## Workshop on fast-slow dynamics

As part of the EPSRC Center for Predictive Modelling in Healthcare there will be a half-day workshop on the dynamics of fast-slow dynamical systems. Details are posted on http://emps.exeter.ac.uk/mathematics/news/event/?semID=1828&dateID=4318

All welcome!

## Upcoming workshop, 20-22nd April 2016 at Exeter

There will be a “Workshop on synchronization and oscillators with generalized coupling” hosted by the Centre on 20th to 22nd April 2016. For more information, see the workshop web pages.

## Positions available in Centre for Predictive Modelling in Healthcare

The EPSRC Center for Predictive Modelling in Healthcare, which incorporates several members from the Centre for Systems, Dynamics and Control, is looking to appoint a number of research fellows and a scientific programmer. The deadline for this round of applications is 1st March 2016.

**Research Fellow in Mathematical Modelling of Excitable Dynamics**

Based around the theme “construction and analysis of excitable dynamics in continuum systems”, the post holder will initially focus on the development of numerical and analytical reduction methods for approximation of dynamical phenomena in continuum models of excitable systems, working with Professors Vadim Biktashev and Peter Ashwin.

**Research Fellow in Mathematical Modelling of Clinical Electrophysiological Data**

Based around the theme “mathematically modelling clinically relevant electrophysiological data”, the post holder will initially focus on the development and analysis of mathematical models that can explain the mechanisms underlying electrophysiological data acquired in clinical practice, such as EEG or ECG, working with Dr Marc Goodfellow and Professor Vadim Biktashev.

**Research Fellow in Neuroendocrine Modelling and Analysis**

Based around the theme “neuroendocrine systems modelling and analysis” the post holder will work on the development of multi-scale network models of endocrine axes and hormonal secretion and understanding the amplitude and timing of exogenous delivery of hormones, working with Professors Krasimira Tsaneva-Atanasova and John Terry.

**Experimental Officer – Scientific Programmer**

The post holder will translate research quality codes into working prototypes suitable for use by end-users in healthcare (e.g. GPs, Clinicians and industry). In this regard, there is the need to communicate with both technical researchers and non-technical end-users, and to develop back-end HPC codes, as well as user-centric front-end GUIs.

## New member of staff: Dalia Terhesiu

We welcome a new member of academic staff, Dr Dalia Terhesiu, who will be joining us from Vienna in January 2016. Currently there is a fully funded (for UK students) PhD studentship available to work at the Centre for Systems, Dynamics and Control with Dr Terhesiu in the area of:

**Statistical properties of dynamical systems with infinite measure.
**

Many such systems characterized by regular variation satisfy appropriate versions of the central limit theorem. The aim of this project is to study analogous results in the absence of regular variation.

The deadline for applications is 4th January 2016, and more details are available from: http://www.exeter.ac.uk/studying/funding/award/?id=2035

## PhD studentships available

There are currently a number of PhD studentships open that are supervised by members of academic staff within the Centre:

EPSRC funded PhD in Mathematics: Statistical properties of dynamical systems with infinite measure | £14,057 per annum plus UK/EU fees for eligible students (2015-16 rates) | Mon 4th Jan 2016 | Regarding statistical properties of dynamical systems with infinite measure, the aim of this project is to focus firstly on dynamical systems that behave like Markov chains and study analogous results in the absence of regular variation. |

EPSRC funded PhD in Mathematics: Stress and Epilepsy: The role of the HPA axis in modulating brain network dynamics | £14,057 per annum plus UK/EU fees for eligible students (2015-16 rates) | Mon 4th Jan 2016 | Based within the EPSRC Centre for Predictive Modelling in Healthcare, you will work on an interdisciplinary project that aims to better understand the interplay between stress and epilepsy. |

EPSRC funded PhD in Mathematics: Modelling Gait in People with Parkinsons Disease. | £14,057 per annum plus UK/EU fees for eligible students (2015-16 rates) | Mon 4th Jan 2016 | Based within the EPSRC Centre for Predictive Modelling in Healthcare, a £2M initiative bringing together mathematicians, statisticians and clinicians, you will work on a project aiming to develop a data-driven mathematical modeling framework in order to study gait impairments in patients with Parkinson’s. |

