challenging data scenarios, where instead current parametric alternatives fail. |
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85/2023 - 11/04/2023
Arnone, E.; De Falco, C.; Formaggia, L.; Meretti, G.; Sangalli, L.M.
Computationally efficient techniques for Spatial Regression with Differential Regularization | Abstract | | We investigate some computational aspects of an innovative class of PDE-regularized statistical models: Spatial Regression with Partial Differential Equation regularization (SR-PDE). These physics-informed regression methods can account for the physics of the underlying phenomena and handle data observed over spatial domains with nontrivial shapes, such as domains with concavities and holes or curved domains. The computational bottleneck in SR-PDE estimation is the solution of a computationally demanding linear system involving a low-rank but dense block. We address this aspect by innovatively using Sherman–Morrison–Woodbury identity. We also investigate the efficient selection of the smoothing parameter in SR-PDE estimates. Specifically, we propose ad hoc optimization methods to perform Generalized Cross-Validation, coupling suitable reformulation of key matrices, e.g., those based on Sherman–Morrison–Woodbury formula, with stochastic trace estimation, to approximate the equivalent degrees of freedom of the problem. These solutions permit high computational efficiency also in the context of massive data. |
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