Adaptive refinement in advection–diffusion problems by anomaly detection: A numerical study

We consider advection–diffusion–reaction problems, where the advective or the reactive term is dominating with respect to the diffusive term. The solutions of these problems are character-ized by the so-called layers, which represent localized regions where the gradients of the solutions are rather large or are subjected to abrupt changes. In order to improve the accuracy of the computed solution, it is fundamental to locally increase the number of degrees of freedom by limiting the computational costs. Thus, adaptive refinement, by a posteriori error estimators, is employed. The error estimators are then processed by an anomaly detection algorithm in order to identify those regions of the computational domain that should be marked and, hence, refined. The anomaly detection task is performed in an unsupervised fashion and the proposed strategy is tested on typical benchmarks. The present work shows a numerical study that highlights promising results obtained by bridging together standard techniques, i.e., the error estimators, and approaches typical of machine learning and artificial intelligence, such as the anomaly detection task

Cubature rules based on bivariate spline quasi-interpolation for weakly singular integrals

In this paper we present a new class of cubature rules with the aim of accurately integrating weakly singular double integrals. In particular we focus on those integrals coming from the discretization of Boundary Integral Equations for 3D Laplace boundary value problems, using a collocation method within the Isogeometric Analysis paradigm. In such setting the regular part of the integrand can be defined as the product of a tensor product B-spline and a general function. The rules are derived by using first the spline quasi-interpolation approach to approximate such function and then the extension of a well known algorithm for spline product to the bivariate setting. In this way efficiency is ensured, since the locality of any spline quasi-interpolation scheme is combined with the capability of an ad--hoc treatment of the B-spline factor. The numerical integration is performed on the whole support of the B-spline factor by exploiting inter-element continuity of the integrand

Splines Parameterization of Planar Domains by Physics-Informed Neural Networks

The generation of structured grids on bounded domains is a crucial issue in the development of numerical models for solving differential problems. In particular, the representation of the given computational domain through a regular parameterization allows us to define a univalent mapping, which can be computed as the solution of an elliptic problem, equipped with suitable Dirichlet boundary conditions. In recent years, Physics-Informed Neural Networks (PINNs) have been proved to be a powerful tool to compute the solution of Partial Differential Equations (PDEs) replacing standard numerical models, based on Finite Element Methods and Finite Differences, with deep neural networks; PINNs can be used for predicting the values on simulation grids of different resolutions without the need to be retrained. In this work, we exploit the PINN model in order to solve the PDE associated to the differential problem of the parameterization on both convex and non-convex planar domains, for which the describing PDE is known. The final continuous model is then provided by applying a Hermite type quasi-interpolation operator, which can guarantee the desired smoothness of the sought parameterization. Finally, some numerical examples are presented, which show that the PINNs-based approach is robust. Indeed, the produced mapping does not exhibit folding or self-intersection at the interior of the domain and, also, for highly non convex shapes, despite few faulty points near the boundaries, has better shape-measures, e.g., lower values of the Winslow functional

Leveraging colour-based pseudo-labels to supervise saliency detection in hyperspectral image datasets

Saliency detection mimics the natural visual attention mechanism that identifies an imagery region to be salient when it attracts visual attention more than the background. This image analysis task covers many important applications in several fields such as military science, ocean research, resources exploration, disaster and land-use monitoring tasks. Despite hundreds of models have been proposed for saliency detection in colour images, there is still a large room for improving saliency detection performances in hyperspectral imaging analysis. In the present study, an ensemble learning methodology for saliency detection in hyperspectral imagery datasets is presented. It enhances saliency assignments yielded through a robust colour-based technique with new saliency information extracted by taking advantage of the abundance of spectral information on multiple hyperspectral images. The experiments performed with the proposed methodology provide encouraging results, also compared to several competitors

IgA-BEM for 3D Helmholtz problems using conforming and non-conforming multi-patch discretizations and B-spline tailored numerical integration

