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 1249 prodotti
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27/2022 - 27/04/2022
Lazzari J., Asnaghi R., Clementi L., Santambrogio M. D.
Math Skills: a New Look from Functional Data Analysis | Abstract | | Mental calculations involve various areas of the brain. The frontal, parietal and temporal lobes of the left hemisphere have a principal role in the completion of this typology of tasks. Their level of activation varies based on the mathematical competence and attentiveness of the subject under examination and the perceived difficulty of the task. Recent literature often investigates patterns of cerebral activity through fMRI, which is an expensive technique. In this scenario, EEGs represent a more straightforward and cheaper way to collect information regarding brain activity. In this work, we propose an EEG based method to detect differences in the cerebral activation level of people characterized by different abilities in carrying out the same arithmetical task. Our approach consists in the extraction of the activation level of a given region starting from the EEG acquired during resting state and during the completion of a subtraction task. We then analyze these data through Functional Data Analysis, a statistical technique that allows operating on biomedical signals as if they were functions. The application of this technique allowed for the detection of distinct cerebral patterns among the two groups and, more specifically, highlighted the presence of higher levels of activation in the parietal lobe in the population characterized by a lower performance. |
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26/2022 - 27/04/2022
Orlando, G.
A filtering monotonization approach for DG discretizations of hyperbolic problems | Abstract | | We introduce a filtering technique for Discontinuous Galerkin approximations of hyperbolic problems. Following an approach already proposed for the Hamilton-Jacobi equations by other authors, we aim at reducing the spurious oscillations that arise in presence of discontinuities when high order spatial discretizations are employed. This goal is achieved using a filter function that keeps the high order scheme when the solution is regular and switches to a monotone low order approximation if it is not. The method has been implemented in the framework of the deal.II numerical library, whose mesh adaptation capabilities are also used to reduce the region in which the low order approximation is used. A number of numerical experiments demonstrate the potential of the proposed filtering technique. |
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25/2022 - 27/04/2022
Cavinato, L; Gozzi, N.; Sollini, M; Kirienko, M; Carlo-Stella, C; Rusconi, C; Chiti, A; Ieva, F.
Perspective transfer model building via imaging-based rules extraction from retrospective cancer subtyping in Hodgkin Lymphoma | Abstract | | Image texture analysis has for decades represented a promising opportunity for cancer assessment and disease progression evaluation, evolving over time in a discipline, i.e., radiomics. However, the road for a complete translation into clinical practice is still hampered by intrinsic limitations. As purely supervised classification models fails in devising univocal imaging-based differences in tumors with different prognosis, cancer subtyping approaches would benefit from the employment of distant supervision, for instance exploiting survival/recurrence information. In this work, we transfer our previous model for Hodgkin Lymphoma subtyping to a multi-center study case. We evaluated model performance in two independent datasets coming from two hospitals, comparing and analyzing the results. Our preliminary data confirmed the instability of radiomics due to across-center lack of reproducibility, leading to meaningful results in one center and poorer performance in the other. We then learnt stratification rules from the first dataset via Random Forest and leveraged those rules to transfer the stratification policy onto the second dataset. In this way, on the one hand, we tested the stratification ability of cancer subtyping in a validation setting and, on the other hand, enriched the noisier dataset with valuable information, in a borrowing strength fashion. The transfer of the model resulted successful. Moreover, having extracted decision rules for cancer subtyping, we were able to draw up risk factors to be considered in clinics. The work shows the potentialities of the proposed pipeline to be further evaluated in larger multi-center datasets, with the goal of translating radiomics into clinical practice. |
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24/2022 - 27/04/2022
Cappozzo, A.; McCrory, C.; Robinson, O.; Freni Sterrantino, A.; Sacerdote, C.; Krogh, V.; Panico, S.; Tumino, R.; Iacoviello, L.; Ricceri, F.; Sieri, S.; Chiodini, P.; Kenny, R.A.; O'Halloran, A.; Polidoro, S.; Solinas, G.; Vineis, P.; Ieva, F.; Fiorito, G.;
A blood DNA methylation biomarker for predicting short-term risk of cardiovascular events | Abstract | | Background. Evidence highlights the epidemiological value of DNA methylation (DNAm) for predicting cardiovascular diseases (CVDs). DNAm surrogates of exposures and risk factors predict diseases and longevity better than self-reported or measured exposures in many cases. Composite biomarkers based on DNAm surrogates, ‘next generation’ epigenetic clocks trained on time-to-death, constitute non-specific biomarkers representing the general health status rather than disease-specific signatures. Training a model on cardiovascular-specific risk factors may improve the identification of
high-risk populations for CVD.
Methods. We developed a DNAm-based biomarker predictive of short-term risk for CVD using a twostep approach: 1) development and validation of novel DNAm surrogates for cardiovascular risk
biomarkers; 2) development and validation of a DNAmCVDscore as a combination of DNAm surrogates. In an independent testing set, we compared the prediction performance of DNAmCVDscore with (a) the ‘next-generation’ epigenetic clock DNAmGrimAge, (b) a DNAm score
for CVD derived through a single-step approach, MRS, and (c) the current state-of-the-art prediction model based on traditional CVD risk factors, SCORE2.
