Well-posedness of mean field games master equations involving non-separable local Hamiltonians (2023)
Journal Article
Ambrose, D. M., & Mészáros, A. R. (2023). Well-posedness of mean field games master equations involving non-separable local Hamiltonians. Transactions of the American Mathematical Society, 376(4), 2481-2523. https://doi.org/10.1090/tran/8760

In this paper we construct short time classical solutions to a class of master equations in the presence of non-degenerate individual noise arising in the theory of mean field games. The considered Hamiltonians are non-separable and local functions o... Read More about Well-posedness of mean field games master equations involving non-separable local Hamiltonians.

A Bayesian Computer Model Analysis of Robust Bayesian Analyses (2022)
Journal Article
Vernon, I., & Gosling, J. (2023). A Bayesian Computer Model Analysis of Robust Bayesian Analyses. Bayesian Analysis, 18(4), 1367-1399. https://doi.org/10.1214/22-ba1340

We harness the power of Bayesian emulation techniques, designed to aid the analysis of complex computer models, to examine the structure of complex Bayesian analyses themselves. These techniques facilitate robust Bayesian analyses and/or sensitivity... Read More about A Bayesian Computer Model Analysis of Robust Bayesian Analyses.

Mean field games master equations with nonseparable Hamiltonians and displacement monotonicity (2022)
Journal Article
Gangbo, W., Mészáros, A. R., Mou, C., & Zhang, J. (2022). Mean field games master equations with nonseparable Hamiltonians and displacement monotonicity. Annals of Probability, 50(6), 2178-2217. https://doi.org/10.1214/22-aop1580

A variational approach to first order kinetic Mean Field Games with local couplings (2022)
Journal Article
Griffin-Pickering, M., & Mészáros, A. R. (2022). A variational approach to first order kinetic Mean Field Games with local couplings. Communications in Partial Differential Equations, 47(10), 1945-2022. https://doi.org/10.1080/03605302.2022.2101003

First order kinetic mean field games formally describe the Nash equilibria of deterministic differential games where agents control their acceleration, asymptotically in the limit as the number of agents tends to infinity. The known results for the w... Read More about A variational approach to first order kinetic Mean Field Games with local couplings.

Global Well‐Posedness of Master Equations for Deterministic Displacement Convex Potential Mean Field Games (2022)
Journal Article
Gangbo, W., & Mészáros, A. R. (2022). Global Well‐Posedness of Master Equations for Deterministic Displacement Convex Potential Mean Field Games. Communications on Pure and Applied Mathematics, 75(12), 2685-2801. https://doi.org/10.1002/cpa.22069

This manuscript constructs global in time solutions to master equations for potential mean field games. The study concerns a class of Lagrangians and initial data functions that are displacement convex, and so this property may be in dichotomy with t... Read More about Global Well‐Posedness of Master Equations for Deterministic Displacement Convex Potential Mean Field Games.

Managing Unusual Sensory Experiences in People with First-Episode Psychosis (MUSE FEP): a study protocol for a single-blind parallel-group randomised controlled feasibility trial (2022)
Journal Article
Dudley, R., Dodgson, G., Common, S., O'Grady, L., Watson, F., Gibbs, C., …Aynsworth, C. (2022). Managing Unusual Sensory Experiences in People with First-Episode Psychosis (MUSE FEP): a study protocol for a single-blind parallel-group randomised controlled feasibility trial. BMJ Open, 12(5), Article e061827. https://doi.org/10.1136/bmjopen-2022-061827

Introduction Hallucinations (hearing or seeing things that others do not) are a common feature of psychosis, causing significant distress and disability. Existing treatments such as cognitive–behavioural therapy for psychosis (CBTp) have modest benef... Read More about Managing Unusual Sensory Experiences in People with First-Episode Psychosis (MUSE FEP): a study protocol for a single-blind parallel-group randomised controlled feasibility trial.

Eliciting judgements about dependent quantities of interest: The SHeffield ELicitation Framework extension and copula methods illustrated using an asthma case study (2022)
Journal Article
Holzhauer, B., Hampson, L. V., Gosling, J. P., Bornkamp, B., Kahn, J., Lange, M. R., …others. (2022). Eliciting judgements about dependent quantities of interest: The SHeffield ELicitation Framework extension and copula methods illustrated using an asthma case study. Pharmaceutical Statistics, 21(5), 1005-1021. https://doi.org/10.1002/pst.2212

Pharmaceutical companies regularly need to make decisions about drug development programs based on the limited knowledge from early stage clinical trials. In this situation, eliciting the judgements of experts is an attractive approach for synthesisi... Read More about Eliciting judgements about dependent quantities of interest: The SHeffield ELicitation Framework extension and copula methods illustrated using an asthma case study.

