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Researcher profile

Ruth E. Baker

Ruth E. Baker contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Quantitative Methodsmath.DSBiological PhysicsCell BehaviorComputationmath.APmath.PRMethodologyMolecular Networks

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Published work

7 published item(s)

preprint2026arXiv

Structural identifiability of partially-observed stochastic processes: from single-particle trajectories to total particle density data

The increasing availability of experimental data has intensified interest in calibrating stochastic models, raising fundamental questions about parameter identifiability. Structural identifiability determines whether parameters can be uniquely recovered from idealised, noise-free data, a prerequisite to allow for parameter estimation. However, existing methods to assess structural identifiability are not generally applicable to stochastic processes. We develop a methodology to analyse structural identifiability for a class of spatio-temporal stochastic processes. We investigate how identifiability depends on the type of available data, distinguishing between single-particle trajectories and total particle density measurements. For trajectory data, we use the individual-based model description that explicitly represents single-particle dynamics. For population-level data, we derive a partial differential equation model representation, that describes the evolution of total particle density, and apply a differential algebra approach, common to ordinary differential equations analysis. We further introduce a novel method to study the initial condition, based on characteristic equations to construct a Taylor expansion of the density evolution, enabling identification of additional identifiable parameter combinations. We apply our methodology to a model, and show it is identifiable with trajectory data but only locally identifiable with density data, and demonstrate the critical role of initial conditions in the identifiability analysis.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

The spontaneous emergence of leaders and followers in a mathematical model of cranial neural crest cell migration

Many agent-based mathematical models of cranial neural crest cell (CNCC) migration impose a binary phenotypic partition of cells into either leaders or followers. In such models, the movement of leader cells at the front of collectives is guided by local chemoattractant gradients, while follower cells behind leaders move according to local cell-cell guidance cues. Although such model formulations have yielded many insights into the mechanisms underpinning CNCC migration, they rely on fixed phenotypic traits that are difficult to reconcile with evidence of phenotypic plasticity in vivo. A later agent-based model of CNCC migration aimed to address this limitation by allowing cells to adaptively combine chemotactic and cell-cell guidance cues during migration. In this model, cell behaviour adapts instantaneously in response to environmental cues, which precludes the identification of a persistent subset of cells as leader-like over biologically relevant timescales, as observed in vivo. Here, we build on previous leader-follower and adaptive phenotype models to develop a polarity-based agent-based model of CNCC migration, in which all cells evolve according to identical rules, interact via a pairwise interaction potential, and carry polarity vectors that evolve according to a dynamical system driven by time-averaged exposure to chemoattractant gradients. Numerical simulations of this model show that a leader-follower phenotypic partition emerges spontaneously from the underlying collective dynamics of the model. Furthermore, the model reproduces behaviour that is consistent with experimental observations of CNCC migration in the chick embryo. Thus, we provide an experimentally consistent, mechanistically-grounded mathematical model that captures the emergence of leader and follower cell phenotypes without their imposition a priori.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Control of diffusion-driven pattern formation behind a wave of competency

In certain biological contexts, such as the plumage patterns of birds and stripes on certain species of fishes, pattern formation takes place behind a so-called "wave of competency". Currently, the effects of a wave of competency on the patterning outcome is not well-understood. In this study, we use Turing's diffusion-driven instability model to study pattern formation behind a wave of competency, under a range of wave speeds. Numerical simulations show that in one spatial dimension a slower wave speed drives a sequence of peak splittings in the pattern, whereas a higher wave speed leads to peak insertions. In two spatial dimensions, we observe stripes that are either perpendicular or parallel to the moving boundary under slow or fast wave speeds, respectively. We argue that there is a correspondence between the one- and two-dimensional phenomena, and that pattern formation behind a wave of competency can account for the pattern organization observed in many biological systems.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Multifidelity multilevel Monte Carlo to accelerate approximate Bayesian parameter inference for partially observed stochastic processes

Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always incomplete observations of reality. This leads to a great challenge for statistical inference because the likelihood function will be intractable for almost all partially observed stochastic processes. This renders many statistical methods, especially within a Bayesian framework, impossible to implement. Therefore, computationally expensive likelihood-free approaches are applied that replace likelihood evaluations with realisations of the model and observation process. For accurate inference, however, likelihood-free techniques may require millions of expensive stochastic simulations. To address this challenge, we develop a new method based on recent advances in multilevel and multifidelity. Our approach combines the multilevel Monte Carlo telescoping summation, applied to a sequence of approximate Bayesian posterior targets, with a multifidelity rejection sampler to minimise the number of computationally expensive exact simulations required for accurate inference. We present the derivation of our new algorithm for likelihood-free Bayesian inference, discuss practical implementation details, and demonstrate substantial performance improvements. Using examples from systems biology, we demonstrate improvements of more than two orders of magnitude over standard rejection sampling techniques. Our approach is generally applicable to accelerate other sampling schemes, such as sequential Monte Carlo, to enable feasible Bayesian analysis for realistic practical applications in physics, chemistry, biology, epidemiology, ecology and economics.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Symmetries of systems of first order ODEs: Symbolic symmetry computations, mechanistic model construction and applications in biology

We discuss the role and merits of symmetry methods for the analysis of biological systems. In particular, we consider systems of first order ordinary differential equations and provide a comprehensive review of the geometrical foundations pertinent to symmetries of such systems. Subsequently, we present an algorithm for finding infinitesimal generators of symmetries for systems with rational reaction terms, and an open-source implementation of the algorithm using symbolic computations. We discuss two complementary perspectives on symmetries in mechanistic modelling; as tools for the analysis of a given model or as a geometrical principle for incorporating biological properties in the construction of new models. Through numerous examples of relevance to modelling in biology we demonstrate the different uses of symmetry methods, and also discuss how to infer symmetries from experimental data.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Biologically-informed neural networks guide mechanistic modeling from sparse experimental data

Biologically-informed neural networks (BINNs), an extension of physics-informed neural networks [1], are introduced and used to discover the underlying dynamics of biological systems from sparse experimental data. In the present work, BINNs are trained in a supervised learning framework to approximate in vitro cell biology assay experiments while respecting a generalized form of the governing reaction-diffusion partial differential equation (PDE). By allowing the diffusion and reaction terms to be multilayer perceptrons (MLPs), the nonlinear forms of these terms can be learned while simultaneously converging to the solution of the governing PDE. Further, the trained MLPs are used to guide the selection of biologically interpretable mechanistic forms of the PDE terms which provides new insights into the biological and physical mechanisms that govern the dynamics of the observed system. The method is evaluated on sparse real-world data from wound healing assays with varying initial cell densities [2].

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Efficiently simulating discrete-state models with binary decision trees

Stochastic simulation algorithms (SSAs) are widely used to numerically investigate the properties of stochastic, discrete-state models. The Gillespie Direct Method is the pre-eminent SSA, and is widely used to generate sample paths of so-called agent-based or individual-based models. However, the simplicity of the Gillespie Direct Method often renders it impractical where large-scale models are to be analysed in detail. In this work, we carefully modify the Gillespie Direct Method so that it uses a customised binary decision tree to trace out sample paths of the model of interest. We show that a decision tree can be constructed to exploit the specific features of the chosen model. Specifically, the events that underpin the model are placed in carefully-chosen leaves of the decision tree in order to minimise the work required to keep the tree up-to-date. The computational efficencies that we realise can provide the apparatus necessary for the investigation of large-scale, discrete-state models that would otherwise be intractable. Two case studies are presented to demonstrate the efficiency of the method.

0 citations0 reviewsNo code linkedOpen access