A static memory sparse spectral method for time-fractional PDEs in arbitrary dimensions

We introduce a method which provides accurate numerical solutions to fractional-in-time partial differential equations posed on $[0,T] \times \Omega$ with $\Omega \subset \mathbb{R}^d$ without the excessive memory requirements associated with the nonlocal fractional derivative operator operator. Our approach combines recent advances in the development and utilization of multivariate sparse spectral methods as well as fast methods for the computation of Gauss quadrature nodes with recursive non-classical methods for the Caputo fractional derivative of general fractional order $\alpha > 0$. An attractive feature of the method is that it has minimal theoretical overhead when using it on any domain $\Omega$ on which an orthogonal polynomial basis is already available. We discuss the memory requirements of the method, present several numerical experiments demonstrating the method's performance in solving time-fractional PDEs on intervals, triangles and disks and derive error bounds which suggest sensible convergence strategies. As an important model problem for this approach we consider a type of wave equation with time-fractional dampening related to acoustic waves in viscoelastic media with applications in the physics of medical ultrasound and outline future research steps required to use such methods for the reverse problem of image reconstruction from sensor data.Comment: 28 pages, 13 figure

Explicit fractional Laplacians and Riesz potentials of classical functions

We prove and collect numerous explicit and computable results for the fractional Laplacian $(-\Delta)^s f(x)$ with $s>0$ as well as its whole space inverse, the Riesz potential, $(-\Delta)^{-s}f(x)$ with $s\in\left(0,\frac{1}{2}\right)$. Choices of $f(x)$ include weighted classical orthogonal polynomials such as the Legendre, Chebyshev, Jacobi, Laguerre and Hermite polynomials, or first and second kind Bessel functions with or without sinusoid weights. Some higher dimensional fractional Laplacians and Riesz potentials of generalized Zernike polynomials on the unit ball and its complement as well as whole space generalized Laguerre polynomials are also discussed. The aim of this paper is to aid in the continued development of numerical methods for problems involving the fractional Laplacian or the Riesz potential in bounded and unbounded domains -- both directly by providing useful basis or frame functions for spectral method approaches and indirectly by providing accessible ways to construct computable toy problems on which to test new numerical methods.Comment: 37 pages, 7 tables, 2 figure

Downscaling of a Three-Dimensional Alveolar In Vitro Model for High-Throughput Screening of Inhalable Respiratory Sensitizers in the Food Industry

Allergic diseases represent an increasing global health problem, among which food and respiratory allergies play an important part. Inhalation of sensitizers from food sources primes the immune system for an exacerbated response upon subsequent exposure via the ingestion route. With the increasing emergence of novel food additives and proteins and growing morbidity in both food and respiratory allergies, the hazard assessment of the allergenicity of food components is of paramount importance. A three-dimensional (3D) alveolar in vitro model for respiratory sensitization prediction was downscaled from the 6- to the 24-well plate insert format, to meet the industry’s high-throughput (HTS) screening requirements. The resemblance of the cellular architecture of the downscaled model to the alveolar region of the lung was evaluated through microscopy techniques and the functionality of the in vitro model was assessed following air-liquid interface (ALI) exposure to ammonium persulfate (APS). The model represents a promising in vitro tool to screen for the respiratory sensitization potential of food components in a fast and reliable approach

Third Virtual Summer School 3Rs for ONE Science: Alternative methods: From complexity to predictivity

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Risk Governance of Emerging Technologies Demonstrated in Terms of its Applicability to Nanomaterials

Nanotechnologies have reached maturity and market penetration that require nano-specific changes in legislation and harmonization among legislation domains, such as the amendments to REACH for nanomaterials (NMs) which came into force in 2020. Thus, an assessment of the components and regulatory boundaries of NMs risk governance is timely, alongside related methods and tools, as part of the global efforts to optimise nanosafety and integrate it into product design processes, via Safe(r)-by-Design (SbD) concepts. This paper provides an overview of the state-of-the-art regarding risk governance of NMs and lays out the theoretical basis for the development and implementation of an effective, trustworthy and transparent risk governance framework for NMs. The proposed framework enables continuous integration of the evolving state of the science, leverages best practice from contiguous disciplines and facilitates responsive re-thinking of nanosafety governance to meet future needs. To achieve and operationalise such framework, a science-based Risk Governance Council (RGC) for NMs is being developed. The framework will provide a toolkit for independent NMs' risk governance and integrates needs and views of stakeholders. An extension of this framework to relevant advanced materials and emerging technologies is also envisaged, in view of future foundations of risk research in Europe and globally

Fish consumption patterns and hair mercury levels in children and their mothers in 17 EU countries

The toxicity of methylmercury (MeHg) in humans is well established and the main source of exposure is via the consumption of large marine fish and mammals. Of particular concern are the potential neurodevelopmental effects of early life exposure to low-levels of MeHg. Therefore, it is important that pregnant women, children and women of childbearing age are, as far as possible, protected from MeHg exposure.Within the European project DEMOCOPHES, we have analyzed mercury (Hg) in hair in 1799 mother–child pairs from 17 European countries using a strictly harmonized protocol for mercury analysis. Parallel, harmonized questionnaires on dietary habits provided information on consumption patterns of fish and marine products. After hierarchical cluster analysis of consumption habits of the mother–child pairs, the DEMOCOPHES cohort can be classified into two branches of approximately similar size: one with high fish consumption (H) and another with low consumption (L). All countries have representatives in both branches, but Belgium, Denmark, Spain, Portugal and Sweden have twice as many or more mother–child pairs in H than in L. For Switzerland, Czech Republic, Hungary, Poland, Romania, Slovenia and Slovakia the situation is the opposite, with more representatives in L than H.There is a strong correlation (r=0.72) in hair mercury concentration between the mother and child in the same family, which indicates that they have a similar exposure situation. The clustering of mother–child pairs on basis of their fish consumption revealed some interesting patterns. One is that for the same sea fish consumption, other food items of marine origin, like seafood products or shellfish, contribute significantly to the mercury levels in hair. We conclude that additional studies are needed to assess and quantify exposure to mercury from seafood products, in particular. The cluster analysis also showed that 95% of mothers who consume once per week fish only, and no other marine products, have mercury levels 0.55 µg/g. Thus, the 95th percentile of the distribution in this group is only around half the US-EPA recommended threshold of 1 µg/g mercury in hair. Consumption of freshwater fish played a minor role in contributing to mercury exposure in the studied cohort.The DEMOCOPHES data shows that there are significant differences in MeHg exposure across the EU and that exposure is highly correlated with consumption of fish and marine products. Fish and marine products are key components of a healthy human diet and are important both traditionally and culturally in many parts of Europe. Therefore, the communication of the potential risks of mercury exposure needs to be carefully balanced to take into account traditional and cultural values as well as the potential health benefits from fish consumption. European harmonized human biomonitoring programs provide an additional dimension to national HMB programs and can assist national authorities to tailor mitigation and adaptation strategies (dietary advice, risk communication, etc.) to their country’s specific requirements