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

Adolescent Cardiovascular Fitness Changes One Year Post Gastric-Band Surgery

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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

Adolescent Strength and Body Composition Changes One Year Post Gastric-Band Surgery

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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

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

Cholesterol derivatives make large part of the lipids from epidermal molts of the desert-adapted Gila monster lizard (Heloderma suspectum)

In order to understand the cutaneous water loss in the desert-adapted and venomous lizard Heloderma suspectum, the microscopic structure and lipid composition of epidermal molts have been examined using microscopic, spectroscopic and chemical analysis techniques. The molt is formed by a variably thick, superficial beta-layer, an extensive mesos-region and few alpha-cells in its lowermost layers. The beta-layer contains most corneous beta proteins while the mesos-region is much richer in lipids. The proteins in the mesos-region are more unstructured than those located in the beta-layer. Most interestingly, among other lipids, high contents of cholesteryl-β-glucoside and cholesteryl sulfate were detected, molecules absent or present in traces in other species of squamates. These cholesterol derivatives may be involved in the stabilization and compaction of the mesos-region, but present a limited permeability to water movements. The modest resistance to cutaneous water-loss of this species is compensated by adopting other physiological strategies to limit thermal damage and water transpiration as previous eco-physiological studies have indicated. The increase of steroid derivatives may also be implicated in the heat shock response, influencing the relative behavior in this desert-adapted lizard

Neurite Orientation Dispersion and Density Imaging Color Maps to Characterize Brain Diffusion in Neurologic Disorders

Purpose: Neurite orientation dispersion and density imaging (NODDI) has recently been developed to overcome diffusion technique limitations in modeling biological systems. This manuscript reports a preliminary investigation into the use of a single color-coded map to represent NODDI-derived information. Materials and methods: An optimized diffusion-weighted imaging protocol was acquired in several clinical neurological contexts including demyelinating disease, neoplastic process, stroke, and toxic/metabolic disease. The NODDI model was fitted to the diffusion datasets. NODDI is based on a three-compartment diffusion model and provides maps that quantify the contributions to the total diffusion signal in each voxel. The NODDI compartment maps were combined into a single 4-dimensional volume visualized as RGB image (red for anisotropic Gaussian diffusion, green for non-Gaussian anisotropic diffusion, and blue for isotropic Gaussian diffusion), in which the relative contributions of the different microstructural compartments can be easily appreciated. Results: The NODDI color maps better describe the heterogeneity of neoplastic as well inflammatory lesions by identifying different tissue components within areas apparently homogeneous on conventional imaging. Moreover, NODDI color maps seem to be useful for identifying vasogenic edema differently from tumor-infiltrated edema. In multiple sclerosis, the NODDI color maps enable a visual assessment of the underlying microstructural changes, possibly highlighting an increased inflammatory component, within lesions and potentially in normal-appearing white matter. Conclusion: The NODDI color maps could make this technique valuable in a clinical setting, providing comprehensive and accessible information in normal and pathological brain tissues in different neurological pathologies

A Plant Bioreactor for the Synthesis of Carbon Nanotube Bionic Nanocomposites

Bionic composites are an emerging class of materials produced exploiting living organisms as reactors to include synthetic functional materials in their native and highly performing structures. In this work, single wall carboxylated carbon nanotubes (SWCNT-COOH) were incorporated within the roots of living plants of Arabidopsis thaliana. This biogenic synthetic route produced a bionic composite material made of root components and SWCNT-COOH. The synthesis was possible exploiting the transport processes existing in the plant roots. Scanning electrochemical microscopy (SECM) measurements showed that SWCNT-COOH entered the vascular bundles of A. thaliana roots localizing within xylem vessels. SWCNT-COOH preserved their electrical properties when embedded inside the root matrix, both at a microscopic level and a macroscopic level, and did not significantly affect the mechanical properties of A. thaliana roots