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 1238 products
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01/2015 - 01/26/2015
Pini, A.; Stamm, A.; Vantini, S.
Hotelling s $T^2$ in functional Hilbert spaces | Abstract | | The field of statistics is at the cusp of a revolution in the way data is collected by measuring instruments. Massive information is retrieved in real-time and/or spatially-referenced, hence producing new kind of data: functional data. Statistical inference for functional data is particularly challenging as it is an extreme case of high-dimensional data for which, no matter how large the sample is, information will always be insufficient to fully characterize the underlying model.
In detail, after a historical excursus over the test statistics introduced for approaching the problem of testing the mean, we provide a generalization of Hotelling s $T^2$ on any functional Hilbert space, naturally dubbed functional Hotelling s $T^2$. We discuss a nonparametric permutational framework that enables statistical testing for the mean function of a population as well as for the difference between the mean functions of two populations. Within this framework, we show how a number of state-of-the-art test statistics can be seen as approximations of functional $T^2$ statistic hereby proposed. |
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02/2015 - 01/26/2015
Menafoglio, A.; Petris, G.
Kriging for Hilbert-space valued random fields: the Operatorial point of view | Abstract | | We develop a comprehensive framework for linear spatial prediction in Hilbert spaces. We explore the problem of Best Linear Unbiased (BLU) prediction in Hilbert spaces through an original point of view, based on a new Operatorial definition of Kriging. We ground our developments on the theory of Gaussian processes in function spaces and on the associated notion of measurable linear transformation. We prove that our new setting allows (a) to derive an explicit solution to the problem of Operatorial Ordinary Kriging, and (b) to establish the relation of our novel predictor with the key concept of conditional expectation of a Gaussian measure. Our new theory is posed as a unifying theory for Kriging, which is shown to include the Kriging predictors proposed in the literature on Functional Data through the notion of finite-dimensional approximations. Our original viewpoint to Kriging offers new relevant insights for the geostatistical analysis of either finite- or infinite-dimensional georeferenced dataset. |
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03/2015 - 01/26/2015
Abramowicz, K.; de Luna, S.; Häger, C.; Pini, A.; Schelin, L.; Vantini, S.
Distribution-Free Interval-Wise Inference for Functional-on-Scalar Linear Models | Abstract | | We introduce a distribution-free procedure for testing a functional-on-scalar linear model with fixed effects.
The procedure does not only test the global hypothesis on all the domain, but also selects the intervals where statistically significant effects are detected.
We prove that the proposed tests are provided with an asymptotic interval-wise control of the family-wise error rate, i.e., the probability of falsely rejecting any interval of true null hypotheses.
The procedure is then applied to one-leg hop data from a study on anterior cruciate ligament injury. We compare knee kinematics of three groups of individuals, taking individual-specific covariates into account. |
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04/2015 - 01/26/2015
Arioli, G.; Gazzola, F.
On a nonlinear nonlocal hyperbolic system modeling suspension bridges | Abstract | | We suggest a new model for the dynamics of a suspension bridge through a system of nonlinear nonlocal hyperbolic differential equations.
The equations are of
second and fourth order in space and describe the behavior of the main components of the bridge: the deck, the sustaining cables and the connecting
hangers. We perform a careful energy balance and we derive the equations from a variational principle. We then prove existence and uniqueness for
the resulting problem. |
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62/2014 - 12/17/2014
Andrà, C.; Parolini, N.; Verani, M.
Using gambling simulators to foster awareness about gambling risks | Abstract | | Stemming from an interest in developing suitable didactical activities to prevent gambling abuse during the school years, this paper explores the use of an Android app that simulates the outcomes of a famous Italian instant lottery. Some features that characterise the phenomenon of gambling abuse are sketchily recalled, the Android app is presented and an example from classroom activities is discussed. We conclude that the simulator support probabilistic thinking and understanding of models about gambling, as traditional random generators do, and also exploits emotional reactions, such as shock, which allow curiosity to emerge and pave the road towards deeper understanding. |
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61/2014 - 12/16/2014
Taffetani, M.; Ciarletta, P.
