Abstract: Tuberculosis is a respiratory infectious disease estimated to kill 1.7 million people annually worldwide. Recently, outbreaks of multi- and extensively-drug-resistant variants of this pathogen have occurred in numerous disparate locations. TB is a fully sequenced organism, so we understand something about its metabolism, and there is a wealth of gene expression data available. But despite the importance of linking genotype to phenotype in pathogens like TB, methods to integrate these datasets have been somewhat lacking. In the first part of the talk, I'll present a computational method based on linear optimisation, for interpreting gene expression data in the context of a metabolic model, and apply it to mycolic acid production in M. tuberculosis. The method uncovers known anti-tuberculosis drugs including isoniazid, one of the main drugs to which TB is now becoming resistant.

Speaker: Dr Yuliya Kyrychko (Bristol)

Speaker: Dr Carlo Laing (Massey University, Albany, New Zealand)

Speaker: Dr Yves Capdeboscq (Oxford)

Speaker: Nigel Gilbert, Professor of Sociology and Director of the Centre for Research in Social Simulation, University of Surrey

Speaker: G.A. Pavliotis, Imperial College London

This talk has been postponed due to illness.

Abstract: 

Geophysical and plasma systems are often mentioned together because of the common basic nonlinear model used for them: Charney-Hassegawa-Mima equation (CHME). In both applications, zonal jets are often formed. This is important process which leads to transport barriers. I will describe two mechanisms, modulational instability and anisotropic inverse cascades, which lead to generation of the zonal jets.

Abstract:

Over the last years so-called {\em set oriented\/} numerical methods have been developed in the context of the numerical treatment of dynamical systems. The basic idea is to cover the objects of interest -- for instance {\em invariant manifolds\/} or {\em invariant measures\/} -- by outer approximations which are created via adaptive multilevel subdivision techniques. These schemes allow for an extremely memory and time efficient discretization of the phase space and have the flexibility to be applied to several problem types.

Abstract: 

This work focuses on the sweep-stick mechanism of particle clustering in turbulent flows whereby heavy particles cluster in a way which mimics the clustering of zero acceleration points. We present this phenomenology in 2D and 3D homogeneous, isotropic turbulence and turbulent channel flow. Crucial to the mechanism in each case is the nature of sweeping in the flow. We quantify the Stokes number dependency of the probability of the heavy particles to be at zero acceleration points and show that in the inertial range of Stokes numbers the sweep-stick mechanism is dominant over the conventionally proposed mechanism of heavy particles being centrifuged from high vorticity regions to high strain regions.

Abstract: Two great puzzles in solar astrophysics concern the source of coronal heating and the distribution of solar flares. The atmosphere of the sun is heated to one million degrees or more, possibly by swarms of tiny flares. These tiny flares could be consequences of the braiding of magnetic field lines. Reconnection between braided threads of magnetic flux can release energy stored in the braid. The larger flares exhibit a power law energy distribution. Several authors have suggested that a self-organization process in the solar magnetic field could lead to such a distribution. Here we show how reconnection of braided lines can organize the small scale structure of the field, leading to power law energy release.

Abstract: In oscillatory systems, invasions often generate periodic spatiotemporal oscillations, which undergo a subsequent transition to chaos. The periodic oscillations have the form of a wavetrain, and occur in a band of constant width. I will describe this phenomenon in detail, and will explain the concept of absolute stability of wavetrains, which is central to a full understanding of the behaviour. In applications, a key question is whether one expects spatiotemporal data to be dominated by regular or irregular oscillations, or to involve a significant proportion of both. This depends on the width of the wavetrain band. I will describe a new method for calculating this width, based on the absolute stability of the wavetrain in moving frames of reference. I will illustrate the work via two examples: the generation of wavetrains in the wake of the invasion of a prey population by predators, and spatiotemporal patterning behind propagating fronts in the complex Ginzburg-Landau equation. The work that I will describe in this talk has been done in collaboration with Matthew Smith (Microsoft Research, Cambridge) and Jens Rademacher (CWI, Amsterdam).

