L3

The birth of fixed-wing, powered flight in the first decade of the twentieth century brought with it significant potential for pilots to return to Earth by unintended, often fatal, means. I will discuss the nature of the contemporary mathematical and engineering debates associated with these facets of flight, and the practical steps taken to facilitate safer aircraft and more robust operating procedures.

We present a framework for the design, analysis and application of computational multiscale methods for slow-fast high-dimensional stochastic processes. We call these processes "microscopic'', and assume existence of an approximate "macroscopic'' model that captures the slow behaviour of a selected set of macroscopic state variables. The methodology combines short bursts of microscopic simulation with extrapolation at the macroscopic level. The methodology requires the careful study of a few key algorithmic ingredients. First, we need to properly initialise the microscopic system, based on a given macroscopic state and (possibly) a prior microscopic state that contains additional information about the system. Second, we need to control the variance of the noise that originates from the microscopic Monte Carlo simulation. Third, we need to analyse stability of the extrapolation step. We will discuss these aspects on two types of model problems -- scale-separated SDEs and kinetic equations -- and show the efficacity of the resulting methods in diverse applications, ranging from tumor growth to fusion energy.

The statistical physics governing phase-ordering dynamics following a symmetry breaking rst-order phase transition is an area of active research. The Coarsening/Ageing of the ensemble of phase domains, wherein irreversible annihilation or joining of domains yields a growing characteristic domain length, is an omniprescent feature whose universal characteristics one would wish to understand. Driven kinetic Ising models and growing nano-faceted crystals are theoretically important examples of such Coarsening (Ageing) Dynamical Systems (CDS), since they additionally break thermodynamic uctuation-dissipation relations. Power-laws for the growth in time of the characteristic size of domains, and a concomitant scale-invariance of associated length distributions, have so frequently been empirically observed that their presence has acquired the status of a principle; the so-called Dynamic-Scaling Hypothesis. But the dynamical symmetries of a given CDS- its Coarsening Group G - may include more than the global spatio-temporal scalings underlying the Dynamic Scaling Hypothesis. In this talk, I will present a recently developed theoretical framework (Ref.[1]) that shows how the symmetry group G of a Coarsening (ageing) Dynamical System necessarily yields G-equivariance (covariance) of its universal statistical observables. We exhibit this theory for a variety of model systems, of both thermodynamic and driven type, with symmetries that may also be Emergent (Ref. [2,3]) and/or Hidden. We will close with a magical theoretical coarsening law that combines Lorentzian and Parabolic symmetries!

References
[1] Lorentzian symmetry predicts universality beyond scaling laws, SJ Watson, EPL 118 (5), 56001, (Aug.2, 2017) Editor's Choice
[2] Emergent parabolic scaling of nano-faceting crystal growth Stephen J. Watson, Proc. R. Soc. A 471: 20140560 (2015)
[3] Scaling Theory and Morphometrics for a Coarsening Multiscale Surface, via a Principle of Maximal Dissipation", Stephen

Brain convolutions are specificity of mammals. Varying in intensity according to the animal species, it is measured by an index called the gyrification index, ratio between the effective surface of the cortex compared to its apparent surface. Its value is closed to 1 for rodents (smooth brain), 2.6 for new-borns and 5 for dolphins.  For humans, any significant deviation is a signature of a pathology occurring in fetal life, which can be detected now by magnetic resonance imaging (MRI). We propose a simple model of growth for a bilayer made of the grey and white matter, the grey matter being in cortical position. We analytically solved the Neo-Hookean approximation in the short and large wavelength limits. When the upper layer is softer than the bottom layer (possibly, the case of the human brain), the selection mechanism is dominated by the physical properties of the upper layer. When the anisotropy favours the growth tangentially as for the human brain, it decreases the threshold value for gyri formation. The gyrification index is predicted by a post-buckling analysis and compared with experimental data. We also discuss some pathologies in the model framework.

Discontinuous solutions, such as cracks or cavities, can suddenly appear in elastic solids when a limiting condition is reached. Similarly, self-contacting folds can nucleate at a free surface of a soft material subjected to a critical compression. Unlike other elastic instabilities, such as buckling and wrinkling, creasing is still poorly understood. Being invisible to linearization techniques, crease nucleation is a problem of high mathematical complexity.

In this talk, I will discuss some recent theoretical insights solving the quest for both the nucleation threshold and the emerging crease morphology.  The analytic predictions are in  agreement with experimental and numerical data. They prove a fundamental insight either for understanding the creasing onset in living matter, e.g. brain convolutions, or for guiding engineering applications, e.g. morphable meta-materials.

This will be a whistle-stop tour of a few topics on infectious disease modelling, mainly influenza. Topics to include:

• challenges in capturing dynamics of pathogens with multiple co-circulating strains
• untangling the 2009 influenza pandemic from medical insurance claims data from the US
• bioinformatic methods to detect viral packaging signals
• and a big science project (top secret until the talk!)

Julia will be visiting the Mathematical Institute on sabbatical this term, and hopes this talk will help us find areas of overlapping interests.

Image use continues to increase in both biomedical sciences and clinical practice. State of the art acquisition techniques allow characterisation from subcellular to whole organ scale, providing quantitative information of structure and function. In the heart, for example, images acquired from a single modality (cardiac MRI) can characterise micro- and macrostructure, describe mechanical function and measure blood flow. In the lungs, new contrast agents can be used to visualise the flow of gas in free breathing subjects. This provides rich new sources of information as well as new challenges to extract data in a way that is useful to clinicians as well as computer modellers.
I will describe efforts in my group to use the latest advances in machine learning to analyse images, and explain how we are applying these to the development of accurate computer models of the heart.
 

Feedback control is found extensively in many natural and technological systems. Indeed, many biological processes use feedback
to regulate key processes – examples include bacterial chemotaxis and negative autoregulation in genetic circuits. Despite the prevalence of
feedback in natural systems, its design and implementation in a Synthetic Biological context is much harder.  In this talk I will give
examples of how we implemented feedback systems in three different biological systems. The first one concerns the design of a synthetic
recombinase-based feedback loop, which results into robust expression. The second describes the use of small RNAs to post-transcriptionally
regulate gene expression through interaction with messenger RNA (mRNA). The third involves the introduction of negative feedback in a
two-component signalling system through a controllable phosphatase.  Closing, I will outline the challenges posed by the design of such
systems, both theoretical and on their implementation.