There are a few possible topics for a PhD study that may attract a scholarship. Guided Self-organisation in Complex Networks Complex Systems such as modern power grids, sensor networks, communication and transport systems, and so on, are characterised by rich interactions among components (hubs, spatial regions, network nodes, agents, neurons, etc.), producing non-trivial information flows, irregular network topologies and nonlinear dynamics. In addition, complex systems evolve over time, making their management and control extremely challenging. Cascading failures in power grids, bottlenecks and loss of data in sensor and communication networks, traffic disruption, are all manifestations of these challenges. An important research area providing solutions to many of these challenges is guided self-organisation.  Typically, self-organisation (SO) is defined as the evolution of a system into an organised form in the absence of external pressures. SO within a system brings about several attractive properties, in particular, robustness, adaptability and scalability. In the face of perturbations caused by adverse external factors or internal component failures, a robust self-organising system continues to function. Moreover, an adaptive system may re-configure when required, degrading in performance “gracefully” rather than catastrophically. In certain circumstances, a system may need to be extended with new components and/or new connections among existing modules — without SO such scaling must be preoptimised in advance, overloading the traditional design process. In general, SO is a not a force that can be applied very naturally during a design process. In fact, one may argue that the notions of design and SO are contradictory: the former approach often assumes a methodical step-by-step planning process with predictable outcomes, while the latter involves non-deterministic spontaneous dynamics with emergent features. Thus, the main challenge faced by designers of self-organising systems is how to achieve and control the desired dynamics. Erring on the one side may result in over-engineering the system, completely eliminating emergent patterns and suppressing an increase in internal organisation with outside influence. Strongly favouring the other side may leave too much non-determinism in the system’s behaviour, making its verification and validation almost impossible. The balance between design and SO is the main theme of  guided self-organisation  (GSO). As many complex systems are amenable to be described as networks (e.g., genetic regulatory networks, structural or functional cortical networks, ecological systems, metabolism of biological species, power grids, etc.), it becomes increasingly clear that GSO applied at the network level may produce particularly interesting results. Among specific areas of GSO at the network level, the PhD study may address the following: various network growth models that have been recently proposed and studied to emulate the features of the real-world networks, e.g. the preferential attachment model, which explains scale-free power law degree distributions observed in many real-world networks; investigation of network motifs and subgraphs in order to understand and analyse the local structure and function of networks: the presence of a certain motif in a network may mean that that motif plays an important role in the overall functionality of the network; propagation and processing of information within networks analysed as (Shannon) information dynamics: such analysis requires to consider not only networks' topology, but also the time-series dynamics at individual nodes; phase transitions of network properties between ordered and chaotic regimes, where information transfer is often maximised, and other nonlinear phenomena related to criticality in networks. Optimal Coding in Distributed Systems One of the most fundamental problems in biology and artificial life is the definition and understanding of “the gene”. As pointed out by Carl Woese, whose work provided a very strong motivation for this study, this problem continues to contribute to much debate between classical biologists who understand “the gene to be defined by the genotype-phenotype relationship, by gene expression as well as gene replication” and many molecular biologists who declared the problem to be solved when the Watson-Crick structure of DNA clearly revealed the mechanism of gene replication (Woese, 2004). Woese strongly argues against fundamentalist reductionism and presents the real problem of the gene as “how the genotype-phenotype relationship had come to be”. In other words, the main question is how the mechanism of translation evolved. The evolution of the translation mechanism is a complicated process, and we may only intend to analyse its simplified models. However, in doing so we shall take a principled approach and consider a model of evolutionary dynamics in a generic information-theoretic way. In taking the information-theoretic view, we hope to understand the pressures that forced a transition from a) the evolutionary stage, where the capacity to represent nucleic acid sequence symbolically in terms of an amino acid sequence did not yet exist,  to b) the phase of nucleic acid life operating with “proto-symbols” that encoded features of primitive cells in dedicated sequences and enabled a rudimentary translation. The assumption is that the reason for the increase in complexity can be identified as communication within a complex, sophisticated network of interactions. Modelling of the evolutionary dynamics proposed in this PhD study may explain mechanisms resolving Eigen’s paradox (Eigen, 1971). Simply stated, Eigen’s paradox amounts to the following: without error correction enzymes, the maximum size of a replicating molecule is about 100 base pairs; in order for a replicating molecule to encode error correction enzymes, it must be substantially larger than 100 bases (Wikipedia, 2009). Another avenue to be explored in this study is the principle of least effort in communications that is related to emergence of power laws (e.g., Zipf’s law) in complex distributed systems. If you are interested in either of these topics, please drop me a line.