Abstract: In this talk the existence and nonexistence of similarity solutions is considered for the PDE arising from a simple model which has applications in both morphogen transport and the diffusion of solvents into polymeric materials.

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Abstract: Symmetries provide useful tools to study and classify differential and discrete equations, as well as to construct solutions for these equations. A new and interesting application of symmetries is that they provide a link between discrete and differential equations. Specifically, one can employ the symmetries of the former in order to derive systems of differential equations. In particular, the discrete potential KdV equation and its symmetries will be used as an illustrative example to present this derivation. It will be shown that integrability aspects, like multidimensional consistency and Bäcklund transformation, are inherited to the resulting system of differential equations by its discrete counterpart. Finally, this analysis will be extended to the class of equations to which the discrete potential KdV belongs.

Abstract: Sets of constrained orbit segments of time continuous flows are collections of trajectories that represent a whole or parts of an invariant set. A non-trivial but simple example is a homoclinic orbit. A typical representation of this set consists of an equilibrium point of the flow and a trajectory that starts close and returns close to this equilibrium point within finite time. More complicated examples are hybrid periodic orbits of piecewise smooth systems or quasi-periodic invariant tori. Even though it is possible to define generalised two-point boundary value problems for computing sets of constrained orbit segments, this is very disadvantageous in practice. In this talk we will present an algorithm that allows the efficient continuation of sets of constrained orbit segments together with the solution of the full variational problem.

Abstract: I will discuss some explicit examples of nonlinear systems that have heteroclinic attractors with depth two - namely chain recurrent attractors composed of a union of relative equilibria, connecting orbits between them as well as connecting orbits between connecting orbits. One of the examples (joint with O Podvigina) arises in the normal form for a mode interaction; the other (joint with T Chawanya) arises in a game dynamical system.

Abstract: I will discuss the effect of extrinsic noise in metabolic networks. In particular I will introduce external random fluctuations at the kinetic level, and show how these lead to a stochastic generalization of standard metabolic control analysis. While summation and connectivity theorems hold true in the presence of extrinsic noise, control coefficients are shown to incorporate its effect through an explicit dependency on the noise intensity. This leads naturally to the introduction of the concept of 'control by noise' as a way of tuning the systemic behaviour of metabolisms. I argue that this framework holds for intrinsic noise too, when time-scale separation is present in the system, and define the noise propagation problem in metabolic networks.

Abstract: When simulating actual geophysical flows, inaccuracies in initial conditions, forcing fields and in the model equations themselves, both numerical and physical, lead to differences between the actual behavior of the system and the simulation. One way to address this problem is to try to incorporate the uncertainties in the simulations, e.g. in the form of probability density functions. The problem then is that for large-dimensional simulations in e.g. numerical weather prediction, the state space is so large, typically a million variables, that no computer is large enough to store these probability density functions.So, if we want to include these uncertainties we need an efficient representation of the pdf's.

Abstract: The Lorenz system still fascinates many people because of the simplicity of the equations that generate such complicated dynamics on the famous butterfly attractor. This talk addresses the role of the stable and unstable manifolds in organising the dynamics more globally.

Abstract: How can one discover a new integrable system? Various approaches have been used to answer this question for integrable PDEs, but relatively few integrable difference equations are known at present. We introduce an approach that is based on the following observation: for a given degree of complexity, integrable difference equations commonly have more low-order conservation laws than nonintegrable ones do. We have used this observation to sift a large class of difference equations, in order to find candidates for integrability.

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Abstract: Subject of the talk will be the derivation and rigorous mathematical justification of macroscopic continuum models describing the effective dynamics of amplitude-modulated plane waves in discrete lattices. We will present different continuum models (e.g. the nonlinear Schrödinger and the three-wave-interaction equations) corresponding to different ansatz'es and describing different physical phenomena.