We propose a least-squares penalization as a means to extend the discontinuous Petrov-Galerkin (DPG) method with optimal test functions to a class of semilinear elliptic problems. The nonlinear contributions are replaced with independent unknowns so that standard DPG techniques apply to the then linear problem with non-trivial kernel. The nonlinear relations are added as least-squares constraints. Assuming solvability of the semilinear problem and an Aubin-Nitsche-type approximation property for the primal variable, we prove a Cea estimate for the approximation error in canonical norms. Numerical results with uniform and adaptively refined meshes illustrate the performance of the scheme.
Abstract Dynamic Flux Balance Analysis (DFBA) enables simulation of microbial culture dynamics under changing environmental conditions, but remains computationally expensive for tasks such as parameter calibration and fermentation optimization when applied using genome-scale metabolic models (GEMs). To address this challenge, we introduce Dynamic Flux Vector Balancing (DFVB), a reformulation of DFBA that solves an equivalent problem using a pre-computed, sparse basis of flux solutions that reduces the dimensionality of the internal optimization problem without information loss. Notably, DFVB provides a compact, interpretable representation of flux states that can readily identify dynamically inactive pathways and enable simulation-based automatic metabolic network reduction. We showed that DFVB produces the same culture dynamics as DFBA across multiple model scales and conditions, and identifies inactive reactions more accurately than Flux Variability Analysis (FVA) when compared to transcriptomic data profiles. Furthermore, computational performance analyses demonstrated that integrating DFVB with solver warm-start strategies and model reduction enhances computational efficiency relative to DFBA, yielding up to 3-fold reductions in simulation time for large-scale metabolic models. Finally, kinetic parameter estimation of culture dynamics with DFVB in two fermentation scenarios using a large-scale yeast GEM reached equal or higher prediction fidelity and narrower confidence intervals than DFBA, indicating improved parameter identifiability and robustness. Together, these results position DFVB as a scalable, robust, and biologically coherent framework for dynamic metabolic modeling, easing the integration of GEMs for culture dynamics simulation.
Background Metabolic dysfunction–associated steatotic liver disease (MASLD) is highly prevalent and frequently undiagnosed, despite liver fibrosis being the strongest predictor of liver-related morbidity and mortality. We aimed to quantify Fibrosis-4 (FIB-4) index-based fibrosis risk and to evaluate guideline-recommended follow-up—FIB-4 documentation, confirmatory testing, and specialist referral—in a large US cohort. Methods We conducted a retrospective study of electronic health record data from the US All of Us Research Program. Among adults aged 35 years or older with sufficient laboratory data, FIB-4 scores were calculated from routinely captured biomarkers, classified as low (<1.3), indeterminate (1.3–2.67; 2.0–2.67 if aged ≥65 years), or high risk (>2.67), and described across sociodemographic and metabolic subgroups; associations with incident major adverse liver outcomes (MALO) were assessed with Cox proportional-hazards regression. We examined FIB-4 documentation, confirmatory testing, and specialty referrals within 365 days of the index FIB-4 date. Findings Among 136,004 participants (mean age 60.8 years [SD 13.5]; 79,365 [58.4%] female; 81,420 [59.9%] White, 21,779 [16.0%] Hispanic or Latino, 20,076 [14.8%] Black), 26,971 (19.8%, 95% CI 19.6–20.0) had indeterminate and 11,217 (8.2%, 8.1–8.4) high FIB-4–based fibrosis risk. Elevated risk was more frequent with cardiovascular disease (41.7% vs 25.6%), hypertension (30.7% vs 23.4%), and type 2 diabetes (29.7% vs 27.4%), rising from 25.6% with no metabolic comorbidities to 36.6% with four. FIB-4 documentation was rare, and fewer than 1% of high-risk participants underwent confirmatory testing or referral; referral was low across risk categories (0.19% high, 0.19% indeterminate, 0.25% low risk). MALO occurred in 1308 (11.7%) high-risk vs 830 (0.8%) low-risk participants (adjusted hazard ratio 19.68, 95% CI 17.88–21.67). Interpretation Routinely collected laboratory data identify substantial liver fibrosis risk in this volunteer US cohort, yet guideline-recommended follow-up is uncommon. Implementation strategies such as automated risk calculation and reflex-based testing pathways could reduce missed opportunities for earlier diagnosis and intervention. Funding No specific funding was received for this study.
We consider an elastic model for a circular arch that incorporates membrane, transverse shear, and bending effects. The central line of the arch is partitioned into elements, and an ultra-weak variational formulation is developed alongside a discontinuous Petrov-Galerkin (DPG) approximation procedure based on so-called optimal test functions. The formulation uses discontinuous stress and displacement interpolations on the element mesh, with corresponding interface variables defined at the nodes. Theoretical analysis establishes well-posedness and quasi-optimal convergence properties of the DPG approximation, while also revealing potential error amplification influenced by the curvature of the arch and the imposed boundary conditions. The method is tested on examples with different support configurations. The numerical experiments confirm the theoretical predictions and further demonstrate that the accuracy of the DPG method can be improved by employing a suitably scaled test space norm.
Robotic technologies for on-site construction are advancing rapidly, driven by labour shortages, safety demands, and productivity and sustainability goals. This paper offers a structured scoping review of robotic and automated systems for direct deployment on construction sites and near-site settings. Following the PRISMA-ScR framework, 129 studies were synthesised through a multi-dimensional taxonomy that classifies systems by operational context of deployment, functionality, team composition, and lifecycle stage. Results show a strong concentration in construction-phase task clusters, especially additive manufacturing, discrete assembly/installation, and perception-driven inspection. Multi-robot deployment recurs across the corpus but remains at demonstrator scale, constrained by the difficulty of on-site validation rather than by conceptual appeal, and operation and end-of-life applications remain sparse. Across contexts, adoption is constrained by site variability, integration effort, and safety assurance. Future research priorities include comparable performance and cost reporting, scalable adoption pathways for small and medium-sized enterprises, and lifecycle expansion toward maintenance and deconstruction.
