We propose a new kernel that quantifies success for the task of computing a core-periphery partition for an undirected network. Finding the associated optimal partitioning may be expressed in the form of a quadratic unconstrained binary optimization (QUBO) problem, to which a state-of-the-art quantum annealer may be applied. We therefore make use of the new objective function to (a) judge the performance of a quantum annealer, and (b) compare this approach with existing heuristic core-periphery partitioning methods. The quantum annealing is performed on a commercially available D-Wave machine. The QUBO problem involves a full matrix even when the underlying network is sparse. Hence, we develop and test a sparsified version of the original QUBO which increases the available problem dimension for the quantum annealer. Results are provided on both synthetic and real data sets, and we conclude that the QUBO/quantum annealing approach offers benefits in terms of optimizing this new quantity of interest.

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.

The circadian clock is an important molecular mechanism that enables many organisms to anticipate and adapt to environmental change. Pokhilko et al. recently built a deterministic ODE mathematical model of the plant circadian clock in order to understand the behaviour, mechanisms and properties of the system. The model comprises 30 molecular species (genes, mRNAs and proteins) and over 100 parameters. The parameters have been fitted heuristically to available gene expression time series data and the calibrated model has been shown to reproduce the behaviour of the clock components. Ongoing work is extending the clock model to cover downstream effects, in particular metabolism, necessitating further parameter estimation and model selection. This work investigates the challenges facing a full Bayesian treatment of parameter estimation. Using an efficient adaptive MCMC proposed by Haario et al. and working in a high performance computing setting, we quantify the posterior distribution around the proposed parameter values and explore the basin of attraction. We investigate if Bayesian inference is feasible in this high dimensional setting and thoroughly assess convergence and mixing with different statistical diagnostics, to prevent apparent convergence in some domains masking poor mixing in others.