Results. We presented novel DNAm surrogates for BMI, blood pressure, fasting glucose and insulin, cholesterol, triglycerides, and coagulation biomarkers, validated in independent datasets. Further, we
derived a DNAmCVDscore outperforming the model based on traditional CVD risk factors and other epigenetic biomarkers for predicting short-term cardiovascular events.
Conclusions. We provided novel DNAm surrogates useful for future epidemiological research, and we described a DNAm based composite biomarker, DNAmCVDscore, predictive of short-term CVD.
Our results highlight the usefulness of DNAm surrogate biomarkers of risk factors and exposures to identify high-risk populations. |
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23/2022 - 27/04/2022
Masci, C.; Ieva, F.; Paganoni, A.M.
A multinomial mixed-effects model with discrete random effects for modelling dependence across response categories | Abstract | | We propose a Semi-Parametric Mixed-Effects Multinomial regression model to deal with estimation and inference issues in the case of categorical and hierarchical data. The proposed modelling assumes the probability of each response category to be identified by a set of fixed and random effects parameters, estimated by means of an Expectation-Maximization algorithm. Random effects are assumed to follow a discrete distribution with an a priori unknown number of support points. For a K-category response, this method identifies a latent structure at the highest level of grouping, where groups are clustered into (K-1)-dimensional subpopulations. This method is an extension of the multinomial semi-parametric EM algorithm proposed in the literature, in which we relax the independence assumption across random-effects relative to different response categories. Since the category-specific random effects arise from the same subjects, their independence assumption is seldom verified in real data. In this sense, the proposed method properly models the natural data structure, as emerges by the results of simulation and case studies, which highlight the importance of taking into account the data dependence structure in real data applications. |
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22/2022 - 17/04/2022
Regazzoni, F.; Pagani, S.; Quarteroni, A.
Universal Solution Manifold Networks (USM-Nets): non-intrusive mesh-free surrogate models for problems in variable domains | Abstract | | We introduce Universal Solution Manifold Network (USM-Net), a novel surrogate model, based on Artificial Neural Networks (ANNs), which applies to differential problems whose solution depends on physical and geometrical parameters. Our method employs a mesh-less architecture, thus overcoming the limitations associated with image segmentation and mesh generation required by traditional discretization methods. Indeed, we encode geometrical variability through scalar landmarks, such as coordinates of points of interest. In biomedical applications, these landmarks can be inexpensively processed from clinical images. Our approach is non-intrusive and modular, as we select a data-driven loss function. The latter can also be modified by considering additional constraints, thus leveraging available physical knowledge. Our approach can also accommodate a universal coordinate system, which supports the USM-Net in learning the correspondence between points belonging to different geometries, boosting prediction accuracy on unobserved geometries. Finally, we present two numerical test cases in computational fluid dynamics involving variable Reynolds numbers as well as computational domains of variable shape. The results show that our method allows for inexpensive but accurate approximations of velocity and pressure, avoiding computationally expensive image segmentation, mesh generation, or re-training for every new instance of physical parameters and shape of the domain. |
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21/2022 - 13/04/2022
Cappozzo, A.; Ieva, F.; Fiorito, G.
A general framework for penalized mixed-effects multitask learning with applications on DNA methylation surrogate biomarkers creation | Abstract | | Recent evidence highlights the usefulness of DNA methylation (DNAm) biomarkers as surrogates for exposure to risk factors for non-communicable diseases in epidemiological studies and randomized trials. DNAm variability has been demonstrated to be tightly related to lifestyle behavior and exposure to environmental risk factors, ultimately providing an unbiased proxy of an individual state of health. At present, the creation of DNAm surrogates relies on univariate penalized regression models, with elastic-net regularizer being the gold standard when accomplishing the task. Nonetheless, more advanced modeling procedures are required in the presence of multivariate outcomes with a structured dependence pattern among the study samples. In this work we propose a general framework for mixed-effects multitask learning in presence of high-dimensional predictors to develop a multivariate DNAm biomarker from a multi-center study. A penalized estimation scheme based on an expectation-maximization (EM) algorithm is devised, in which any penalty criteria for fixed-effects models can be conveniently incorporated in the fitting process. We apply the proposed methodology to create novel DNAm surrogate biomarkers for multiple correlated risk factors for cardiovascular diseases and comorbidities. We show that the proposed approach, modeling multiple outcomes together, outperforms state-of-the-art alternatives, both in predictive power and bio-molecular interpretation of the results. |
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20/2022 - 13/04/2022
Clementi, L.; Gregorio, C; Savarè, L.; Ieva, F; Santambrogio, M.D.; Sangalli, L.M.
A Functional Data Analysis Approach to Left Ventricular Remodeling Assessment | Abstract | | Left ventricular remodeling is a mechanism common to various cardiovascular diseases affecting myocardial morphology. It can be often overlooked in clinical practice since the parameters routinely employed in the diagnostic process (e.g., the ejection fraction) mainly focus on evaluating volumetric aspects. Nevertheless, the integration of a quantitative assessment of structural modifications can be pivotal in the early individuation of this pathology. In this work, we propose an approach based on functional data analysis to evaluate myocardial
contractility. A functional representation of ventricular shape is introduced, and functional principal component analysis and depth measures are used to discriminate healthy subjects from those affected by left ventricular hypertrophy. Our approach enables the integration of higher informative content compared to the traditional clinical parameters, allowing for a synthetic representation of morphological changes in the myocardium, which could be further explored and considered for future clinical practice implementation. |
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