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Scalability, Robustness and Fundamental Limits in Large Scale Heterogeneous Networks

Final Report Summary - SCALEHETNET (Scalability, Robustness and Fundamental Limits in Large Scale Heterogeneous Networks)

This project has been associated with the analysis and control of large scale networks of interacting dynamical systems focusing on the decentralized control of engineering networks and the reverse engineering of biological networks. A main emphasis has been given in the study of specific applications. In particular, the project funding was primarily used for the employment of a postdoctoral researcher. Two PhD students, funded from other sources, have also contributed to the research carried out.

More precisely, an investigation has been carried out on the practical relevance and implementation of decentralized control schemes whereby network stability is guaranteed by means of local conditions on the subsystems, such as ones based on passivity properties. In particular, a main application area that has been studied is stability problems in large scale electrical power systems. By considering detailed models for both generation and the transmission lines, the passivity properties of the subsystems have been explored under different transformations that can appropriately transform the mathematical representations of the systems considered and their interconnections. This allows to provide stability guarantees with more advanced models and relax various assumptions often made in the literature that can hinder the practical relevance of the analysis. Extensive simulations have been carried out as well as analysis based on realistic data, and various heuristic design approaches have been explored so as to demonstrate that the proposed stability conditions can be satisfied in practical implementations and are not conservative. We expect these results can be used as a basis for further theoretical developments that can lead to more refined design methodologies for control system design in large scale power systems, and also other application areas where stability and network optimality guarantees need to be provided.

For the case of biological networks a main emphasis has been given to the study of the effects of noise in biochemical reaction networks. Calcium signaling has been investigated as a case study, and in particular, the way intrinsic noise affects the efficiency of this mechanism. More precisely, many signaling pathways within the cells and across cells involve calcium. This is used as a means of conveying information and plays an important role in various cellular processes such as fertilization and embryogenesis, atherosclerosis, and cancer. Noise is ubiquitous in calcium signalling. Calcium channels open and close randomly, generating calcium blips and puffs and these events lead to oscillations and waves which carry information that is used to trigger or regulate cellular processes downstream, such as gene expression. A major challenge is to understand the role of noise in calcium signalling, i.e. whether it enhances or degrades information propagation. To carry out this study appropriate stochastic models for calcium oscillations and corresponding decoding mechanisms have been developed. We first considered calcium oscillations in the form of square pulses, as often used in corresponding deterministic studies, and randomization has been introduced in the period, amplitude and duty ratio of the oscillations. The effect of these randomized oscillatory signals in the regulation of a protein downstream was then investigated. Furthermore, more advanced stochastic models for calcium oscillations, which build upon existing ODE models, have been considered, and simulations were carried out by means of a hybrid Gillespie algorithm. A main finding in both cases is that when calcium is used to regulate the expression of a protein downstream, the specificity of this regulation is robust to the presence noise, and in some regimes it can even enhance it. This observation could have important implications and opens up many interesting directions for further research. It could provide, for example, further insight to the intriguing phenomenon that calcium signaling is carried out by means of oscillatory signals, as well as a better understanding to the functionality of the processes it triggers or regulates.

The outcomes above of the research have been recognized through publications, initiation of collaborations with academics at other institutions and a job offer received by a researcher who has contributed to this study. In particular, a conference paper has already been accepted at one of the leading conferences in the area of power systems and a corresponding journal paper is under review, collaborations have been initiated in the area of systems biology with academics at the university of Nottingham, and the postdoctoral researcher who has worked on the project has been offered a faculty position at a UK university.