An information-dynamical approach to characterise and model complex systems

This project has as its main goal the determination of the pathways for the information flow in complex systems and complex networks. We also aim at proposing ways to determine how much information can be exchanged among the many subsystems forming those complex systems. We will then apply this knowledge to characterise, predict, and model data coming from complex systems. These applications can be imagined as a sophisticated, simple and innovative way for conditional monitoring a complex system. By a COMPLEX NETWORK we mean networks formed by nodes whose dynamical description is known in a way that if needed we can simulate the system in the computer. Examples of complex networks that we will be considering in this project are neural networks, chaotic networks, and ecological stochastic networks. By a COMPLEX SYSTEM we mean a system formed by a large number of subsystems (which we conveniently refer to as nodes) that interact with other subsystems in a complicated manner and is subject to the influence and interactions with its environment. Its equations of motion, assumed to be higher dimensional, are unknown. Examples of complex systems we will be considering in this project are the weather, cardiac cells, and the human heart and brain. The reason for studying simultaneously complex networks and complex systems is essentially because our fundamental and more mathematical oriented work in complex networks will permit us to construct and test theoretical tools to be applied in the analysis of the data coming from complex systems. Besides, the data will guide us in the right direction to derive theoretical tools aimed in solving long-lasting problems in complex systems.Measuring information transfer in complex networks and complex systems is a very difficult task. In the real world data sets do not always contain a sufficient amount of points with a sufficient resolution to calculate accurate probability of events. As a result, standard techniques provide often biased results with the value for the amount of information obtained depending on the resolution of the experiment and on the number of points. For that reason, we have developed an alternative approach for measuring the amount of information exchanged between two nodes in a complex network or the amount of information shared between two data sets, without having to calculate probabilities. And this project will test, apply and generalise this approach within the context of complex systems. For example, we will show that our approach allows one to measure information exchange not only between two nodes in a complex network but also between groups of nodes. This will allow us to measure how much information two data sets share even when the data sets have different dimensions. Another example of how the proposed approach will be helpful for treating complex systems is because it can be applied to data sets acquired with completely different sampling rates. We will separate this work into two Research projects. Research Project 1 is devoted to study complex networks, and it will be mainly carried out by one post-doc, whereas Research Project 2 is devoted to study complex systems, and it will be mainly carried out by 2 PhD students (with assistance from the post-doc). One of the main outcomes of this project is to provide minimal models for the complex networks and the complex systems studied by creating the Network of Measured Data, which is the network that represents how nodes in the networks are functionally connected and how data in the complex systems are also functionally connected. The Network of Measured Data can be imaged as the skeleton of the system which will assist us in the modelling of data coming from complex systems. These models will not yield the dynamics responsible for a given data set, but will approximately reconstruct a data set based on another data set that is functionally connected to the data set to be modelled.

Short-term: How can we monitor the brain? How measurements should be done? How many places in the brain should be monitored? Which data should be stored? How to predict the behaviour of a place in the brain by observing another place? These questions are universal in the sense that not only neuroscientists would benefit from them but also people from a large spectra of other areas. Replace the word brain appearing in this paragraph by temperature or humidity, patient by station, comma by a place in the Earth and healthy by another place in the Earth, and then, our project would provide answers for these same problems in the area of climate or whether, economy and health. Our knowledge will be immediately transferred to the society and academical world in a series of ways. We will train 2 PhD students and 1 post-doc who may deliver this knowledge to the industrial and academical word. Additionally, we will make available open-source computer codes in Matlab for industrialist and academic people to treat their data and allowing them to answer similar questions to those previously stated. Another way we plan to transfer our knowledge will be by inviting researchers of related fields to Aberdeen, to participate in conferences and to submit manuscripts to scientific journals, including the open-access journals. Long-term impact: From the academic point of view, I propose to identify the deterministic dynamical components of a complex system. But, the applicability of the proposed approaches are beyond the spectra of the academic world. It will provide a powerful tool to deal with problems the society is currently facing. Some examples are the geophysical hazards caused by climatic and meteorological conditions (e.g, floods, hurricanes and droughts) and the ones caused by geological and geomorphological reasons (e.g., landslides, tsunamis and earthquakes). In all these cases, monitoring of the Earth needs to be done in a huge amount of points, the data is higher-dimensional and, in spite of that one wants to predict when the next tsunami is about to happen, by making observations in a place where it will probably not happen. The transition to a low carbon economy will require an electricity grid that provides a more reliable and cost effective system for transporting electricity from power stations to homes, business and industry. The solution for this is the construction of a smarter grid that understands variation in energy source and demand. In order to construct and use a ``smarter'' grid the energy agencies of the UK have firstly to bear in mind that: (i) a complete monitoring of all the grid state variables is very unlikely; (ii) optimal supply of demand can only be achieved if a good prediction of both supply and demand is accomplished. This project proposes an intelligent way to make an autonomous an efficient monitoring of a complex system as the ``smarter'' grid and it proposes a way to model and make predictions for the supply and demand of energy in this grid. My plan to transfer the acquired knowledge to the people responsible for constructing a ``smarter'' power grid is already taking place. I am participating in the energy theme meetings and discussions of the Scottish Universities Physics Alliance (SUPA) in order to use physics to solve strategic problems related to energy. Maintaining reliable energy supplies and promoting competitive markets in the UK is one of the resons why the subsea should be explored. This work can contribute to that by allowing one to make an efficient monitoring of the subsea oil & gas fields. Our scientific achievements will be transported to the oil and gas industries through our current participation in the series of meetings organised by the National Subset Research Institute (www.nsri.org.uk) to create a common environment between academics and the oil & gas industry for the development of new technologi