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Multigrid Monte Carlo Revisited:Theory and Bayesian Inference
Get PDFGaussian random fields play an important role in many areas of science and engineering. In practice, they are often simulated by sampling from a high-dimensional multivariate normal distribution, which arises from the discretisation of a suitable precision operator. Existing methods such as Cholesky factorization and Gibbs sampling become prohibitively expensive on fine meshes due to their high computational cost. In this work, we revisit the Multigrid Monte Carlo (MGMC) algorithm developed by Goodman & Sokal (Physical Review D 40.6, 1989) in the quantum physics context. To show that MGMC can overcome these issues, we establish a grid-size-independent convergence theory based on the link between linear solvers and samplers for multivariate normal distributions, drawing on standard multigrid convergence theory. We then apply this theory to linear Bayesian inverse problems. This application is achieved by extending the standard multigrid theory to operators with a low-rank perturbation. Moreover, we develop a novel bespoke random smoother which takes care of the low-rank updates that arise in constructing posterior moments. In particular, we prove that Multigrid Monte Carlo is algorithmically optimal in the limit of the grid-size going to zero. Numerical results support our theory, demonstrating that Multigrid Monte Carlo can be significantly more efficient than alternative methods when applied in a Bayesian setting.<br/
Multigrid Monte Carlo Revisited:Theory and Bayesian Inference
Get PDFGaussian random fields play an important role in many areas of science and engineering. In practice, they are often simulated by sampling from a high-dimensional multivariate normal distribution, which arises from the discretisation of a suitable precision operator. Existing methods such as Cholesky factorization and Gibbs sampling become prohibitively expensive on fine meshes due to their high computational cost. In this work, we revisit the Multigrid Monte Carlo (MGMC) algorithm developed by Goodman & Sokal (Physical Review D 40.6, 1989) in the quantum physics context. To show that MGMC can overcome these issues, we establish a grid-size-independent convergence theory based on the link between linear solvers and samplers for multivariate normal distributions, drawing on standard multigrid convergence theory. We then apply this theory to linear Bayesian inverse problems. This application is achieved by extending the standard multigrid theory to operators with a low-rank perturbation. Moreover, we develop a novel bespoke random smoother which takes care of the low-rank updates that arise in constructing posterior moments. In particular, we prove that Multigrid Monte Carlo is algorithmically optimal in the limit of the grid-size going to zero. Numerical results support our theory, demonstrating that Multigrid Monte Carlo can be significantly more efficient than alternative methods when applied in a Bayesian setting.<br/
Slopes of Siegel cusp forms and geometry of compactified Kuga varieties
Get PDFWe study the Kodaira dimension of the compactified n-fold Kuga variety over the moduli space of principally polarised abelian g-folds. We construct a suitable compactification, which we call a Namikawa compactification, and show that in most cases it has canonical singularities. We then use results about the slope of Siegel modular forms to determine the Kodaira dimension for all g>1 and n>0
Slopes of Siegel cusp forms and geometry of compactified Kuga varieties
Get PDFWe study the Kodaira dimension of the compactified n-fold Kuga variety over the moduli space of principally polarised abelian g-folds. We construct a suitable compactification, which we call a Namikawa compactification, and show that in most cases it has canonical singularities. We then use results about the slope of Siegel modular forms to determine the Kodaira dimension for all g>1 and n>0
Experimental assessment of stiffening geometries for thin-walled structural steel plates made by wire arc additive manufacturing
