David Hartman Charles University
Prague



 David Hartman

   Everything is both simpler
than we can imagine,
and more complicated
that we can conceive.

Johann Wolfgang von Goethe

Theses

Topics for theses

There are several meta-topics, which means that we can meet and discuss in order to derive an actual topics. This part is quite dynamical, so I do not guarantee that all topics are still free. The best way is to contact me directly.
  • Complex networks
    (meta-topic - can generate more topics)

    Complex networks represents well-known still quite new field of analysis of real world systems with network character like social, biological or climate networks; there are several problems how to model them, compute their characterstics or define processes over them. Topics may include from theoretical exploration of various characteristics such as

    • extremal properties of complex network characteristics, or
    • novel approaches in graph clustering and community detection, or
    • application of random graph theory to complex network
    to actual processing of different data including
    • neurological data from studies using fMRI, EEG, iEEG etc., or
    • financial data including stock markets, or
    • Earth's climate data.

    References:
  • Communities in heterophilic networks

    This topic covers some limitations of the network community detection, namely the usability of graph neural networks while considering heterophilic networks.

    References:
  • Community detection in networks with uncertainty

    This topic discusses community detection methods in the presence of uncertainty. The result is therefore not only a set of communities, but also a certain uncertainty in community assignment.

    References:
  • Robust influence maximization

    This topic covers solving the problem of maximizing influence on networks in the presence of uncertainties or edge correlations..

    References:
  • Symmetric graphs

    This topic stay on the boundary of graph theory and algebra representing by so called algebraic graph theory. The interest of this topic is to explore graphs with various sources of symmetry. Immediate example are regular graphs having all degrees the same or more complicated vertex transitive graphs for which any pair of vertices can be mapped one into the other by an automorphism. The interest of this meta-topic is to explore various forms of highly symmetric graphs (or even more general structures) where any local morphism (e.g. isomorphism of homomorphism) can be extended to the global one (over the whole structure, e.g. automorphism or endomorphism). For example of such structure, please, refer yourself to the following review.

    References:
  • Using hypergraphs in brain networks

    The goal of this topic is to explore potential strengths of hypergraphs when used to analyze functional connectivity in Human brain. This work has graph theoretical as well as pure practical and applied part. In applied part students should be ready to get familiar to working with brain data and create tools runing particular data analysis on respective samples. For basic idea see the following paper:

    References:

Selected defended theses

Defended master theses Defended Bachelor theses