We present a neural-network-based framework for the solution of three-dimensional boundary value problems where the solution is expressible in terms of harmonic potentials. The approach leverages the Whittaker integral formula, which allows representing the solution through functions that are holomorphic with respect to a suitable complex variable. These functions are subsequently approximated using holomorphic neural networks, which guaranty fulfillment of the holomorphicity requirement. A key feature of the proposed formulation is that the governing partial differential equations (PDEs) are satisfied exactly by construction. Therefore, in contrast to standard physics-informed neural networks, no residual minimization of PDEs is required in the interior of the domain, and training is based exclusively on boundary collocation points. The method is validated against three-dimensional Laplace and linear elasticity problems, where, in the latter case, displacement and stress fields are expressed via the Papkovich-Neuber potentials. The numerical results show an accurate approximation of both scalar and vector fields, with errors remaining controlled throughout the domain. Overall, the work demonstrates that the incorporation of analytical structures into neural network architectures provides a natural and effective framework for the meshless approximation of three-dimensional boundary value problems while preserving the underlying properties of the governing equations.
European coastal waters contain hundreds of thousands to millions of submerged munitions following World Wars I and II. This war legacy poses critical ecological, human health, economic, and security risks through accidental detonations and leakage of toxic substances from corroding munitions, underscoring the urgent need for remediation. We conducted a structured survey of knowledgeable stakeholders to identify their needs, constraints, and priorities for remediating submerged marine munitions. The largest proportion of respondents (50%) were affiliated with Germany-based organizations. Stakeholders reported high concern about the environmental, economic, and security-related impacts of submerged munitions and largely agreed that remediation would provide benefits across these domains. However, they also identified key concerns and barriers to remediation, including unclear institutional responsibilities; permit issuance and bureaucracy; inadequate risk assessment; remediation costs; and safety and security threats. Notably, none of the respondents in the present study preferred Blast in Place (BiP) as a remediation method, despite its historical prevalence, likely reflecting growing awareness of BiP's ecological and security/safety risks. These stakeholder insights provide a timely snapshot that may inform ongoing European policy initiatives, especially the development of the EU Oceans Pact (adopted in 2025) and the drafting of the forthcoming EU Ocean Act. The findings may also guide ongoing EU co-funded projects and the frameworks of regional institutions, such as HELCOM and OSPAR, toward a comprehensive strategy for safe and sustainable remediation of submerged munitions in European coastal waters.
Biological tillage by roots has been proposed as a sustainable strategy for subsoil structural recovery following compaction; however, the potential of perennial grassland mixtures remains insufficiently quantified. This study evaluated two well-established perennial grassland mixtures (three vs twelve species) using field-incubated ingrowth soil cores. Two root-contact conditions were imposed: direct root contact (DCR; roots allowed into cores) and isolated root contact (ICR; roots excluded by mesh). X-ray & micro;CT was used to analyze the total CTdetectable pore space (CTtotal) and vertically continuous biopores (VCBio), before and after incubation. Following incubation, soil physical characteristics, root intensity, arbuscular mycorrhizal fungi (AMF) biomarkers (PLFA and NLFA C16:1 omega 5), and glomalin-related soil protein (GRSP-EE) were measured, followed by destructive assessment of structural quality. VCBio was more sensitive to root-induced structural changes than CTtotal. In DCR twelve-species mixture, macroporosity (mvrel) and macropore length density (rho L) derived from VCBio increased with incubation by 39% and 52%, respectively, while total macropore volume (mvCT) within the 0.24-0.5 mm diameter class increased 2.50 times with incubation. No significant increases in mvrel, rho L, mvCT from CTtotal were found. The DCR twelve-species mixture exhibited greater increases in CT-derived parameters than the DCR three-species mixture, indicating stronger biological subsoiling potential. This coincided with higher concentrations of AMF biomarkers PLFA and NLFA than all other treatments. Air-filled porosity and visual structural quality showed significant treatment effects. These results indicate that early subsoil recovery under perennial grassland mixtures is driven by changes in VCBio, with AMF biomarkers and soil physical characteristics responding at different rates.
Balanced incomplete block designs (BIBDs) underpin Case 1 Best–Worst Scaling (BWS; MaxDiff) and are widely used to elicit preference structures. This study introduces and evaluates performance indices to guide the selection of BIBDs for consumer research applications. Two key aspects are examined: (i) design quality, assessed via the stability of the theoretical maximum error variance (ErrVarTMAX), and (ii) item discrimination, captured through two novel indices—the Global Discrimination Index (GDI) and Pairwise Discrimination Index (PDI). Using simulations based on perfectly consistent respondents, 32 systematically varied and 11 additional BIBDs were analysed to isolate the effects of structural design parameters, including the number of items, set size, and pairwise co-occurrence. Results show that ErrVarTMAX stability is not guaranteed and is primarily influenced by the relationship between the number of items and set size, with smaller sets (k = 3) generally yielding stable designs. Item discrimination was strongly driven by set size, with smaller sets producing greater dispersion in item B–W scores and, thus, stronger discrimination. Comparisons with empirical consumer data from 11 studies revealed substantial compression in observed B–W scores relative to theoretical maxima, although meaningful discrimination was retained. The findings demonstrate that BIBD structure directly shapes both theoretical and empirical performance in Case 1 BWS studies. Practical recommendations are provided to support design selection aligned with study objectives, particularly regarding trade-offs between design stability and item discrimination. A flow chart for selecting BIBDs for use in Case 1 BWS consumer research is introduced.
The gap between nutritional knowledge and dietary behaviour remains poorly understood, yet may partly reflect systematic biases in how individuals evaluate food and assess their own nutritional judgements. Here, we introduce the MetaBites task, a novel two-alternative forced-choice paradigm in which 32 healthy volunteers compared foods on either caloric density or nutritional quality, quantified using the Nutrient-Rich Foods (NRF) 9.3 index, under adaptive difficulty control. Participants provided both trial-level and block-level confidence ratings, enabling assessment of metacognitive monitoring across multiple levels. Task validity was confirmed through staircase convergence, a clear speed-accuracy trade-off, and higher confidence in correct relative to incorrect trials. Results revealed a consistent dissociation across conditions: participants showed higher objective performance when judging nutritional quality, yet reported significantly higher confidence and greater metacognitive efficiency for calorie judgements. Global confidence decreased significantly in the NRF condition but remained stable for calorie judgements. Furthermore, familiarity with food items biased choice behaviour in opposing directions across conditions, consistent with a tendency to perceive familiar foods as more nutritious and less calorie-dense. These findings indicate that metacognitive monitoring in nutritional judgements is not a straightforward readout of objective performance, and that domain familiarity modulates choice behaviour. The MetaBites task offers a promising tool for investigating metacognitive contributions to nutritional decision-making in both healthy and clinical populations.