An Isogeometric Boundary Element Method (IgA-BEM) is considered for the numerical solution of Helmholtz problems on 3D bounded or unbounded domains, admitting a smooth multi-patch representation of their finite boundary surface. The discretization spaces are formed by C0 inter-patch continuous functional spaces whose restriction to a patch simplifies to the span of tensor product B-splines composed with the given patch NURBS parameterization. Both conforming and non-conforming spaces are allowed, so that local refinement is possible at the patch level. For regular and singular integration, the proposed model utilizes a numerical procedure defined on the support of each trial B-spline function, which makes possible a function-by-function implementation of the matrix assembly phase. Spline quasi-interpolation is the common ingredient of all the considered quadrature rules; in the singular case it is combined with a B-spline recursion over the spline degree and with a singularity extraction technique, extended to the multi-patch setting for the first time. A threshold selection strategy is proposed to automatically distinguish between nearly singular and regular integrals. The non-conforming C0 joints between spline spaces on different patches are implemented as linear constraints based on knot removal conditions, and do not require a hierarchical master-slave relation between neighbouring patches. Numerical examples on relevant benchmarks show that the expected convergence orders are achieved with uniform discretization and a small number of uniformly spaced quadrature nodes

Integrating diffusion tensor imaging and neurite orientation dispersion and density imaging to improve the predictive capabilities of CED models

This paper aims to develop a comprehensive and subject-specific model to predict the drug reach in Convection-Enhanced Delivery (CED) interventions. To this end, we make use of an advance diffusion imaging technique, namely the Neurite Orientation Dispersion and Density Imaging (NODDI), to incorporate a more precise description of the brain microstructure into predictive computational models. The NODDI dataset is used to obtain a voxel-based quantification of the extracellular space volume fraction that we relate to the white matter (WM) permeability. Since the WM can be considered as a transversally isotropic porous medium, two equations, respectively for permeability parallel and perpendicular to the axons, are derived from a numerical analysis on a simplified geometrical model that reproduces flow through fibre bundles. This is followed by the simulation of the injection of a drug in a WM area of the brain and direct comparison of the outcomes of our results with a state-of-the-art model, which uses conventional diffusion tensor imaging. We demonstrate the relevance of the work by showing the impact of our newly derived permeability tensor on the predicted drug distribution, which differs significantly from the alternative model in terms of distribution shape, concentration profile and infusion linear penetration length

Novel Reconstruction Errors for Saliency Detection in Hyperspectral Images

When hyperspectral images are analyzed, a big amount of data, representing the reflectance at hundreds of wavelengths, needs to be processed. Hence, dimensionality reduction techniques are used to discard unnecessary information. In order to detect the so called “saliency”, i.e., the relevant pixels, we propose a bottom-up approach based on three main ingredients: sparse non negative matrix factorization (SNMF), spatial and spectral functions to measure the reconstruction error between the input image and the reconstructed one and a final clustering technique. We introduce novel error functions and show some useful mathematical properties. The method is validated on hyperspectral images and compared with state-of-the-art different approaches

Analysis of MUM1/IRF4 Protein Expression Using Tissue Microarrays and Immunohistochemistry

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Functional MR Imaging Correlates of Neuropsychological Impairment in Primary-Progressive Multiple Sclerosis

BACKGROUND AND PURPOSE: Cognitive deficits affect ≤30% of patients with PPMS. We investigated the functional correlates of cognitive network dysfunction in patients with PPMS and their correlation with the extent of structural MR imaging damage. MATERIALS AND METHODS: From 16 right-handed patients with PPMS and 17 matched controls, structural and fMRIs (during the performance of the 2-back task) were acquired. Neuropsychological tests exploring memory, attention, and frontal lobe cognitive domains were administered. T2 LL, NBV, and CC areas were measured. RESULTS: Six patients with PPMS were CI. Structural MR imaging measures did not differ between patients who were CI and those who were CP. Compared with patients who were CI, patients who were CP had increased activations of the left caudate nucleus, PFC, and inferior parietal lobule. Compared with controls and patients who were CP, patients who were CI had increased activations of the SII, cerebellum, and insula. Compared with controls, they also had increased activations of the right precentral gyrus and a reduced recruitment of the left PFC. In patients with PPMS, a decreased composite cognitive score correlated with increased activity of the cerebellum, insula, and SII, as well as decreased PFC activity. T2 LL correlated with decreased PFC recruitment and increased SII recruitment. CONCLUSIONS: In PPMS, an increased recruitment of cognitive-related networks might represent a functional reserve with the potential to limit the severity of cognitive impairment. The accumulation of T2 lesions and the consequent exhaustion of frontal lobe plasticity might contribute to cognitive impairment in PPMS