Get PDFAn innovative strategy of imposing geometric sinusoidal waves has been proven effective in enhancing the local buckling resistance of steel plates made by selective laser melting (SLM). However, its efficiency on wire arc additively manufactured (WAAM) steel, which is a more economically and environmentally viable alternative, remains unexplored, particularly given the manufacturing defects such as material anisotropy and geometric inaccuracy associated with WAAM. This work presents an experimental investigation into the stiffening effect of sinusoidal wave patterns on WAAM-fabricated steel plated sections. Stub column tests and geometric measurements were conducted on square hollow sections (SHS) and I-sections fabricated in 316 L stainless steel. The specimens incorporated the sinusoidal wavy geometries previously validated in equal-leg angle sections under external plate boundary conditions. The present study extends their application to internal plate elements in SHS stub columns and examines the combined behaviour of internal and outstanding plate elements in I-sections with sinusoidal stiffening. The obtained results demonstrate a normalised strength enhancement of up to 9% with equal or even less material consumption (0.2% to -4.5%). Comparisons are made with conventionally manufactured and existing WAAM-fabricated stainless steel plated elements, as well as with current Eurocode 3 design equations and provisional design rules proposed for SLM-fabricated stiffened plates. Based on the findings, design recommendations for such structures have been made.</p
Determining the best discriminatory physical functioning outcome measurement instrument for psoriatic arthritis trials:A meta-epidemiological study
Get PDFOBJECTIVES: To empirically compare the discriminant capacities of three outcome measurement instruments for assessment of physical functioning for psoriatic arthritis (PsA): HAQ-DI, SF36-PF and SF36-PCS.METHODS: We applied a network meta-analysis technique in a sample of randomized trials (RCTs) for PsA. For randomized comparison, we calculated net effect size estimates for each outcome measurement instrument using standardized mean differences (SMDs); positive values indicated a beneficial effect of the intervention compared to the control groups. We analyzed the differences between outcome measurement instruments at the trial level by applying a multiple-treatment meta-analysis to compare the SMDs within and across randomized comparisons for each outcome measurement instrument.RESULTS: From 42 articles (31 RCTs), 57, 18, and 18 randomized comparisons enabled a direct comparison between HAQ-DI and SF36-PCS (difference in SMDs: 0.057, 95 % confidence interval, CI: 0.003 to 0.110), SF36-PF and SF36-PCS (difference in SMDs: 0.101, 95 % CI: 0.018 to 0.184); and HAQ-DI and SF36-PF (difference in SMDs:0.059, 95 % CI:0.142 to 0.024), respectively. The network meta-analysis technique confirmed that both HAQ-DI and SF36-PF were more responsive to change than SF36-PCS, with differences between SMDs of 0.057 (95 % CI: 0.003 to 0.110) and 0.109 (95 % CI: 0.032 to 0.185), respectively. No difference in discriminatory capacity between HAQ-DI and SF36-PF was noted.CONCLUSIONS: HAQ-DI and SF-36-PF were equally responsive to change and superior to SF36-PCS in PsA RCTs. We illustrated a new method for quantitative comparison of the performance of different outcome measurement instruments for a particular domain.</p
Dataset for "Pioneering Net Zero Carbon Construction Policy in Bath & North East Somerset: Evaluating the effectiveness of novel planning policies over time"
No full textThis data was collected as part of a continuing collaboration between the University of Bath and Bath and North East Somerset Council, exploring the impacts of (and reception to) pioneering sustainable planning policies for new buildings which were first introduced in January 2023. This project evaluates the success of the policies two years on, establishing long-term trends, opportunities for refinement, and the national policy implications of this unique policy case study. The deposited data relates to two parts of the methodology. The first is an analysis of incoming planning application, relating to the characteristics of proposed buildings and key parameters submitted to comply with the net zero energy requirements. The second is the results of a questionnaire sent out to applicants
Ten questions on indoor greening and environmental quality
Get PDFWhile outdoor urban greening is recognised for its benefits, indoor green infrastructure (iGI) in shaping indoor environmental quality (IEQ) - including air quality, thermal comfort, and bioaerosols - remains underexplored. This ten-question paper identifies key challenges, opportunities, and research gaps in the iGI-IEQ nexus, organised under 10 questions across five thematic clusters: (1) biophysical and technical performance; (2) ecological and microbiological dynamics; (3) human health and wellbeing; (4) equity, access, and socio-economic factors; and (5) implementation and systems integration. Findings indicate that iGI can improve air quality, regulate humidity, and enhance thermal comfort. However, its performance depends strongly