Ph.D. Projects Proposals

Open doctoral projects (as of 2018) that can be done at Complex Systems Thory Department are listed below:

  • Application of the categorization based on network local properties to empirical data analysis
  • One of the objectives of empirical data analysis is a correct classificastion of the data. In the case of large data sets or in the case of data sets that differ too delicately among themselves, the classification is carried out by means of specific algorithms that often exploit machine learning. The aim of this project is an application and development of a methodology that uses graph theory to automatic classification of data that represents different systems. As this methodology has already been applied successfully to stylometric analyses of literary texts, where it allowed us to identify authors based on the properties of the language they used, it is desired to verify its applicability also in respect to other types of data.

  • Modelling of the mountain range evolution by means of complex network formalism
  • Among the processes shaping mountaineous terrains one can list the upthrust and folding as well as the erosion triggered by atmospheric conditions, water flows and glacier movements. The most characteristic feature of the mountain landscapes are mutually complementing ridges and valleys that typically form dendritic structures with a clear hierarchy. These structures can be expressed by graphs (networks), where, fo instance, each ridge is a node and each ridge junction is an edge. The project objective is the development of a network model that reflects the ridge-system evolution and that is compliant with contemporary knowledge on the mountain forming and shaping processes.

  • Exploring linguistic networks through random walk and multifractals
  • Natural language is doubtlessly example of one of the most complex system. Study of this system is traditionally related to the analysis of written texts which are treated as observables from physics viewpoint. Characterization of the text sample can be performed within the framework of complex network formalism where the sample is represented by a network constructed through adjacency relations between words. Topological properties of such linguistic networks can be investigated through random walk on the graphs and related time series consisting of properties of visited vertices. In turn, analysis of the multifractal properties of these time series is able to uncover its possible non-trivial temporal organization directly related with network structure. Within this topic, the analysis of well-known literary works will be performed by means of above-mentioned methodology. Conducted studies, among others, will answer the question about universality of the literary networks as well as their uniqueness according to the authorship, literary genre and time of work creation.

  • Self-similarity between edges and paths in emergent networks
  • A striking fact about Nature is that it tends to create structures that are self-similar, meaning that they have features which recur across levels of scale. A well-known example is the shape of Romanesco broccoli buds. In fact, self-similarity seems to be evident also in networks of the most diverse types, from interactions between people, to proteins and brain regions, insofar as these arise from some sort of "self-organization" process. This project will build upon a recent publication of our group, wherein a new measure of network self-similarity was introduced. The candidate will apply this measure across a broad range of networks, to better understand its physical and biological significance.

  • Synchronization in networks of heterogeneous oscillators
  • When large groups of non-linear oscillators are coupled via some connections, it is often observed that they synchronize in patterns which do not trivially reflect the architecture of the connections. In fact, this is often observed even in simple arrangements such as a ring network. The synchronization patterns which emerge spontaneously have interesting features, such as the presence of "communities", and some of these features may even recall the organization of brain networks. A crucial prerequisite for this sort of emergence, is the presence of parametric mismatches between the oscillators. Networks made up of oscillators that have the same internal structure (i.e. dynamical equations) but have slightly different parameter settings have been studied extensively. However, rather little is known about networks which contain oscillators that are structurally different, such as comprising different electronic circuits. This is a limitation, because in natural networks and systems, interactions are often between completely different agents, such as different types of cells, or different species. In this project, the candidate will conduct theoretical work, numerical simulations and possibly also electronic experiments to begin to shed light onto how such networks may behave.

All the projects are expected to be completed within 4 years. Prospective candidates have to be university graduates with M.Sc. degree in physics, computer science, or related disciplines. They have to enroll on International Ph.D. Studies Programme at Institute of Nuclear Physics, Polish Academy of Sciences after passing the introductory exam.

Master degree projects

We invite graduate students to work on their diploma projects at our Department. Essentially, we do not impose any restrictions regarding the topics of such projects provided they are interesting and innovative enough to be worth dedicating months of student's time. Thus, we welcome both the students who have their own ideas that they want to work on and the students who prefer to pick one of the topics proposed by us.

We are also open to M.Sc. projects that can be done in collaboration with external companies, especially from the financial or the IT sector. This refers, for example, to students who plan to obtain their master degree while already working in industry.

We currently propose topics of master projects in the following areas:
  • →   modelling of financial markets and money
  • →   modelling of natural language
  • →   (multi)fractal analysis of empirical data
  • →   random walks on complex networks

For more details, please contact us via e-mail or our contact form.

List of former M.Sc. theses that were done at CSTD can be found here.