Gaussian process modeling of heterogeneity and discontinuities using Voronoi tessellations (2021)
Journal Article
Pope, C. A., Gosling, J. P., Barber, S., Johnson, J. S., Yamaguchi, T., Feingold, G., & Blackwell, P. G. (2021). Gaussian process modeling of heterogeneity and discontinuities using Voronoi tessellations. Technometrics, 63(1), 53-63

A clinical and cost effectiveness trial of a parent group intervention to manage challenging restricted and repetitive behaviours in young children with autism spectrum disorder: study protocol for a randomized controlled trial (2021)
Journal Article
Grahame, V., Dixon, L., Fletcher-Watson, S., Garland, D., Glod, M., Goodwin, J., …Rodgers, J. (2021). A clinical and cost effectiveness trial of a parent group intervention to manage challenging restricted and repetitive behaviours in young children with autism spectrum disorder: study protocol for a randomized controlled trial. Trials, 22, Article 240. https://doi.org/10.1186/s13063-021-05175-y

Background Restricted and repetitive behaviours vary greatly across the autism spectrum, and although not all are problematic some can cause distress and interfere with learning and social opportunities. We have, alongside parents, developed a parent... Read More about A clinical and cost effectiveness trial of a parent group intervention to manage challenging restricted and repetitive behaviours in young children with autism spectrum disorder: study protocol for a randomized controlled trial.

Degenerate nonlinear parabolic equations with discontinuous diffusion coefficients (2021)
Journal Article
Kwon, D., & Mészáros, A. R. (2021). Degenerate nonlinear parabolic equations with discontinuous diffusion coefficients. Journal of the London Mathematical Society, 104(2), 688-746. https://doi.org/10.1112/jlms.12444

This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in particular on... Read More about Degenerate nonlinear parabolic equations with discontinuous diffusion coefficients.

Artificial Intelligence for chemical risk assessment (2020)
Journal Article
Wittwehr, C., Blomstedt, P., Gosling, J. P., Peltola, T., Raffael, B., Richarz, A., …Whelan, M. (2020). Artificial Intelligence for chemical risk assessment. Computational Toxicology, 13,

Tackling selection bias in sentencing data analysis: a new approach based on a scale of severity (2020)
Journal Article
Pina-Sánchez, J., & Gosling, J. P. (2020). Tackling selection bias in sentencing data analysis: a new approach based on a scale of severity

Potential of ToxCast data in the safety assessment of food chemicals (2020)
Journal Article
Punt, A., Firman, J., Boobis, A., Cronin, M., Gosling, J. P., Wilks, M. F., …Fussell, K. C. (2020). Potential of ToxCast data in the safety assessment of food chemicals. Toxicological Sciences, 174(2), 326-340

Weak Solutions to the Muskat Problem with Surface Tension Via Optimal Transport (2020)
Journal Article
Jacobs, M., Kim, I., & Mészáros, A. R. (2020). Weak Solutions to the Muskat Problem with Surface Tension Via Optimal Transport. Archive for Rational Mechanics and Analysis, 239(1), 389-430. https://doi.org/10.1007/s00205-020-01579-3

Inspired by recent works on the threshold dynamics scheme for multi-phase mean curvature flow (by Esedoḡlu–Otto and Laux–Otto), we introduce a novel framework to approximate solutions of the Muskat problem with surface tension. Our approach is based... Read More about Weak Solutions to the Muskat Problem with Surface Tension Via Optimal Transport.

Generation of TD50 values for carcinogenicity study data (2019)
Journal Article
Thresher, A., Gosling, J. P., & Williams, R. (2019). Generation of TD50 values for carcinogenicity study data

The importance of mathematical modelling in chemical risk assessment and the associated quantification of uncertainty (2019)
Journal Article
Gosling, J. P. (2019). The importance of mathematical modelling in chemical risk assessment and the associated quantification of uncertainty. Computational Toxicology, 10, 44-50

Next generation physiologically based kinetic (NG-PBK) models in support of regulatory decision making (2019)
Journal Article
Paini, A., Leonard, J., Joossens, E., Bessems, J., Desalegn, A., Dorne, J., …others. (2019). Next generation physiologically based kinetic (NG-PBK) models in support of regulatory decision making. Computational Toxicology, 9, 61-72

Rank pruning for dominance queries in CP-nets (2019)
Journal Article
Laing, K., Thwaites, P. A., & Gosling, J. P. (2019). Rank pruning for dominance queries in CP-nets. Journal of Artificial Intelligence Research, 64, 55-107

Uncertainty quantification of density and stratification estimates with implications for predicting ocean dynamics (2019)
Journal Article
Manderson, A., Rayson, M., Cripps, E., Girolami, M., Gosling, J., Hodkiewicz, M., …Jones, N. (2019). Uncertainty quantification of density and stratification estimates with implications for predicting ocean dynamics. Journal of Atmospheric and Oceanic Technology, 36(7), 1313-1330

Emulation of vessel motion simulators for computationally efficient uncertainty quantification (2019)
Journal Article
Astfalck, L., Cripps, E., Gosling, J., & Milne, I. (2019). Emulation of vessel motion simulators for computationally efficient uncertainty quantification. Ocean Engineering, 172, 726-736