1,720,980 research outputs found
An algorithm for locally adaptive bivariate penalized splines
No full textThis paper introduces a penalized spline model for bivariate smoothing that locally adjusts to gridded data set affected by noise varying across different areas of the domain. As for all penalized spline methods, the approach requires the definition of suitable penalty terms and the selection of the regularization parameters. In our model, the regularization parameters are chosen anisotropically using a data-driven approach that adapts the roughness amount to the noise level. The proposed approach alternates the construction of univariate penalized spline based on B-spline basis functions along both coordinates, and uses a tensor product structure to capture interactions between the two dimensions. Numerical experiments confirm the efficacy of the approach, the anisotropy of the model, and the ability to locally adapt the amount of regression to different noise levels in different areas. The model is compared with two state-of-the-art smoothers, for which we also provide an original reformulation highlighting their construction as penalized splines
An analytical model for carrier-facilitated solute transport in weakly heterogeneous porous media
Full text linkCarrier-facilitated solute transport in heterogeneous aquifers is studied within a Lagrangian framework. Dissolved solutes and carriers are advected by steady random groundwater flow, which is modeled by Darcy’s law with uncertain hydraulic conductivity that is treated as a stationary random space function. We derive general expressions for the spatial mo- ments of the dissolved concentration and the concentration associated with the carrier phase. In order to reduce the computational effort, we use previously derived solutions for the flow field. This enables us to obtain closed-form solutions for the spatial moments of the two concentration fields. The mass and center of gravity of the two propagat- ing plumes depend only on the mean velocity field and chemical/degradation processes. The higher (second and third) moments are affected by the coupling between reactions (sorption/desorption and degradation) among the three phases (i.e., dissolved, carrier and sorbed concentrations) and the aquifer’s heterogeneity. We investigate the potentially en- hancing effect of carriers by comparing spatial moments of the two propagating plumes. The forward/backward mass transfer rates between the liquid and carrier phases, and the degradation coefficients are identified as critical parameters. The carrier’s role is most prominent when detachment from carrier sites is slow, provided that degradation on the carriers is smaller than that in the liquid phase
A Hermite spline model for data regression
No full textThis paper introduces a novel Hermite spline model for data regression, integrating both function values and derivatives along with a penalty term to control smoothness. A comparative analysis is conducted with conventional penalized models, specifically with P-spline models. The primary objective of this study is to empirically demonstrate the superior performance of the proposed model in reconstructing data, even in the absence of a penalty term (pure regression)
Adaptive Generalized P-Splines for Functional Data: A Statistical Framework via Blockwise GSVD
No full textIn this work, we introduce a novel approach for functional data approximation based on generalized P-splines with non-uniform and adaptively placed knots. The key innovation of our proposal is the integration of a conditioning-aware strategy for selecting both the number and positions of the knots, as well as the regularization parameters. By reformulating the Tikhonov regularization problem, we propose a computationally efficient criterion that controls model complexity while ensuring numerical stability. The resulting approximation framework not only improves the fit across the entire functional domain but also maintains compactness and robustness. Extensive numerical experiments conducted on both synthetic and real-world datasets demonstrate that our approach significantly outperforms traditional free knot and smoothing spline methods in terms of approximation error and conditioning
ReLaTIve: an Ansi C software package for the Real Laplace Transform Inversion
No full textsoftware package della libreria NUMERALGO di Numerical Algorith
Instantaneous Frequency Estimation via Spectrogram Projection and P-Spline Approximation
No full textFrequency Modulated (FM) signals are usually characterized by two or more components having different waveforms and time-dependent frequencies. The estimation of the instantaneous frequency (IF) represents a very challenging topic when there are two or more interfering components. In this case, available approaches, like the reassignment-based ones, fail in correspondence to the interference region, where IFs of each individual mode are not far enough to be considered separable. In this paper, a novel approach for IF estimation based on spectrogram analysis is proposed. Firstly, it is proved that the projection of signal spectrogram on the temporal axis is itself an amplitude and frequency modulated signal. Its IF depends on the instantaneous frequencies of the individual signal components and the functional dependence can be explicitely given. Then, under proper assumptions, a regression method for the individual IFs estimation is provided using a few selected 'good' points lying in the interference region. The regression method benefits from a penalized-spline (P-spline) model where a second-order discrete penalty term is also used. Experimental results show that the proposed model is very effective to estimate the individual IFs of multicomponent FM signals in the interference region, making it a suitable method for correcting reassignment estimation where the separability condition is not satisfied
An algorithm for a constrained P-spline
No full textRegression splines are largely used to investigate and predict data behavior, attracting the interest of mathematicians for their beautiful numerical properties, and of statisticians for their versatility with respect to the applications. Several penalized spline regression models are available in the literature, and the most commonly used ones in real-world applications are P-splines, which enjoy the advantages of penalized models while being easy to generalize across different functional spaces and higher degree order, because of their discrete penalty term. To face the different requirements imposed by the nature of the problem or the physical meaning of the expected values, the P-spline definition is often modified by additional hypotheses, often translated into constraints on the solution or its derivatives. In this framework, our work is motivated by the aim of getting approximation models that fall within pre-established thresholds. Specifically, starting from a set of observed data, we consider a P-spline constrained between some prefixed bounds. In our paper, we just consider 0 as lower bound, although our approach applies to more general cases. We propose to get nonnegativity by imposing lower bounds on selected sample points. The spline can be computed through a sequence of linearly constrained problems. We suggest a strategy to dynamically select the sample points, to avoid extremely dense sampling, and therefore try to reduce as much as possible the computational burden. We show through some computational experiments the reliability of our approach and the accuracy of the results compared to some state-of-the-art models
Erratum to: ReLaTIve. An Ansi C90 software package for the Real Laplace Transform Inversion
No full textA software package for numerical inversion of Laplace transforms computable everywhere on the real axis is described. Besides the function to invert the user has only to provide the numerical value (even if it is an approximate value) of the abscissa of convergence and the accuracy required for the inverse function. The software provides a controlled accuracy, i.e. it dynamically computes the so-called maximum attainable accuracy such that numerical results are provided within the greatest value between the user’s required accuracy and the maximum attainable accuracy. This is done because the intrinsic ill posedness of the real inversion problem sometime may prevent to reach the desired accuracy. The method implemented is based on a Laguerre polynomial series expansion of the inverse function and belongs to the class of polynomial-type methods of inversion of the Laplace transform, formally characterized as Collocation methods (C-methods)
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