L3

We study “bottom-up” models for the collective motion of large groups of animals. Similar models can be encoded into (micro)robotic matter, capable of sensing light and processing information. Agents are endowed only with visual sensing and information processing. We study a model in which moving agents reorientate to maximise the path-entropy of their visual environment over paths into the future. There are general arguments that principles like this that are based on retaining freedom in the future may confer fitness in an uncertain world. Alternative “top-down” models are more common in the literature. These typically encode coalignment and/or cohesion directly and are often motivated by models drawn from physics, e.g. describing spin systems. However, such models can usually give little insight into how co-alignment and cohesion emerge because these properties are encoded in the model at the outset, in a top-down manner. We discuss how our model leads to dynamics with striking similarities with animal systems, including the emergence of coalignment, cohesion, a characteristic density scaling anddifferent behavioural phenotypes. The dynamics also supports a very unusual order-disorder transition in which the order (coalignment) initially increases upon the addition of sensory or behavioural noise, before decreasing as the noise becomes larger.

During the last fifteen years, there has been a paradigm shift in the continuum modelling of granular materials; most notably with the development of rheological models, such as the μ(I)-rheology (where μ is the friction and I is the inertial number), but also with significant advances in theories for particle segregation. This talk details theoretical and numerical frameworks (based on OpenFOAM®) which unify these disconnected endeavours. Coupling the segregation with the flow, and vice versa, is not only vital for a complete theory of granular materials, but is also beneficial for developing numerical methods to handle evolving free surfaces. This general approach is based on the partially regularized incompressible μ(I)-rheology, which is coupled to a theory for gravity/shear-driven segregation (Gray & Ancey, J. Fluid Mech., vol. 678, 2011, pp. 353–588). These advection–diffusion–segregation equations describe the evolving concentrations of the constituents, which then couple back to the variable viscosity in the incompressible Navier–Stokes equations. A novel feature of this approach is that any number of differently sized phases may be included, which may have disparate frictional properties. The model is used to simulate the complex particle-size segregation patterns that form in a partially filled triangular rotating drum. There are many other applications of the theory to industrial granular flows, which are the second most common material used after fluids. The same processes also occur in geophysical flows, such as snow avalanches, debris flows and dense pyroclastic flows. Depth-averaged models, that go beyond the μ(I)-rheology, will also be derived to capture spontaneous self-channelization and levee formation, as well as complex segregation-induced flow fingering effects, which enhance the run-out distance of these hazardous flows.

We present a new formulation of string and particle amplitudes that emerges from simple one-dimensional models. The key is a new way to parametrize the positive part of Teichmüller space. It also builds on the results of Mirzakhani for computing Weil-Petterson volumes. The formulation works at all orders in the perturbation series, including non-planar contributions. The relationship between strings and particles is made manifest as a "tropical limit". The results are well adapted to studying the scattering of large numbers of particles or amplitudes at high loop order. The talk will in part cover results from arXiv:2309.15913, 2311.09284.

Bone regeneration processes are complex multiscale intrinsic mechanisms in bone tissue whose primary outcome is restoring function and form to a bone insufficiency. The effect of mechanics on the newly formed bone (the woven bone), is fundamental, at the tissue, cellular or even molecular scale. However, at these multiple scales, the identification of the mechanical parameters and their mechanisms of action are still unknown and continue to be investigated. This concept of mechanical regulation of biological processes is the main premise of mechanobiology and is used in this seminar to understand the multiscale response of the woven bone to mechanical factors in different bone regeneration processes: bone transport, bone lengthening and tissue engineering. The importance of a multidisciplinary approach that includes both in vivo and in silico modeling will be remarked during the seminar.

I shall say some stuff about quasilinear reaction-diffusion equations, motivated by tissue growth in particular.

For many systems (certainly those in biology, medicine and pharmacology) the mathematical models that are generated invariably include state variables that cannot be directly measured and associated model parameters, many of which may be unknown, and which also cannot be measured.  For such systems there is also often limited access for inputs or perturbations. These limitations can cause immense problems when investigating the existence of hidden pathways or attempting to estimate unknown parameters and this can severely hinder model validation. It is therefore highly desirable to have a formal approach to determine what additional inputs and/or measurements are necessary in order to reduce or remove these limitations and permit the derivation of models that can be used for practical purposes with greater confidence.

