# MiR@W: Predictive Modelling @ W

12 June 2017

Organisers: Christoph Ortner, Matteo Icardi, James Kermode (Engineering), Peter Brommer (Engineering) and

Colm Connaughton

**Speakers**

Peter Brommer (Engineering)

Colm Connaughton (Mathematics)

Andreas Dedner (Mathematics)

Weisi Guo (Engineering)

Igor Khovanov (Engineering)

Mohad Mousavi-Nezhad (Engineering)

Simon Spencer (Statistics and WASC)

**Schedule (Talks will be in Room MS.04, Mathematics Instiute)**

1000: Peter Brommer, Introduction to WCPM

1030: Weisi Gui, Molecular Communications - Information Capacity of Random Walkers

1100: Andreas Dedner, Utilizing C++ and Python for solving complex PDE systems

1130: Simon Spencer, Scalable inference for epidemic models

1200: buffet lunch in D1.07

1300: WCPM/CSC Seminar, Colm Connaughton, Oscillatory kinetics in cluster-cluster aggregation

1400: Igor Khovanov, Predictability and robustness of mathematical models: non-hyperbolicity, fluctuations and complexity

1430: Mohad Mousavi Nezhad, Computational models for heterogeneous porous media

1500: Coffee + discussion in D1.07

**Abstracts**

**Colm Connaughton**

*Oscillatory kinetics in cluster-cluster aggregation
*I will discuss the mean field kinetics of irreversible coagulation in the presence of a source of monomers and a sink at large cluster sizes which removes large particles from the system. These kinetics are described by the Smoluchowski coagulation equation supplemented with source and sink terms. In common with many driven dissipative systems with conservative interactions, one expects this system to reach a stationary state at large times characterised by a constant flux of mass in the space of cluster sizes from the small-scale source to the large-scale sink. While this is indeed the case for many systems, I will present here a class of systems in which this stationary state is dynamically unstable. The consequence of this instability is that the long-time kinetics are oscillatory in time. This oscillatory behaviour is caused by the fact that mass is transferred through the system in pulses rather than via a stationary current in such a way that the mass flux is! constant on average. The implications of this unusual behaviour the non-equilibrium kinetics of other systems will be discussed.

**Weisi Guo
**

*Molecular Communications - Information Capacity of Random Walkers*

For most of human history, we have known that nature uses chemical molecules to transfer information across multiple distance scales. At the microscopic scale, cell signalling pathways (i.e., hormones) form the foundation of multi-cellular organism functionality. At the macroscopic scale, a range of marine and airborne species conduct molecular signalling in highly stochastic channels (i.e., pheromones). Despite knowing this, we have not been able to exploit its advantages in engineering applications. Many new frontiers of engineering now demand communications in highly stochastic and hostile environments, where conventional electromagnetic and acoustic radiation fails. Examples include inside human bodies and in heavy industry applications. Dr. Weisi Guo will discuss his recent research funded by Royal Society (2016-18) and US Air Force (2017-21) on how to exploit and build molecular communication systems for a new generation of Internet-of-Nano-Things. Open challenges in this area that he is interested in Mir@W collaboration include better understanding of the achievable mutual information of random walk channels.

**Igor Khovanov**

*Predictability and robustness of mathematical models: non-hyperbolicity, fluctuations and complexity*

The modelling, analysis, design, identification, validation, prediction and control of systems' dynamic are typical tasks in engineering. The key aspect for all these tasks is the selection of essential components for a mathematical model based on a "simplification" of the reality. Ideally such a simplified model should be robust to uncertainties and perturbations. In this talk I briefly describe the concept of structurally stability which is related to the robustness of models and consider some models including micro-scale trampoline, super-lattice and ion channel. The relationship between robustness, the structure of state space, complexity and predictive power of these models are discussed.

**Simon Spencer**

*Scalable inference for epidemic models*

Statistical inference for epidemic models often relies on data augmentation techniques for imputation of hidden information, such as the times of infection. As the dimensionality and complexity of the data increase some data augmentation methods become inefficient, either because they produce chains with high autocorrelation or because they become computationally intractable. We develop a novel Markov chain Monte Carlo algorithm, which is a modification of the forward filtering backward sampling algorithm, that achieves a good balance between computational complexity and mixing properties, and thus can be used to analyse complex models on large datasets. (Joint work with Panayiota Touloupou and Barbel Finkenstadt.)