Controversy in mechanistic modelling with Gaussian processes

Parameter inference in mechanistic models based on non-affine differential equations is computationally onerous, and various faster alternatives based on gradient matching have been proposed. A particularly promising approach is based on nonparametric Bayesian modelling with Gaussian processes, which exploits the fact that a Gaussian process is closed under differentiation. However, two alternative paradigms have been proposed. The first paradigm, proposed at NIPS 2008 and AISTATS 2013, is based on a product of experts approach and a marginalization over the derivatives of the state variables. The second paradigm, proposed at ICML 2014, is based on a probabilistic generative model and a marginalization over the state variables. The claim has been made that this leads to better inference results. In the present article, we offer a new interpretation of the second paradigm, which highlights the underlying assumptions, approximations and limitations. In particular, we show that the second paradigm suffers from an intrinsic identifiability problem, which the first paradigm is not affected by

Bifurcation analysis informs Bayesian inference in the Hes1 feedback loop

<p>Background Ordinary differential equations (ODEs) are an important tool for describing the dynamics of biological systems. However, for ODE models to be useful, their parameters must first be calibrated. Parameter estimation, that is, finding parameter values given experimental data, is an inference problem that can be treated systematically through a Bayesian framework.</p> <p>A Markov chain Monte Carlo approach can then be used to sample from the appropriate posterior probability distributions, provided that suitable prior distributions can be found for the unknown parameter values. Choosing these priors is therefore a vital first step in the inference process. We study here a negative feedback loop in gene regulation where an ODE incorporating a time delay has been proposed as a realistic model and where experimental data is available. Our aim is to show that a priori mathematical analysis can be exploited in the choice of priors.</p> <p>Results By focussing on the onset of oscillatory behaviour through a Hopf Bifurcation, we derive a range of analytical expressions and constraints that link the model parameters to the observed dynamics of the system. Computational tests on both simulated and experimental data emphasise the usefulness of this analysis.</p> <p>Conclusion Mathematical analysis not only gives insights into the possible dynamical behaviour of gene expression models, but can also be used to inform the choice of priors when parameters are inferred from experimental data in a Bayesian setting.</p&gt

Corporate climate change responsibilities under the OECD Guidelines for Multinational Enterprises

In 2023, the Organisation for Economic Co-operation and Development (OECD) launched an updated version of the OECD Guidelines for Multinational Enterprises on Responsible Business Conduct. The changes represent substantial and potentially far-reaching implications for business, particularly in the areas of climate change and biodiversity. This article examines the 14 climate-related complaints filed under the Guidelines prior to the adoption of the 2023 Update, showing how many of these cases illustrate the potential interlinkages between the human rights and climate change dimensions of the Guidelines. The article then discusses how the updated provisions may influence future complaints concerning climate change. Based on this analysis, the article concludes that the Guidelines could have been strengthened by the explicit integration of climate change into the scope of corporate human rights responsibilities under the Guidelines

Global trends in climate change litigation: 2022 snapshot

Climate change litigation continues to grow in importance year-on-year as a way of either advancing or delaying effective action on climate change. In 2022, the Intergovernmental Panel on Climate Change (IPCC) recognised the role of litigation in affecting “the outcome and ambition of climate governance”. The latest edition of our annual report on global trends in climate change litigation takes stock of developments over the period May 2021 to May 2022, and draws on a number of recent case studies from around the world. It also identifies areas where climate litigation cases are likely to increase in the future. The goal in these reports is to help readers understand the ways in which the law is being used as a tool to advance a variety of often inconsistent climate-related agendas. Legal practitioners may use the law to advance climate action, or, less frequently, seek to challenge the way in which climate policy is designed or implemented or to deter policymakers from implementing more restrictive measures on private parties responsible for greenhouse gas emissions

Taking companies to court over climate change: who is being targeted?

To deepen understanding of climate litigation against private sector actors, Catherine Higham and Honor Kerry analyse climate cases filed in 2021 against companies in different sectors and consider what the future holds. They find that that while fossil fuel companies remain a primary target of activist litigation, climate litigants are now casting their net more broadly

Quantum deep learning by sampling neural nets with a quantum annealer

Experimental results obtained from the quantum annealer. Files are in preparation and will be available to download on this page by 2023-03-17

Dynamic DNA and human disease: mathematical modelling and statistical inference for myotonic dystrophy type 1 and Huntington disease