Structural identifiability arises in the inverse problem of inferring from the known, or assumed, properties of a biomedical or biological system a suitable model structure and estimates for the corresponding rate constants and other model parameters.  Structural identifiability analysis considers the uniqueness of the unknown model parameters from the input-output structure corresponding to proposed experiments to collect data for parameter estimation (under an assumption of the availability of continuous, noise-free observations).  This is an important, but often overlooked, theoretical prerequisite to experiment design, system identification and parameter estimation, since estimates for unidentifiable parameters are effectively meaningless.  If parameter estimates are to be used to inform about intervention or inhibition strategies, or other critical decisions, then it is essential that the parameters be uniquely identifiable. 

Numerous techniques for performing a structural identifiability analysis on linear parametric models exist and this is a well-understood topic.  In comparison, there are relatively few techniques available for nonlinear systems (the Taylor series approach, similarity transformation-based approaches, differential algebra techniques and the more recent observable normal form approach and symmetries approaches) and significant (symbolic) computational problems can arise, even for relatively simple models in applying these techniques.

In this talk an introduction to structural identifiability analysis will be provided demonstrating the application of the techniques available to both linear and nonlinear parameterised systems and to models of (nonlinear mixed effects) population nature.

The ability of biological matter to move and deform itself is facilitated by microscopic out-of-equilibrium processes that convert chemical energy into mechanical work. In many cases, this mechano-chemical activity takes place on effectively two-dimensional domains formed by, for example, multicellular structures like epithelial tissues or the outer surface of eukaryotic cells, the so-called actomyosin cortex.
We will show in the first part of the talk, that the large-scale dynamics and self-organisation of such structures can be captured by the theory of active fluids. Specifically, using a minimal model of active isotropic fluids, we can rationalize the emergence of asymmetric epithelial tissue flows in the flower beetle during early development, and explain cell rotations in the context of active chiral flows and left-right symmetry breaking that occurs as the model organism C. elegans sets up its body plan.
To develop a more general understanding of such processes, specifically the role of geometry, curvature and interactions with the environment, we introduce in the second part a theory of active fluid surfaces and discuss analytical and numerical tools to solve the corresponding momentum balance equations of curved and deforming surfaces. By considering mechanical interactions with the environment and the fully self-organized shape dynamics of active surfaces, these tools reveal novel mechanisms of symmetry breaking and pattern formation in active matter.

Malignant transformation of somatic tissues is an evolutionary process, driven by selection for oncogenic mutations. Understanding when these mutations occur, and how fast mutant cell clones expand can improve diagnostic schemes and therapeutic intervention. However, clonal dynamics are not directly accessible in humans, posing a need for inference approaches to reconstruct the division history in normal and malignant cell clones, and to predict their future evolution. Inspired from population genetics theory, we develop mathematical models to detect imprints of clonal selection in the variant allele frequency distribution measured in a single tissue sample of a homeostatic tissue. I will present the theoretical basis of our approach and inference results for the tissue dynamics in physiological and clonal hematopoiesis, obtained from variant allele frequencies measured by snapshot bulk whole genome sequencing of human bone marrow samples.

Unraveling the intricacies of intracellular signalling through predictive mathematical models holds great promise for advancing precision medicine and enhancing our foundational comprehension of biology. However, navigating the labyrinth of biological mechanisms governing signalling demands a delicate balance between a faithful description of the underlying biology and the practical utility of parsimonious models.
In this talk, I will present methods that enable training of large ordinary differential equation models of intracellular signalling and showcase application of such models to predict sensitivity to anti-cancer drugs. Through illustrative examples, I will demonstrate the application of these models in predicting sensitivity to anti-cancer drugs. A critical reflection on the construction of such models will be offered, exploring the perpetual question of complexity and how intricate these models should be.
Moreover, the talk will explore novel approaches that meld machine learning techniques with mathematical modelling. These approaches aim to harness the benefits of simplistic and unbiased phenomenological models while retaining the interpretability and biological fidelity inherent in mechanistic models.