The presented diploma thesis aims to analyze EEG signals from a nonlinear dynamics perspective and identify characteristics of deterministic chaos within them. The topic is rather challenging, requiring a solid mathematical background and some experience in the subsequent statistical processing. Unfortunately, the student's approach to this task significantly reduced the overall quality of the work.

The thesis's greatest weakness is its considerable inconsistency and poor logical coherence; mainly in Section 2. In particular, many concepts appear to be taken out of context; on the other hand, some more important ones are missing. There is a lack of a smooth transition from theoretical definitions to practical implementation, and the chosen statistical methodology is not sufficiently introduced.

The formal side of the text is also rather poor. In particular, the thesis suffers from inconsistencies in mathematical notation. The typographical layout and overall typesetting could also be better. Clearly, the text did not undergo thorough final proofreading, which should be obvious for a submission of this type.

All the aforementioned shortcomings stem mainly from bad time management during thesis preparation. The student left the crucial part of the practical calculations and the writing of the text to the last minute. The resulting time pressure precluded any deeper iteration of the text, adequate consultation on partial problems, and meaningful revision of formal and logical errors. It also seems the given dataset offered greater potential for mathematical/statistical processing.

Despite the above-mentioned rather harsh criticism, the student eventually achieved results and performed a set of calculations. The thesis thus meets the minimum requirements and can be recommended for defense.

The present thesis is focused to the detection of chaos in neural time-series.

I would like to appreciate:

1. The author conducted numerous numerical simulations and composed a text that is quite consistent and meaningful, concerning an interesting and non-trivial topic.
2. The conclusion is quite well-formulated.

Unfortunately, I have many objections, in particular:

1. The mathematical background lacks precise definitions of some terms used in the text (e.g., trajectory, dense orbit, quasiperiodic orbit).
2. The crucial notion of the text - Lyapunov's exponent - is defined in a very vague way.
3. The description of Wolf's algorithm contains inaccuracies and typographical errors.
4. On p. 28, the author claims that "Sample entropy does not directly reflect chaos but can be a valuable indicator." - What can a sample entropy be an indicator of?
5. On p. 37, it is written that "we choose m=9" and on p. 39 that "we use m=10".
6. In Section 5.3, it is written that "the phase space reconstruction is still limited by the quality of the signal, which even after filtering out most of the noise might not fulfill the original assumption on smoothness. This problem can be visible in Figure 5.6, which was recorded on electrode closer to skull and therefore being more noisy.". Unfortunately, I do not see that at all. I would appreciate a better explanation.
7. In Section 5.3, it is not explained why the number of evolution steps used to estimate LLE is set to 30.
8. In Section 6.1, it is written that "In most patients, only a small number of contacts, typically between 2 and 10, are marked as SOZ, while the remaining contacts, sometimes up to approximately 200, are considered NON-SOZ." However, in the tables presenting the conducted statistics, there are three groups: NON-SOZ, Resection, and SOZ.
9. No assumptions about the data are stated. Consequently, I am not convinced that ANOVA is an appropriate method for analysing the data. This concern is particularly relevant given that only two groups are compared and that one of them has a very small sample size (as few as two observations).

CONCLUSION:

Although the submitted text is quite complete and meaningful, its form is closer to the first iteration. It seems to me that the author did not have time to make the necessary corrections in the text. However, in my opinion, the main goals of the thesis have been achieved except for item 3 in the assignment. In view of the above, I can recommend the thesis for defence and propose an evaluation of E. Topics for thesis defence:

1. Please explain what we should see in Figures 5.5 and 5.6.
2. Please explain why you chose 30 evolution steps to estimate LLE.
3. Please explain your formulation "Since for experimental time series we do not know the tangent directions of the underlying system, the separation of nearby trajectories cannot be renormalised in the exact direction." on p. 22.