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 1238 prodotti
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45/2013 - 08/10/2013
Sangalli, L.M.; Secchi, P.; Vantini, S.
Analysis of AneuRisk65 data: K-mean Alignment | Abstract | | We describe the k-mean alignment procedure, for the joint alignment and clustering of functional data and we apply it to the analysis of
AneuRisk65 data. Thanks to the efficient separation of the variability in phase variability and within/between clusters amplitude variability, we are able to discriminate subjects having aneurysms in di fferent cerebral districts and identifying diff erent morphological shapes of Inner Carotid Arteries, unveiling a strong association between vessel morphologies and the aneurysmal pathology. |
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44/2013 - 07/10/2013
Sangalli, L.M.; Secchi, P.; Vantini, S.
AneuRisk65: a dataset of three-dimensional cerebral vascular geometries | Abstract | | We describe AneuRisk65 data, obtained from image reconstruction of three-dimensional cerebral angiographies. This dataset was collected
for the study of the aneurysmal pathology, within the AneuRisk Project. It includes the geometrical reconstructions of one of the main cerebral vessels, the Inner Carotid Artery, described in terms of the vessel centreline and of the vessel radius profile. We briefly illustrate the data derivation and processing, explaining various aspects that are of interest for this applied problem, while also discussing the peculiarities
and critical issues concerning the definition of phase and amplitude variabilities for these three-dimensional functional data. |
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43/2013 - 06/10/2013
Patriarca, M.; Sangalli, L.M.; Secchi, P.; Vantini, S.
Analysis of Spike Train Data: an Application of K-mean Alignment | Abstract | | We analyze the spike train data by means of the k-mean alignment algorithm in a double perspective: data as non periodic and data as periodic. In the first analysis, we show that alignment is not needed to identify paths. Indeed, without allowing for warping, we
detect four clusters strongly associated to the four possible paths. In the second analysis, by exploiting the circular nature of data and allowing for shifts, we detect two clusters distinguishing between spike trains presenting higher or lower neuronal activity during the bottom-left/bottom-right movement respectively. In this latter case, the alignment procedure is able to match the four movements across paths. |
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42/2013 - 05/10/2013
Bernardi, M.; Sangalli, L.M.; Secchi, P.; Vantini, S.
Analysis of Juggling Data: an Application of K-mean Alignment | Abstract | | We analyze the juggling data by means of the k-mean alignment algorithm using cycles as the experimental units of the analysis. Allowing for affine warping, we detect two clusters distinguishing between mainly-planar trajectories and trajectories tilted toward the body of the juggler in the lower part of the cycle. In particular we detect an anomalous presence of tilted trajectories among the record third cycles. We also find warping functions to be clustered according to records suggesting that each record is performed at a di fferent pace and thus associated to a diff erent typical cycle-duration. |
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41/2013 - 04/10/2013
Bernardi, M.; Sangalli, L.M.; Secchi, P.; Vantini, S.
Analysis of Proteomics data: Block K-mean Alignment | Abstract | | We analyze the proteomics data introducing a block k-mean alignment procedure. This technique is able to jointly align and cluster the data, accounting appropriately for the block structure of these data, that includes measurement repetitions for each patient. An analysis of area-under-peaks, following the alignment, separates patients who respond and those who do not respond to treatment. |
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40/2013 - 03/10/2013
Pacciarini P.; Rozza G.
Stabilized reduced basis method for parametrized advection-diffusion PDEs | Abstract | | In this work, we propose viable and efficient strategies for the stabilization of the reduced basis
approximation of an advection dominated problem. In particular, we investigate the combination
of a classic stabilization method (SUPG) with the Offline-Online structure of the RB method. We
explain why the stabilization is needed in both stages and we identify, analytically and numerically,
which are the drawbacks of a stabilization performed only during the construction of the reduced
basis (i.e. only in the Offline stage). We carry out numerical tests to assess the performances
of the double stabilization both in steady and unsteady problems, also related to heat transfer
phenomena. |
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39/2013 - 02/10/2013
Ieva, F.; Marra, G.; Paganoni, A.M.; Radice, R.
A semiparametric bivariate probit model for joint modeling of outcomes in STEMI patients | Abstract | | In this work we analyse the relationship among in-hospital mortality and a treatment effectiveness outcome in patients affected by ST-Elevation Myocardial Infarction. The main idea is to carry out a joint modelling of the two outcomes applying a Semiparametric Bivariate Probit Model to data arising from a clinical registry called STEMI Archive. A realistic quantification of the relationship between outcomes can be problematic for various reasons. First, latent factors associated with hospitals organization can affect the treatment efficacy and/or interact with patient s condition at admission time, then they can influence the mortality outcome. Such factors can be hardly measurable. Thus, the use of classical estimation methods will clearly result in inconsistent and biased parameter estimates. Secondly, covariate-outcomes relationships can exhibit non-linear patterns. Provided that proper statistical methods for model fitting in such framework are available, it is possible to employ a simultaneous estimation approach to account for unobservable confounders. Such a framework can also provide flexible covariate structures and model the whole conditional distribution of the response. |
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38/2013 - 17/09/2013
Bonizzoni, F.; Nobile, F.
Perturbation analysis for the Darcy problem with log-normal permeability | Abstract | | We study the single-phase flow in a saturated, bounded heterogeneous porous medium. We model the permeability as a log-normal random field. We perform a perturbation analysis, expanding the solution in Taylor series. The series is directly computable in the case of a random field parametrized by a finite number of random variables. On the other hand, in the case of an infinite dimensional random field, suitable equations satisfied by the derivatives of the stochastic solution can be derived. We give a theoretical upper bound for the norm of the residual of the Taylor expansion which predicts the divergence of the series as the polynomial degree goes to infinity.
We provide a formula to compute the optimal degree for the Taylor polynomial and the maximum achievable accuracy of the perturbation approach.
Our theoretical findings are confirmed by numerical experiments in the simple case where the permeability field is described using one random variable.
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