on plant density, species selection, and ventilation. Most evidence comes from controlled settings. iGI may offer positive psychological and cognitive benefits, and can reduce health inequalities through affordable indoor interventions. However, significant data scarcity exists for long-term field studies, indoor microbial ecosystem effects, and socio-economic accessibility. Widespread adoption of iGI requires quantification of proven benefit conditions, followed by overcoming technical, operational, and regulatory barriers via adaptive design, digital monitoring, and interdisciplinary collaboration. As a culminating synthesis, this study introduces a newly developed comprehensive matrix that classifies twenty-six indoor greening types across twenty IEQ parameters, incorporating an assessment of current data confidence. This matrix lays a foundational framework for informed decision-making and design guidance. This review offers evidence-based insights for researchers, policymakers, and practitioners to effectively leverage iGI where suitable, in creating healthier, climate-resilient residential and commercial buildings, addressing both immediate IEQ challenges and supporting long-term sustainability objectives.</p
Multi-Objective Optimisation of a Hydrogen Combustion Mechanism with Direct Kinetic Modelling:Application to Combustion Engines
Get PDFHydrogen combustion can decarbonise difficult-to-abate sectors. However, practical deployment depends on reliable prediction of combustion behaviour under transient conditions, which contrasts with the steady-state experiments typically used for combustion mechanism development. This study presents a fully optimised H2-NOx mechanism, calibrated against 118 fundamental combustion datasets containing 1695 datapoints, which shows significant improvements in the prediction of ignition onset in an internal combustion engine with nitric oxide injection into the intake system.In contrast to prior single-objective approaches, this study introduces a fundamentally new approach to chemical kinetic mechanism optimisation, which leverages a Multi-Objective Particle Swarm Optimisation framework on a High-Performance Computing platform. The framework simultaneously balances accuracy and consistency across datasets, explicitly incorporates experimental uncertainty, and evaluates all candidate mechanisms with full chemical simulations. Prediction accuracy is quantified using the normalised root mean square error (nRMSE) to experimental measurements and the proportion of predictions within experimental uncertainty limits. Relative to the best existing mechanism, the optimised model achieves a 35 % reduction in nRMSE and a 19 % increase in the number of predictions within uncertainty bounds, demonstrating improved predictive performance for fundamental combustion targets.When the optimised mechanism was applied to autoignition timing in a Homogeneous Charge Compression Ignition engine, significant improvements were found for data with nitric oxide. Nevertheless, the overall accuracy in autoignition prediction is insufficient for practical applications, indicating that transient engine conditions are not adequately represented by steady-state datasets. These findings underscore that even fully optimised mechanisms based solely on fundamental experiments will not deliver high-accuracy predictions under real-world, transient conditions and integration of transient combustion data into future development of chemical mechanisms is recommended.<br/
Electoral politics over automation in a dual economy
Get PDFWhen automation in a developing economy displaces low-skilled workers in the advanced sector, backward sector wages may fall due to in-migration of the ‘newly’ unemployed. Fear of job and income loss may then induce office-seeking political parties to announce regulatory policies on automation for electoral success. We show that absent sectoral spillover, democratic adoption of automation is relatively higher and protects only high-skilled jobs in the advanced sector. However, the possibility of spillover limits this adoption. More specifically, if the backward sector is large, automation faces full resistance. In contrast, if the advanced sector is large, automation is moderate, making only the low-skilled jobs vulnerable. But these vulnerable workers, unlike their counterparts in the backward sector, may prefer automation because their advanced-sector wages fall below the severance pay plus backward-sector opportunities. When neither sector is large, the size of automation becomes uncertain, pushing similar economies into different growth paths
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