Elasto-capillarity controls the formation and the morphology of beads-on-string structures in solid fibres | Abstract | | Beads-on-string patterns have been experimentally observed in solid cylinders for a wide range of material properties and structural lengths, from millimetric soft gels to nanometric hard fibres. In this work, we combine theoretical analysis and numerical tools to investigate the formation and the nonlinear dynamics of such beaded structures. We show that this morphological transition is driven by elasto-capillarity, i.e. a complex interplay between the effects of surface tension and bulk elasticity. Unlike buckling or wrinkling, the presence of an axial elongation is found here to favour the onset of fibre beading, in agreement with existing experimental results on electrospun fibres, hydrogels and nerves. Our results also prove that the applied stretch can be used in fabrication techniques to control the morphology of the emerging beads-on-string patterns. Such quantitative predictions open the way to several applications, from tissue engineering to the design of stretchable electronics and the micro-fabrication of functionalized surfaces. |
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57/2014 - 12/12/2014
Giverso, C.; Verani, M.; Ciarletta P.;
Branching instability in expanding bacterial colonies | Abstract | | Self-organization in developing living organisms relies on the capability of cells to duplicate and perform a collective motion inside the surrounding environment.
Chemical and mechanical interactions coordinate such a cooperative behavior, driving the dynamical evolution of the macroscopic system. In this work, we perform an analytical and computational analysis to study pattern formation during the spreading of an initially circular bacterial colony on a Petri dish. The continuous
mathematical model addresses the growth and the chemotactic migration of the living monolayer, together with the diffusion and consumption of nutrients in the agar. The governing equations contain four dimensionless parameters, accounting for the interplay among the chemotactic response, the bacteria-substrate
interaction and the experimental geometry. The spreading colony is found to be always linearly unstable to perturbations of the interface, whilst branching instability arises in finite-element numerical simulations. The typical length-scales of such fingers, which align in the radial direction and later undergo further branching, are controlled by the size parameters of the problem, whilst the emergence of branching is favored if the diffusion is dominant on the chemotaxis. The model is able to predict the experimental morphologies and their dynamical evolution,
confirming that compact (resp. branched) patterns arise for fast (resp. slow) expanding colonies. Such results, while providing new insights on pattern selection in bacterial colonies, may finally have important applications for designing controlled patterns. |
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58/2014 - 12/12/2014
Menafoglio, A.; Secchi, P.; Guadagnini, A.
A Class-Kriging predictor for Functional Compositions with Application to Particle-Size Curves in Heterogeneous Aquifers | Abstract | | We address the problem of characterizing the spatial field of soil particle-size curves (PSCs) within a heterogeneous aquifer system. We conceptualize the medium as a composite system, associated with an uncertain spatial arrangement of geomaterials. We tie the identification of the latter to the spatially varying arrangement of soil textural properties, which is in turn estimated by an available set of observed PSCs. We analyze these PSCs through their particle-size densities (PSDs), which are interpreted as points in the infinite-dimensional Hilbert space of functional compositions (FCs). To model the heterogeneity of the system, we introduce an original hierarchical model for FCs, conducive to a Functional Compositional Class-Kriging (FCCK) predictor. To tackle the problem of lack of information when the spatial arrangement of soil types is unobserved, we propose a novel clustering method for spatially dependent FCs. The latter allows inferring a grouping structure from sampled PSDs, consistent with our theoretical framework. This enables one to project the complete information content embedded in the set of heterogenous PSDs to unsampled locations in the system, thus providing predictions of the spatial arrangement of (a) regions associated with each identified textural class, and (b) the PSDs within each region. Our methodological developments are tested on a field application relying on a set of particle-size curves observed within an alluvial aquifer in the Neckar river valley, in Germany. |
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