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Found 15 papers, 13 papers with code
A generalised sigmoid population growth model with energy dependence: application to quantify the tipping point for Antarctic shallow seabed algae
Sigmoid growth models are often used to study population dynamics.
Structured methods for parameter inference and uncertainty quantification for mechanistic models in the life sciences
Parameter inference and uncertainty quantification are important steps when relating mathematical models to real-world observations, and when estimating uncertainty in model predictions.
Implementing measurement error models with mechanistic mathematical models in a likelihood-based framework for estimation, identifiability analysis, and prediction in the life sciences
A fundamental and often overlooked choice in this approach involves relating the solution of a mathematical model with noisy and incomplete measurement data.
Exact sharp-fronted solutions for nonlinear diffusion on evolving domains
We obtain the solution by identifying a series of transformations that converts the model of a nonlinear diffusive process on an evolving domain to a nonlinear diffusion equation on a fixed domain, which admits known exact solutions for certain choices of diffusivity functions.
Exact solutions for diffusive transport on heterogeneous growing domains
The exact solutions reveal the relationship between model parameters, such as the diffusivity and the type and rate of domain growth, and key statistics, such as the survival and splitting probabilities.
Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework
One way of exploring this question is to study population dynamics using reaction-diffusion equations, where migration is usually represented as a linear diffusion term, and birth-death is represented with a bistable source term.
Bayesian uncertainty quantification for data-driven equation learning
Equation learning aims to infer differential equation models from data.
Extinction of bistable populations is affected by the shape of their initial spatial distribution
In this work we study population survival or extinction using a stochastic, discrete lattice-based random walk model where individuals undergo movement, birth and death events.
Learning differential equation models from stochastic agent-based model simulations
We propose that methods from the equation learning field provide a promising, novel, and unifying approach for agent-based model analysis.
Dynamical Systems
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.
A novel mathematical model of heterogeneous cell proliferation
As motivation for our model we provide experimental data that illustrate the induced-switching process.
A practical guide to pseudo-marginal methods for computational inference in systems biology
For many stochastic models of interest in systems biology, such as those describing biochemical reaction networks, exact quantification of parameter uncertainty through statistical inference is intractable.
Rapid Bayesian inference for expensive stochastic models
In this work, we present new computational Bayesian techniques that accelerate inference for expensive stochastic models by using computationally inexpensive approximations to inform feasible regions in parameter space, and through learning transforms that adjust the biased approximate inferences to closer represent the correct inferences under the expensive stochastic model.
Computation Cell Behavior Molecular Networks
Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art
Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling.
Molecular Networks
New homogenization approaches for stochastic transport through heterogeneous media
In this work, we present a new class of homogenization approximations by considering a stochastic diffusive transport model on a one-dimensional domain containing an arbitrary number of layers with different jump rates.
Biological Physics Computational Physics 82C70
