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 1326 prodotti
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72/2022 - 19/10/2022
Spreafico, M.; Ieva, F.; Arlati, F.; Capello, F.; Fatone, F.; Fedeli, F.; Genalti, G.; Anninga, J.; Gelderblom, H.; Fiocco, M.
Novel longitudinal multiple overall toxicity score to quantify adverse events experienced by patients during chemotherapy treatment: a retrospective analysis of the MRC BO06 trial in osteosarcoma | Abstract | | Aim: This work is intended to study the evolution of chemotherapy-induced toxicity over treatment, introducing a new method for summarize multiple toxic adverse events (AEs), i.e., the longitudinal Multiple Overall Toxicity (MOTox) score. A retrospective analysis of patients from MRC BO06/EORTC 80931 Randomized Controlled Trial for osteosarcoma was conducted.
Methods: Patients were randomised to six cycles of conventional versus dose-intense regimens of doxorubicin and cisplatin. Non-haematological toxicity data were collected prospectively and graded according to the Common Terminology Criteria for Adverse Events (CTCAE). The MOTox score was defined by condensing the worst AE and the overall toxic condition, including a time dimension. Multivariate models were constructed to assess the evolution of high overall toxicity, examining cycle-by-cycle the impact of personalized characteristics, such as achieved chemotherapy dose, previous toxic events, or biochemical factors.
Results: The flexible longitudinal depiction of MOTox score represents the strength of our method. A cycle-by-cycle dimension allowed to reconstruct different evolution patterns over treatment, leading to informative ramifications on patients’ health statuses. Patient’s toxic history played an important role in the quality of life over therapy, showing an autoregressive impact of previous toxicity. Conventional regimen had to be preferred to dose-intense one in terms of toxic AEs in the first half of the treatment.
Conclusion: This study shows that working in this direction is a difficult but profitable approach. The flexibility of our method, added to a cooperation with medical staff, could lead to improvements in the definition of useful tools for health care assessment and treatment planning. |
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71/2022 - 19/10/2022
Calabrò, D.; Lupo Pasini, M.; Ferro, N.; Perotto, S.
A deep learning approach for detection and localization of leaf anomalies | Abstract | | The detection and localization of possible diseases in crops are usually automated by resorting to supervised deep learning approaches. In this work, we tackle these goals with unsupervised models, by applying three different types of autoencoders to a specific open-source dataset of healthy and unhealthy pepper and cherry leaf images. CAE, CVAE and VQ-VAE autoencoders are deployed to screen unlabeled images of such a dataset, and compared in terms of image reconstruction, anomaly removal, detection and localization. The vector-quantized variational architecture turns out to be the best performing one with respect to all these targets. |
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70/2022 - 19/10/2022
Andrini, D.; Balbi, V.; Bevilacqua, G.; Lucci, G.; Pozzi, G.; Riccobelli, D.
Mathematical modelling of axonal cortex contractility | Abstract | | The axonal cortex is composed of a regular structure of F-actin and spectrin able to contract thanks to myosin II motors. Such an active tension is of fundamental importance in controlling the physiological shape of axons. Recent experiments show that axons modulate the contraction of the cortex when subject to mechanical deformations, exhibiting a non-trivial coupling between the hoop and the axial active tension. However, the underlying mechanisms are still poorly understood. In this paper, we propose a continuum model of the axon based on the active strain theory. By using the Coleman-Noll procedure, we shed light on the coupling between the hoop and the axial active strain through the Mandel stress tensor. We propose a qualitative analysis of the system under the simplifying assumption of incompressibility, showing the existence of a stable equilibrium solution. In particular, our results show that the axon regulates the active contraction to maintain a homeostatic stress state. Finally, we propose numerical simulations of the model, using a more suitable compressible constitutive law. The results are compared with experimental data, showing an excellent quantitative agreement. |
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69/2022 - 19/10/2022
Franco, N.R; Manzoni, A.; Zunino, P.
