184 citations · 704 across the 38 of their papers we have counts for
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Equivariant vector bundles on Drinfeld's halfspace over a finite field
Sascha Orlik
Let be Drinfeld's halfspace over a finite field and let be a homogeneous vector bundle on . The paper deals w…
Spatio-temporal modelling of phenotypic heterogeneity in tumour tissues and its impact on radiotherapy treatment
Giulia L. Celora, Helen M. Byrne, P. G. Kevrekidis
We present a mathematical model that describes how tumour heterogeneity evolves in a tissue slice that is oxygenated by a single blood vessel. Phenotype is identified with the stem…
Travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion
Chloé Colson, Faustino Sánchez-Garduño, Helen M. Byrne +2
In this paper, we carry out a travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion. We consider two types of invasive fronts of tumour…
A method to coarse-grain multi-agent stochastic systems with regions of multistability
Daria Stepanova, Helen M. Byrne, Philip K. Maini +1
Hybrid multiscale modelling has emerged as a useful framework for modelling complex biological phenomena. However, when accounting for stochasticity in the internal dynamics of age…
Explicit physics-informed neural networks for non-linear upscaling closure: the case of transport in tissues
Ehsan Taghizadeh, Helen M. Byrne, Brian D. Wood
In this work, we use a combination of formal upscaling and data-driven machine learning for explicitly closing a nonlinear transport and reaction process in a multiscale tissue. Th…
Phenotypic variation modulates the growth dynamics and response to radiotherapy of solid tumours under normoxia and hypoxia
Giulia L. Celora, Helen M. Byrne, Christos Zois +1
In cancer, treatment failure and disease recurrence have been associated with small subpopulations of cancer cells with a stem-like phenotype. In this paper, we develop and investi…
Topological data analysis distinguishes parameter regimes in the Anderson-Chaplain model of angiogenesis
John T. Nardini, Bernadette J. Stolz, Kevin B. Flores +2
Angiogenesis is the process by which blood vessels form from pre-existing vessels. It plays a key role in many biological processes, including embryonic development and wound heali…