EPSRC funded PhD in Mathematics: Predictive models for epilepsy surgery | £14,057 per annum plus UK/EU fees for eligible students (2015-16 rates) | Mon 4th Jan 2016 | Using dynamical systems theory, you will develop and study mathematical models of brain networks to understand why seizures emerge in people with epilepsy and how treatment perturbations to these networks may alleviate seizures. |

EPSRC funded PhD in Mathmatics: Mathematical modelling of neuronal activity in the nucleus reuniens: a thalamic region contributing to mammalian cognitive processing. | £14,057 per annum plus UK/EU fees for eligible students (2015-16 rates) | Mon 4th Jan 2016 | Computational modelling of the nucleus reuniens (NRe): a thalamic area contributing to mammalian cognitive processing. This project will combine mathematical analysis, numerical techniques and evolutionary optimisation to build biophysical models of neural excitability in the NRe. |

## David Rees visiting fellowship

The David Rees Distinguished Visiting Fellowship scheme enables mathematicians of international renown to spend an extended period of time at the University of Exeter to enable them to contribute to the University’s academic and intellectual activities. If you are interested in visiting Exeter for a period of up to one month, do please look at the following link for more details and how to apply.

http://emps.exeter.ac.uk/mathematics/research/david-rees-fellowship/

## A one day study in Ergodic Theory and Dynamical Systems

**22nd October 2015**, CEMPS – University of Exeter, Organiser: Ana Rodrigues

###### Morning session (in Harrison Building, room HAR 171)

- 11:30 – 12:30 Paulo Varandas (UFBA, Brasil)
- 12:30 – 13:30 Thomas Jordan (Bristol, UK)

###### Afternoon session (in Laver Building, room Laver 212)

- 15:30 – 16:30 Peter Ashwin (Exeter, UK)
- 16:30 – 17:30 Yiwei Zhang (Exeter, UK)

###### Abstracts

###### Paulo Varandas – Topological methods for problems in ergodic theory

Many chaotic dynamical systems are ‘rich’ from the topological viewpoint. This richness can be expressed by the fact that pseudo-orbits are shadowed by true orbits for the dynamics (shadowing property) or that pieces of orbits are well approximated by a orbit (specification property). These properties are satisfied by uniformly hyperbolic dynamics and some weaker versions have been established for wide classes of non-uniformly hyperbolic dynamical systems. In this talk we shall recall some of these weaker notions of shadowing and specification and describe how these can be used as very usefull tools in some problems arising in ergodic theory.

###### Thomas Jordan – Minkowski’s question mark function

Minkowski’s question mark function is a homeomprphism from [0,1] to itself which maps quadratic irrationals into the rationals. We’ll show how to view this function as a conjugacy between dynamical systems and as an invariant measure for the Gauss map (x\to 1/x\mod 1). We’ll then outline how a combination of large deviations and methods from a paper of Kaufman can be used to show the Fourier-Stieltjes transform of this function decays polynomially and give a few consequences of this fact. (Joint work with Tuomas Sahlsten).

###### Peter Ashwin – Piecewise isometric dynamics; some puzzles and problems

I will introduce and discuss some aspects of the dynamics of piecewise isometries (PWIs). These are iterated maps that are geometrically very simple (just isometries) on a number of “atoms” – convex regions that form a partition of phase space. They can be seen generalizations of interval exchange transformations to higher dimensions. PWis may arise in a number of applications but are hard to understand using standard dynamical tools based around hyperbolicity. I will outline a few results and some unsolved problems related to the dynamics, geometry and measure of the various invariant subsets that arise for PWIs in two dimensions.

###### Yiwei Zhang – A glimpse of thermodynamics formalism for interval maps

I will take a short survey on the basic setting of thermodynamics formalism for interval maps. In particular, I will introduce the standard transfer operator method in the uniformly hyperbolic maps setting, and explain how the spectral structure of this operator links with the existence/uniqueness of equilibrium state and its exponential decay of correlation. I will also explain how to extend this method for the non-uniformly hyperbolic interval maps.