Molecular subtyping of breast cancer serves as a cornerstone for personalised diagnosis and therapeutic monitoring; nevertheless, the deployment of advanced deep learning models is often hindered by the lack of accurate tumour segmentations in extensive datasets and the intrinsic class imbalance among molecular subtypes, particularly the under-representation of the HER2-enriched subtype in public archives. This study introduces a comprehensive and practical pipeline for characterising breast cancer phenotypes, effectively addressing these challenges. We have collected publicly accessible images belonging to breast cancer from different datasets using magnetic resonance imaging, encompassing categorised molecular subtypes, with or without manual tumour segmentations.Using a 3D Convolutional Neural Network (3D CNN) model trained exclusively on the Duke Breast Cancer MRI dataset, which contains bounding box annotations and molecular subtypes, we developed a robust classifier. To extend our analysis to data without annotations, we applied a Faster R-CNN model, pre-trained on the same Duke dataset, to generate lesion detections in the remaining multicentric datasets. From these, we strategically selected a balanced subset of 200 cases (50 for each phenotype: Luminal A, Luminal B, HER2-enriched and Triple-Negative), based on the highest detection confidence, thus solving the class imbalance problem and ensuring equitable representation of all subtypes for rigorous testing of our classifier. The final validation was performed on an independent clinical dataset from a public hospital in Setúbal, Portugal, where the model demonstrated strong discriminative performance with AUC-ROC values ranging from 0.8786 to 0.9825 across the four molecular subtypes, providing promising evidence of cross-institutional generalisation under a pronounced subtype prior shift between the North American training distribution and the Portuguese evaluation cohort. This work, complemented by a data anonymisation system and close collaboration with clinical specialists, establishes a scalable and effective methodology for precision radiogenomics that simultaneously overcomes the challenges of data imbalance and the absence of detailed annotations. Further multi-site prospective validation on larger and ethnically diverse cohorts is required before clinical deployment.
River-crossing bridges in seismic regions are increasingly exposed to flood-induced scouring and earthquake shaking during their service life. Although vertical ground motions are known to affect the response of bridge structures, the specific interactions with the boundary condition changes introduced by flood-induced scour have not been studied sufficiently. In this study, a probabilistic fragility assessment framework for scoured bridges is developed by comparing the cases of coupled horizontal and vertical excitations with those of horizontal-only excitations. A three-dimensional nonlinear finite element model with soil–structure interaction is established in OpenSees, and probabilistic seismic demand models are constructed using paired horizontal and vertical records across multiple scour depths. The results indicate that considering the vertical component generally increases the estimated seismic fragility, with effects that depend on the PGA level, scour depth, and damage state. Under slight and moderate damage conditions, coupled excitations produce only marginal alterations in fragility, suggesting that horizontal excitations primarily influence damage initiation. At higher damage levels, the effect of vertical excitations is more pronounced because of the acceleration of post-yield stiffness and strength degradation, thereby increasing the deformation demand for a given PGA. In the case of deep scouring, the mechanism is amplified, thereby making this effect even more significant. Record-to-record variability also governs the vertical contribution, indicating that constant vertical scaling rules may underestimate the tail behavior relevant to the reliability. Overall, omitting vertical excitation can lead to non-conservative estimates of the exceedance probability for scoured bridges, particularly after the initial yielding. The framework supports the explicit consideration of coupled horizontal and vertical excitations when assessing the vulnerability of scoured bridges in multi-hazard environments.
This paper investigates the Lateral-Torsional Buckling (LTB) resistance of continuous hot-rolled steel I-beams with localized cross-sectional damage. Due to the alternating sagging and hogging moment regions, continuous beams exhibit spatially varying compression flanges and buckling mechanisms that differ fundamentally from those of simply supported beams. An integrated experimental-numerical program was conducted. Six continuous beam specimens with bottom flange loss, web openings, and combined defects were tested under four-point bending. Initial geometric imperfections were measured to establish maximum out-of-straightness amplitudes, which were subsequently used to scale the first elastic buckling mode shape in the finite element models. A large-scale parametric study involving numerous simulations was then developed to assess the effects of damage location, beam slenderness, damage severity, and sectional thickness reduction. The results reveal that the beam's capacity is most sensitive to defects located in high-bending-moment regions. A significant “slenderness convergence effect” was observed, where short beams exhibited severe capacity reduction (approximately 42%) dominated by cross-sectional yielding, while slender beams were less sensitive due to global elastic buckling governance. Based on these findings, simplified design formulas for the load reduction factor βL are proposed following a lower-bound envelope approach. This method enables the rapid and safe estimation of the residual capacity of locally damaged continuous beams, a scenario that is not currently addressed in existing design standards.
The index of a matrix is a fundamental invariant in the analysis of singular matrices and their generalized inverses. While sharp results are available for block triangular matrices, the corresponding theory for anti-triangular block matrices is less developed. In this paper, we study matrices of the formM=[ABC0],under algebraic constraints on the blocks.Building on additive decompositions involving von Neumann inverses, we relate the index of M to invariance properties of the index and minimal polynomial of expressions of the form A2A−+I−AA−, where A− is any von Neumann inverse of A. This connection provides an effective mechanism to control the index of M through suitable factorizations and associated block products.As a consequence, we derive explicit lower and upper bounds for the index of M in terms of the index of A and of BC, and characterize situations in which these bounds are attained. Under additional annihilation or orthogonality conditions on the blocks, we obtain closed-form representations for the Drazin inverse of M. Applications to adjacency matrices of directed graphs illustrate the sharpness of the bounds and the applicability of the results to structured matrices arising in graph-theoretic settings.
The increasing reuse of greywater in decentralised systems requires disinfectant formulations capable of providing both rapid antimicrobial action and sustained residual activity under variable operational conditions. This study systematically evaluated physicochemical stability and antimicrobial performance of a ready-to-use gel-based disinfectant formulation (PipeUCare) containing hydrogen peroxide, chlorhexidine and ethanol. Accelerated ageing studies (54 °C for 14 days and 30 °C for 6 weeks) were conducted alongside real-time ageing over 24 months to assess long-term stability within a reduced experimental timeframe. Physicochemical parameters, including pH, density and viscosity, were monitored, and the concentrations of the active ingredients were quantified using validated high-performance liquid chromatography (HPLC) methods. The formulation’s antimicrobial activity under study conditions was evaluated against a panel of bacteria, yeasts and filamentous fungi relevant in greywater systems. The results showed that all active ingredients remained within the regulatory acceptance limits defined by the European Chemicals Agency (ECHA), with relative losses of the less than ± 15 % for hydrogen peroxide and chlorhexidine and less than ± 5 % for ethanol. Despite small reductions in the formulation, it maintained broad-spectrum antimicrobial efficacy after both accelerated and long-term ageing. Overall, PipeUCare demonstrates chemical stability and sustained antimicrobial performance, supporting its suitability for long-term use in greywater piping systems.
