This thesis deals with an implementation of algorithm for computation of generator of almost split sequences ending at an indecomposable nonprojective module of path algebra over finite quiver. Algorithm is implemented in algebra system GAP (Groups, Algorithms, Programming) with additional package QPA (Quivers and Path Algebras). Powered by TCPDF (www.tcpdf.org)

Title: Algebraic, Structural and Complexity Aspects of Geometric Representations of Graphs Author: Peter Zeman Department: Computer Science Institute Supervisor: RNDr. Pavel Klavík Supervisor's e-mail: klavik@iuuk.mff.cuni.cz Keywords: automorphism groups, interval graphs, circle graphs, comparability graphs, H-graphs, recognition, dominating set, graph isomorphism, maximum clique, coloring Abstract: We study symmetries of geometrically represented graphs. We describe a tech- nique to determine the automorphism group of a geometrically represented graph, by understanding the structure of the induced action on all geometric representations. We prove that interval graphs have the same automorphism groups as trees, and for a given interval graph, we construct a tree with the same automorphism group which answers a question of Hanlon [Trans. Amer. Math. Soc 272(2), 1982]. For permutation and circle graphs, we give an inductive characterization by semidirect and wreath prod- ucts. We also prove that every abstract group can be realized by the automorphism group of a comparability graph/poset of the dimension at most four. We also study H-graphs, introduced by Biró, Hujter, and Tuza in 1992. Those are intersection graphs of connected subgraphs of a subdivision of a graph H. This thesis is the first comprehensive...

Video retrieval represents a challenging problem with many caveats and sub-problems. This thesis focuses on two of these sub-problems, namely shot transition detection and text-based search. In the case of shot detection, many solutions have been proposed over the last decades. Recently, deep learning-based approaches improved the accuracy of shot transition detection using 3D convolutional architectures and artificially created training data, but one hundred percent accuracy is still an unreachable ideal. In this thesis we present a deep network for shot transition detection TransNet V2 that reaches state-of- the-art performance on respected benchmarks. In the second case of text-based search, deep learning models projecting textual query and video frames into a joint space proved to be effective for text-based video retrieval. We investigate these query representation learning models in a setting of known-item search and propose improvements for the text encoding part of the model. 1

Práce se zabývá otázkami reprezentace zvolené částky pomocí libovolného množství mincí předep- saného typu. V první kapitole odvozujeme vzorce pro počet nereprezentovatelných částek a hodnotu největší nereprezentovatelné částky pro dvoumincové systémy. Dále ukazujeme grafový algoritmus pro výpočet Frobeniova čísla a d·kaz NP-úplnosti rozhodovacího problému reprezentovatelnosti zvolené částky v systému s více mincemi. V druhé kapitole se zabýváme výpočtem počtu reprezentací částky zvláš' v systémech o dvou nebo více mincích. Ve třetí kapitole se věnujeme otázce, zda lze ve zvoleném systému mincí použít hladový algoritmus pro nalezení reprezentace částky pomocí nejmenšího možného množství mincí. Poslední kapitola obsahuje sbírku řešených logických úloh o mincích. 1

The topic of the diploma thesis is symplectic spinor geometry. Its re- search was started by D. Shale, B. Kostant and K. Habermann. We focus our attention to one of the so called symplectic twistor operators introduced by S. Kr'ysl. We investigate the action of this operator on real even dimensio- nal vector spaces considered as symplectic manifold, its invariance properties and regularity. We describe a part of the kernel of the symplectic twistor operator when acting on symplectic spinors on R2. The kernel forms a repre- sentation of the so called metaplectic group (double cover of the symplectic group). 1

The diploma thesis deals with the sources of trust in artificial intelligence, and how these sources are conditioned by social representations. It examines what risks the user is aware of when using artificial intelligence and how various factors affect the user's thinking. Artificial intelligence is represented in my work by intelligent virtual assistants (IVA). Based on semi-structured research interviews with their users, I have identified as the main sources of trust: neutrality, belief in the future, fulfillment of expectations and closeness. The first two sources are constant and based on social structure, while the last two sources of trust are based directly on user experience and are variable over time. It was also found that social representations have a significant impact on sources of trust. I divided all social representations into three categories - mechanicality, personification, intangibility, according to which the user's perception of artificial intelligence could be assessed and, based on that, his thinking about it. Because of this, I have proved that the trust of users is conditioned by social representations. An important part of trust is risk awareness. In my work, I have identified six main risks that users are aware of: unexpected software error, mechanical error, misuse of...