Learning Operators with Mesh-Informed Neural Networks | Abstract | | Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed Neural Networks (MINNs), a class of architectures specifically tailored to handle mesh based functional data, and thus of particular interest for reduced order modeling of parametrized Partial Differential Equations (PDEs). The driving idea behind MINNs is to embed hidden layers into discrete functional spaces of increasing complexity, obtained through a sequence of meshes defined over the underlying spatial domain. The approach leads to a natural pruning strategy which enables the design of sparse architectures that are able to learn general nonlinear operators. We assess this strategy through an extensive set of numerical experiments, ranging from nonlocal operators to nonlinear diffusion PDEs, where MINNs are compared to classical fully connected Deep Neural Networks. Our results show that MINNs can handle functional data defined on general domains of any shape, while ensuring reduced training times, lower computational costs, and better generalization capabilities, thus making MINNs very well-suited for demanding applications such as Reduced Order Modeling and Uncertainty Quantification for PDEs. |
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68/2022 - 19/10/2022
Orlando, G.; Benacchio, T.; Bonaventura, L.
An IMEX-DG solver for atmospheric dynamics simulations with adaptive mesh refinement | Abstract | | We present an accurate and efficient solver for atmospheric dynamics simulations that allows for non-conforming mesh refinement. The model equations are the conservative Euler equations for compressible flows. The numerical method is based on an h-adaptive Discontinuous Galerkin spatial discretization and on a second order Additive Runge Kutta IMEX method for time discretization, especially designed for low Mach regimes. The solver is implemented in the framework of the deal.II library, whose mesh refinement capabilities are employed to enhance efficiency. A number of numerical experiments based on classical benchmarks for atmosphere dynamics demonstrate the properties and advantages of the proposed method. |
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67/2022 - 19/10/2022
Alghamdi, M. M.; Boffi, D.; Bonizzoni, F.
A greedy MOR method for the tracking of eigensolutions to parametric elliptic PDEs | Abstract | | In this paper we introduce an algorithm based on a sparse grid adaptive refinement, for the approximation of the eigensolutions to parametric problems arising from elliptic partial differential equations. In particular, we are interested in detecting the crossing of the hypersurfaces describing the eigenvalues as a function of the parameters.
The a priori matching is followed by an a posteriori verification, driven by a suitably defined error indicator. At a given refinement level, a sparse grid approach is adopted for the construction of the grid of the next level, by using the marking given by the a
posteriori indicator.
Various numerical tests confirm the good performance of the scheme. |
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65/2022 - 05/10/2022
Dassi, F.; Fumagalli, A.; Mazzieri, I.; Vacca, G.
Mixed Virtual Element approximation of linear acoustic wave equation | Abstract | | We design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In absence of external load, the semi-discrete method exactly conserves the system energy. To integrate in time the semi-discrete problem we consider a classical theta-method scheme. We carry out the stability and convergence analysis in the energy norm for the semi-discrete problem showing optimal rate of convergence with respect to the mesh size. We further study the property of energy conservation for the fully-discrete system. Finally, we present some verification tests as well as engineering application of the method. |
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64/2022 - 05/10/2022
Massi, M.C., Dominoni, L., Ieva, F., Fiorito, G.
A Deep Survival EWAS approach estimating risk profile based on pre-diagnostic DNA methylation: an application to Breast Cancer time to diagnosis | Abstract | | Previous studies for cancer biomarker discovery based on pre-diagnostic blood DNA methylation profiles, either ignore the explicit modeling of the time to diagnosis (TTD) as in a survival analysis setting, or provide inconsistent results. This lack of consistency is likely due to the limitations of standard EWAS approaches, that model the effect of
DNAm at CpG sites on TTD independently. In this work, we argue that a global approach to estimate CpG sites effect profile is needed, and we claim that such approach should capture the complex (potentially non-linear) relationships interplaying between sites. To prove our concept, we develop a new Deep Learning-based approach assessing the relevance of individual CpG Islands (i.e., assigning a weight to each site) in determining TTD while modeling their combined effect in a survival analysis scenario.
The algorithm combines a tailored sampling procedure with DNAm sites agglomeration, deep non-linear survival modeling and SHapley Additive exPlanations (SHAP) values estimation to aid robustness of the derived effects profile. The proposed approach deal with the common complexities arising from epidemiological studies, such as small sample size, noise, and low signal-to-noise ratio of blood-derived DNAm. We apply our approach to a prospective case-control study on breast cancer nested in the EPIC Italy cohort and we perform weighted gene-set enrichment analyses to demonstrate the biological meaningfulness of the obtained results. We compared the results of Deep Survival EWAS with those of a traditional EWAS approach, demonstrating that our method performs better than the standard approach in identifying biologically relevant pathways. |
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