# David Hartman

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

Johann Wolfgang von Goethe

## Teaching

### Actual teaching

Following subjects are organized Summer term 2024.

### Past teaching

Following subjects are organized Winter term 2023.

Following subjects are organized Summer term 2023.

Following subjects are organized Winter term 2022.

Following subjects are organized Summer term 2022.

Following subjects are organized Winter term 2021.

Following subjects are organized Summer term 2021.

Following subjects are organized winter term 2020.

Following subjects are organized summer term 2020.

Following subjects were organized winter term 2019.

Following subjects were organized summer term 2019.

### Older

• NDMI096 - Complex network analysis
• NOPT008 - Algorithms of nonlinear optimization
• NOPT051 - Interval optimization
• NDMI002 - Discrete Math

## 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:
• 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

### Ročníkové projekty (in czech)

Nabízené projekty jsou různého druhu - buďto více programovací či teoretické. Ideálním postupem řešení je následné rozšíření témat na bakalářské prace a ideální způsobem domluvy je kontakt přes email a domluva konkrétního zadání.
1. Komparativní studie komutních algoritmů

V tomto zadání je cílem vytvořit komparativní studii chování různých algoritmů detekce komunit. Cílem bude porovnání různých přístupů a selekce nejlepších algoritmů dle různých kritérií. Požadovaný jazyk implementace je Python.

Reference:

2. Centrality v hyper-grafech a multigrafech

V tomto zadání je cílem vytvořit přehled o centralitách v rozšířených strukturách grafů a hypergrafů.

Reference:
• Boccaletti, S., Bianconi, G., Criado, R., Del Genio, C. I., Gómez-Gardenes, J., Romance, M., ... & Zanin, M. (2014). The structure and dynamics of multilayer networks. Physics reports, 544(1), 1-122.
• Estrada, E., and Rodriguez-Velazquez, J. A. (2005). Complex networks as hypergraphs. arXiv preprint physics/0505137.

3. Porovnání estimátorů vzájemných informací

V tomto zadání je vytvořit či převzít srovnatelné estimátory vzájemných informací a vytvořit testující prostředí pro jejich efektivní porovnání.

Reference:
• Kraskov, A., Stögbauer, H., and Grassberger, P. (2004). Estimating mutual information. Physical review E, 69(6), 066138.
• Walters-Williams, J., and Li, Y. (2009, July). Estimation of mutual information: A survey. In International Conference on Rough Sets and Knowledge Technology (pp. 389-396). Springer, Berlin, Heidelberg.