CICADA Cross-disciplinary Feasibility Account

The Manchester Centre for Interdisciplinary Dynamical and Computational Analysis (CICADA) is a collaboration between mathematicians, computer scientists and engineers. Many new ideas and new collaborations have been started which go beyond the original brief of CICADA, and several very novel approaches to important problems have been discovered. The purpose of this proposal is to develop resources which allow us to explore the feasibility of these new ideas in new areas. The resources included programmers to implement computational models, funds which allow CICADA to collaborate with new partners, pay for data collection and experiments to test the feasibility of the proposed approaches. There are five themes to be explored. Theme 1 is called tropical algebra of molecular processes . Tropical algebra is a branch of pure mathematics, applied in CICADA to analyse the timing of events in certain types (asynchronous) computer hardware. We have come to recognize that this formalism is equivalent to an algorithm used in molecular modelling. Therefore, we ask, can we use this approach to provide tools for modeling the timing of molecular processes within cells? If we can, will this lead to methods for summarizing the behaviour over ranges of conditions without having to simulate them all? This would have enormous implications for computational modeling.Theme 2 is about using mathematical and computational tools to model control of complex industrial processes. The aim for this feasibility project will be to set up a demonstrator project, in conjunction with the existing EPSRC project investigating energy efficiency, which is focussed on the analysis and optimizationof hybrid sub processes in paper making. This will involve both industrial trials as well as validatation by the pilot paper machine that exists at the University of Manchester. A number of machine trials need to be conducted to collect relevant data and test the control and optimization algorithms. The expected output will be an industrially-relevant case study involving both hybrid analysis and hybrid optimization. Theme 3 is called Models of the kinetics of human balance and falling . Falls are a cause of disability and even death amongst older people,and are caused by a number of different factors. Identifying strategies to help people avoid falling, or to fall more safely, would greatly improve older people's lives. Part of the CICADA project involved developing hybrid dynamical systems controllers for a walking humanoid robot. We found ourselves considering the complementary question to how do people walk; why do people fall? We are starting to develop models of how falling is perceived and reacted to by the human body using mathematical dynamical systems models and control, and plan to extend our models of control processes to walking robotics to develop strategies to help understand how falls can be prevented.Theme 4 is called Rank-order neural codes and balance . If we are trying to control the balance of a human or a robot, time is of the essence. How can spiking neurons do the real-time information processing to stabilize and balance an unstable system? Many neural systems use rank-order codes to encode information in terms of arrival times with the most important information arriving first. It is thought that this form of coding is used in certain neural systems; it is certainly the case that rank-order codes can be implemented using networks of bursting neurons. We will design a control system which using rank-order codes to see whether this principle can work. This may lead to a better understanding of neural coding as well as the origins of balance problems in humans. Theme 5 - Embedded adaptive systems must learn in changing environments. It is challenging to make a system which adapts to changes in the environment but does not learn noise. We will dynamical systems theory to develop new algorithms based on sound principles.

There are five themes outlined in the proposal, plus mechanisms to develop more. We will discuss the impact of the themes. Theme 1 - Tropical algebra of molecular processes. This proposes to develop new methods to replace simulation with analysis in certain types of complex molecular modelling, and other kinds of simulations in which formation of complexes governs the dynamics. If successful, this could contribute to understanding how processes in cells work. Immediate beneficiaries will be molecular and systems biologists and computational scientists; in the long term this could have wide implications in mathematical modelling. It will provide new formalisms for analysing large-scale complex computational models and may led to new algorithms. If this can increase the information we can get from systems models of processes in cells, it may contribute to new understanding of health or disease or the action of drugs. Theme 2 - Hybrid dynamical systems for optimising complex industrial processes. The beneficiaries of this work will be industries which need to control industrial processes, particular those with safety critical components, and engineers and companies which provide controllers for such systems. The particular study is about using controllers to reduce energy use. This could have positive impact on the bottom lines of companies who adopt these control strategies, and could help reduce carbon emissions and energy use. Theme 3 - Models of the kinetics of human balance and falling. This will explore sources of instability leading to falling in models of humans. Immediate beneficiaries will include researchers in human kinetics. Balance problems are ubiquitious in aging populations, so long term beneficiaries will include medical providers and the patients and their families. Theme 4 - Rank-order codes neural codes and balance. This will have the same beneficiaries as above, because it is also trying to understand how balance is achieved in humans, from a neural coding point of view. However, this will undoubtedly lead to new digital hardware designs, so it will benefit digital industry and robot designers and real-time sensing systems designers. Theme 5 - Hybrid dynamical systems for adaptive control in changing environments. The beneficiaries will be computational scientists such as researchers in machine learning who develop algorithms for learning in drifting environments, and companies who use these systems. We will hold workshops involving the two comm, the first is accessible through Dr. Shapiro's involvement in the machine learning community, and the latter could be assessed through CICADA's connections with Unilever and BT.