Several human genetic diseases, including myotonic dystrophy type 1 (DM1) and Huntington disease (HD), are associated with inheriting an abnormally large unstable DNA simple sequence tandem repeat. These sequences mutate, by changing the number of repeats, many times during the lifetime of those affected, with a bias towards expansion. High repeat numbers are associated with early onset and disease severity. The presence of somatic instability compromises attempts to measure intergenerational repeat dynamics and infer genotype-phenotype relationships. Modelling the progression of repeat length throughout the lifetime of individuals has potential for improving prognostic information as well as providing a deeper understanding of the underlying biological process. Dr Fernando Morales, Dr Anneli Cooper and others from the Monckton lab have characterised more than 25,000 de novo somatic mutations from a large cohort of DM1 patients using single-molecule polymerase chain reaction (SM-PCR). This rich dataset enables us to fully quantify levels of somatic instability across a representative DM1 population for the first time. We establish the relationship between inherited or progenitor allele length, age at sampling and levels of somatic instability using linear regression analysis. We show that the estimated progenitor allele length genotype is significantly better than modal repeat length (the current clinical standard) at predicting age of onset and this novel genotype is the major modifier of the age of onset phenotype. Further we show that somatic variation (adjusted for estimated progenitor allele length and age at sampling) is also a modifier of the age of onset phenotype. Several families form the large cohort, and we find that the level of somatic instability is highly heritable, implying a role for individual-specific trans-acting genetic modifiers. We develop new mathematical models, the main focus of this thesis, by modifying a previously proposed stochastic birth process to incorporate possible contraction. A Bayesian likelihood approach is used as the basis for inference and parameter estimation. We use model comparison analysis to reveal, for the first time, that the expansion bias observed in the distributions of repeat lengths is likely to be the cumulative effect of many expansion and contraction events. We predict that mutation events can occur as frequently as every other day, which matches the timing of regular cell activities such as DNA repair and transcription, but not DNA replication. Mutation rates estimated under the models described above are lower than expected among individuals with inherited repeat lengths less than 100 CTGs, suggesting that these rates may be suppressed at the lower end of the disease causing range. We propose that a length-specific effect may be operating within this range and test this hypothesis by introducing such an effect into the model. To calibrate this extended model, we use blood DNA data from DM1 individuals with small alleles (inherited repeat lengths less than 100 CTGs) and buccal DNA from HD individuals who almost always have inherited repeat lengths less than 100 CAGs. These datasets comprise single DNA molecules sized using SM-PCR. We find statistical support for a general length-specific effect which suppresses mutational rates among the smaller alleles and gives rise to a distinctive pattern in the repeat length distributions. In a novel application of this new model, fitted to a large cohort of DM1 individuals, we also show that this distinctive pattern may help identify individuals whose effective repeat length, with regards to somatic instability, is less than their actual repeat length. A plausible explanation for this distinction is that the expanded repeat tract is compromised by interruptions or other unusual features. For these individuals, we estimate the effective repeat length of their expanded repeat tracts and contribute to the on-going discussion about the effect of interruptions on phenotype. The interpretation of the levels of somatic instability in many of the affected tissues in the triplet repeat diseases is hindered by complex cell compositions. We extend our model to two cell populations whose repeat lengths have different rates of mutation (fast and slow). Swami et al. have recently characterised repeat length distributions in end stage HD brain. Applying our model, we infer for each frontal cortex HD dataset the likely relative weight of these cell populations and their corresponding contribution towards somatic variation. By comparison with data from laser captured single cells we conclude that the neuronal repeat lengths most likely mutate at a higher rate than glial repeat lengths, explaining the characteristic skewed distributions observed in mixed cell tissue from the brain. We confirm that individual-specific mutation rates in neurons are, in addition to the inherited repeat length, a modifier of age of onset. Our results support a model of disease progression where individuals with the same inherited repeat length may reach age of onset, as much as 30 years earlier, because of greater somatic expansions underpinned by higher mutational rates. Therapies aimed at reducing somatic expansions would therefore have considerable benefits with regard to extending the age of onset. Currently clinical diagnosis of DM1 is based on a measure of repeat length from blood cells, but variance in modal length only accounts for between 20 - 40% of the variance in age of onset and, therefore, is not a an accurate predictive tool. We show that in principle progenitor allele length improves the inverse correlation with age of onset over the traditional model length measure. We make use of second blood samples that are now available from 40 DM1 individuals. We show that inherited repeat length and the mutation rates underlying repeat length instability in blood, inferred from samples at two time points rather than one, are better predictors of age of onset than the traditional modal length measure. Our results are a step towards providing better prognostic information for DM1 individuals and their families. They should also lead to better predictions for drug/therapy response, which is emerging as key to successful clinical trials. Microsatellites are another type of tandem repeat found in the genome with high levels of intergenerational and somatic mutation. Differences between individuals make microsatellites very useful biomarkers and they have many applications in forensics and medicine. As well as a general application to other expanded repeat diseases, the mathematical models developed here could be used to better understand instability at other mutational hotspots such as microsatellites

Deep learnability: using neural networks to quantify language similarity and learnability

Learning a second language (L2) usually progresses faster if a learner's L2 is similar to their first language (L1). Yet global similarity between languages is difficult to quantify, obscuring its precise effect on learnability. Further, the combinatorial explosion of possible L1 and L2 language pairs, combined with the difficulty of controlling for idiosyncratic differences across language pairs and language learners, limits the generalisability of the experimental approach. In this study, we present a different approach, employing artificial languages and artificial learners. We built a set of five artificial languages whose underlying grammars and vocabulary were manipulated to ensure a known degree of similarity between each pair of languages. We next built a series of neural network models for each language, and sequentially trained them on pairs of languages. These models thus represented L1 speakers learning L2s. By observing the change in activity of the cells between the L1-speaker model and the L2-learner model, we estimated how much change was needed for the model to learn the new language. We then compared the change for each L1/L2 bilingual model to the underlying similarity across each language pair. The results showed that this approach can not only recover the facilitative effect of similarity on L2 acquisition, but can also offer new insights into the differential effects across different domains of similarity. These findings serve as a proof of concept for a generalisable approach that can be applied to natural languages

Efficient Bayesian Deep Inversion for Depth Prediction

Signal data and computer code to reproduce the results in the pape