The University of Manchester is a public research university in Manchester, England. The main campus is south of Manchester City Centre on Oxford Road. The university owns and operates major cultural assets such as the Manchester Museum, The Whitworth art gallery, the John Rylands Library, the Tabley House Collection and the Jodrell Bank Observatory—a UNESCO World Heritage Site. The University of Manchester is considered a red brick university, a product of the civic university movement of the late 19th century. The current University of Manchester was formed in 2004 following the merger of the University of Manchester Institute of Science and Technology (UMIST) and the Victoria University of Manchester. This followed a century of the two institutions working closely with one another.The University of Manchester Institute of Science and Technology was founded in 1824 as the Mechanics' Institute. The founders believed that all professions somewhat relied on scientific principles. As such, the institute taught working individuals branches of science applicable to their existing occupations. They believed that the practical application of science would encourage innovation and advancements within those trades and professions. The Victoria University of Manchester was founded in 1851, as Owens College. Academic research undertaken by the university would be published via the Manchester University Press from 1904. The University of Manchester is a member of the Russell Group, the N8 Group, and the worldwide Universities Research Association. The University of Manchester, inclusive of its predecessor institutions, has had 25 Nobel laureates amongst its past and present students and staff, the fourth-highest number of any single university in the United Kingdom. In 2020/21, the university had a consolidated income of £1.1 billion, of which £237.0 million was from research grants and contracts (6th place nationally behind Oxford, UCL, Cambridge, Imperial and Edinburgh). It has the fifth-largest endowment of any university in the UK, after the universities of Cambridge, Oxford, Edinburgh and King's College London.
Context: Integrating autonomous and adaptive behavior into software-intensive systems presents significant challenges for software development, as uncertainties in the environment or decision-making processes must be explicitly captured. These challenges are amplified in safety- and mission-critical systems, which must undergo rigorous scrutiny during design and development. Key among these challenges is the difficulty of specifying requirements that use probabilistic constructs to capture the uncertainty affecting these systems. To enable formal analysis, such requirements must be expressed in precise mathematical notations such as probabilistic logics. However, expecting developers to write requirements directly in complex formalisms is unrealistic and highly error-prone. Objective: We extend the structured natural language used by NASA’s Formal Requirement Elicitation Tool (FRET) with support for the specification of unambiguous and correct probabilistic requirements, and develop an automated approach for translating these requirements into logical formulas. Methods: We propose and develop a formal, compositional, and automated approach for translating structured natural-language requirements into formulas in probabilistic temporal logic. To increase trust in our formalizations, we provide assurance that the generated formulas are well-formed and conform to the intended semantics through an automated validation framework and a formal proof. Results: We demonstrate applicability through a comprehensive evaluation using more than 300 requirements from the research literature, public repositories and an industry-led case study. The results of this evaluation show that our approach can successfully specify a wide range of probabilistic requirements, confirming its expressiveness and utility. Conclusion: The extended FRET tool enables developers to specify probabilistic requirements in structured natural language, and to automatically translate them into probabilistic temporal logic, making the formal analysis of autonomous and adaptive systems more practical and less error-prone.
BACKGROUND AND OBJECTIVE:Intellectual disability (ID) is increasingly recognised as a hidden driver of cancer mortality. However, evidence on prostate cancer (PC) care in this population is limited. METHODS:The study population comprised 29 554 men with an ID and 518 739 comparators from the Clinical Practice Research Datalink Aurum database, which is linked to hospital, mortality, and cancer registry data. Poisson and Cox regression analyses were used to estimate incidence rate ratios (IRRs), risk ratios (RRs), and hazard ratios (HRs) with 95% confidence intervals (CIs) for outcomes related to PC presentation, diagnosis, treatment, and survival. KEY FINDINGS AND LIMITATIONS:The ID group presented more frequently with symptoms suggestive of PC (IRR 1.35, 95% CI 1.28-1.43) but were less likely to have a prostate-specific antigen (PSA) test within 90 d (RR 0.66, 95% CI 0.63-0.70). Following detection of elevated PSA, the ID group had fewer referrals (RR 0.83, 95% CI 0.72-0.96), biopsies (RR 0.54, 95% CI 0.41-0.71), and PC diagnoses (RR 0.51, 95% CI 0.41-0.65). The ID group were also more likely to be diagnosed on the date of death (RR 5.96, 95% CI 2.70-11.77), have missing Gleason scores (RR 1.61, 95% CI 1.27-2.01), and present with de novo metastatic PC (RR 1.79, 95% CI 1.15-2.77). Among those with Gleason scores, the rate of clinically significant PC (Gleason ≥7) was comparable between the ID and control groups, while receipt of radical treatment for nonmetastatic PC was slightly lower in the ID group (RR 0.73, 95% CI 0.51-1.00). Men with an ID had twofold higher risk of death from PC following diagnosis (HR 2.11, 95% CI 1.64-2.73). CONCLUSIONS AND CLINICAL IMPLICATIONS:Men with an ID face disparities across the PC care pathway from investigation of relevant symptoms to survival after diagnosis. Targeted interventions are needed to address these inequities.
Mesh-free numerical methods provide flexible discretisations for complex geometries; however, classical meshless discrete differential operators typically trade low computational cost for limited accuracy or high accuracy for substantial per-stencil computation. We introduce a parametrised framework for learning mesh-free discrete differential operators using a graph neural network trained via polynomial moment constraints derived from truncated Taylor expansions. The model maps local stencils relative positions directly to discrete operator weights. The current work demonstrates that neural networks can learn classical polynomial consistency while retaining robustness to irregular neighbourhood geometry. The learned operators depend only on local geometry, are resolution-agnostic, and can be reused across particle configurations and governing equations. We evaluate the framework using standard numerical analysis diagnostics, showing improved accuracy over Smoothed Particle Hydrodynamics, and a favourable accuracy-cost trade-off relative to a representative high-order consistent mesh-free method in the moderate-accuracy regime. Applicability is demonstrated by solving the weakly compressible Navier-Stokes equations using the learned operators.
Activation functions serve as the primary mechanism for introducing nonlinearity into deep learning models, playing an indispensable role in both model training and inference. By incorporating nonlinear transformations, they significantly enhance the representational capacity of neural networks, thereby improving overall model performance, particularly for complex tasks – such as Computer Vision (CV) and Natural Language Processing (NLP). However, most mainstream activation functions suffer from a common limitation: they tend to degenerate into linear-like behaviors when inputs assume extremely large or small values, consequently impairing their ability to model complex, nonlinear relationships across all non-saturated input domains.To address this limitation, this paper proposes a novel Sinusoidal Wave Integration (SWIn) framework. The core innovation lies in superimposing adjusted sinusoidal wave onto the activation function, which ensures that the composite function preserves the original monotonicity and global trend of the base activation function while guaranteeing persistent nonlinear characteristics within all non-plateau regions of the continuous base activation functions.We conducted extensive evaluations comparing standard activation functions with their SWIn-enhanced counterparts on image classification (CIFAR-100 and ImageNet-1K), machine translation (WMT14 DE-EN, CS-EN, RU-EN) tasks. Experimental results demonstrate that the SWIn framework yields significant performance improvements for continuous activation functions such as SiLU, Mish, and GELU. This is attributed to the enriched function representation and improved gradient propagation introduced by the controlled oscillations. In contrast, for inherently non-smooth functions like PReLU and SELU, the SWIn transformation tends to amplify existing gradient discontinuities, resulting in marginal or no performance gains.
