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Speaker Diarization of Meeting Data
Tůma, Radovan ; Konečný, Matej (referee) ; Karafiát, Martin (advisor)
This work is trying to propose Diarization System based on Bayesian Information Criterion (BIC). In this paper is possible to find description of background theory and short description of previously used systems. Idea of this work is to try to use methods proposed earlier in a faster and more reliable way. Proposed system was tested on some records to prove its error rate. Results of tests are not very good but some possible improvements are proposed.
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Model theory and extremal combinatorics
Konečný, Matěj ; Hubička, Jan (advisor) ; Solecki, Slawomir (referee) ; Macpherson, Dugald (referee)
This thesis is concerned with combinatorial properties of homogeneous structures such as the Ramsey property, big Ramsey degrees, EPPA, and others. What these properties have in common is that, while being finitary problems on classes of finite structures, they are equivalent to various dynamical properties of automorphism groups of the cor- responding homogeneous structures. This thesis consists of an extended introduction to these areas, a list of open problems, and ten papers of which the author is a co-author, seven of which have been published at the time of writing this thesis, the other three have been submitted. The goal is to demonstrate that, at least on the combinatorial side of things, there are many interplays of these properties which can be (and have been) exploited to further each of the areas. 1
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The Extension Property for Partial Automorphisms (EPPA) of Reducts of Relational Structures
Beliayeu, Mikhail ; Hubička, Jan (advisor) ; Konečný, Matěj (referee)
The Extension Property for Partial Automorphisms (EPPA), also called Hrusovski property, is a crucial concept in the realms of combinatorics, group theory, and model theory, linking the properties of structures and the classes of finitely generated substruc- tures that embed into them. The notion of EPPA, established by Hodges, Hodkinson, Lascar, and Shelah, has spurred significant advancements in understanding graph struc- tures and the automorphism groups associated with them. A milestone was achieved by Hrusovski, who demonstrated EPPA for the class of finite graphs. The research since has centered on categorizing more classes with EPPA, simplifying proof techniques, and understanding the broader implications of EPPA. This thesis contributes to this ongoing pursuit, specifically aiming to demonstrate EPPA for graph classes enriched by comple- mentary automorphisms. It includes an analysis of undirected and directed graphs with loops and extends the exploration to a class of general structures in a finite relational language. 1
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Semigroup-valued metric spaces
Konečný, Matěj ; Hubička, Jan (advisor)
The structural Ramsey theory is a field on the boundary of combinatorics and model theory with deep connections to topological dynamics. Most of the known Ramsey classes in finite binary symmetric relational language can be shown to be Ramsey by utilizing a variant of the shortest path completion (e.g. Sauer's S-metric spaces, Conant's generalised metric spaces, Braunfeld's Λ-ultrametric spaces or Cherlin's metrically homogeneous graphs). In this thesis we explore the limits of the shortest path completion. We offer a unifying framework - semigroup-valued metric spaces - for all the aforementioned Ramsey classes and study their Ramsey expansions and EPPA (the extension property for partial automorphisms). Our results can be seen as evidence for the importance of studying the completion problem for amalgamation classes and have some further applications (such as the stationary independence relation). As a corollary of our general theorems, we reprove results of Hubička and Nešetřil on Sauer's S-metric spaces, results of Hubička, Nešetřil and the author on Conant's generalised metric spaces, Braunfeld's results on Λ-ultrametric spaces and the results of Aranda et al. on Cherlin's primitive 3-constrained metrically homogeneous graphs. We also solve several open problems such as EPPA for Λ-ultrametric...
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Semigroup-valued metric spaces
Konečný, Matěj ; Hubička, Jan (advisor)
The structural Ramsey theory is a field on the boundary of combinatorics and model theory with deep connections to topological dynamics. Most of the known Ramsey classes in finite binary symmetric relational language can be shown to be Ramsey by utilizing a variant of the shortest path completion (e.g. Sauer's S-metric spaces, Conant's generalised metric spaces, Braunfeld's Λ-ultrametric spaces or Cherlin's metrically homogeneous graphs). In this thesis we explore the limits of the shortest path completion. We offer a unifying framework - semigroup-valued metric spaces - for all the aforementioned Ramsey classes and study their Ramsey expansions and EPPA (the extension property for partial automorphisms). Our results can be seen as evidence for the importance of studying the completion problem for amalgamation classes and have some further applications (such as the stationary independence relation). As a corollary of our general theorems, we reprove results of Hubička and Nešetřil on Sauer's S-metric spaces, results of Hubička, Nešetřil and the author on Conant's generalised metric spaces, Braunfeld's results on Λ-ultrametric spaces and the results of Aranda et al. on Cherlin's primitive 3-constrained metrically homogeneous graphs. We also solve several open problems such as EPPA for Λ-ultrametric...
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Semigroup-valued metric spaces
Konečný, Matěj ; Hubička, Jan (advisor) ; Pultr, Aleš (referee)
The structural Ramsey theory is a field on the boundary of combinatorics and model theory with deep connections to topological dynamics. Most of the known Ramsey classes in finite binary symmetric relational language can be shown to be Ramsey by utilizing a variant of the shortest path completion (e.g. Sauer's S-metric spaces, Conant's generalised metric spaces, Braunfeld's Λ-ultrametric spaces or Cherlin's metrically homogeneous graphs). In this thesis we explore the limits of the shortest path completion. We offer a unifying framework - semigroup-valued metric spaces - for all the aforementioned Ramsey classes and study their Ramsey expansions and EPPA (the extension property for partial automorphisms). Our results can be seen as evidence for the importance of studying the completion problem for amalgamation classes and have some further applications (such as the stationary independence relation). As a corollary of our general theorems, we reprove results of Hubička and Nešetřil on Sauer's S-metric spaces, results of Hubička, Nešetřil and the author on Conant's generalised metric spaces, Braunfeld's results on Λ-ultrametric spaces and the results of Aranda et al. on Cherlin's primitive 3-constrained metrically homogeneous graphs. We also solve several open problems such as EPPA for Λ-ultrametric...
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Combinatorial Properties of Metrically Homogeneous Graphs
Konečný, Matěj ; Hubička, Jan (advisor) ; Nešetřil, Jaroslav (referee)
Ramsey theory looks for regularities in large objects. Model theory studies algebraic structures as models of theories. The structural Ramsey theory com- bines these two fields and is concerned with Ramsey-type questions about certain model-theoretic structures. In 2005, Nešetřil initiated a systematic study of the so-called Ramsey classes of finite structures. This thesis is a contribution to the programme; we find Ramsey expansions of the primitive 3-constrained classes from Cherlin's catalogue of metrically homogeneous graphs. A key ingredient is an explicit combinatorial algorithm to fill-in the missing distances in edge-labelled graphs to obtain structures from Cherlin's classes. This algorithm also implies the extension property for partial automorphisms (EPPA), another combinatorial property of classes of finite structures. 1
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Speaker Diarization of Meeting Data
Tůma, Radovan ; Konečný, Matej (referee) ; Karafiát, Martin (advisor)
This work is trying to propose Diarization System based on Bayesian Information Criterion (BIC). In this paper is possible to find description of background theory and short description of previously used systems. Idea of this work is to try to use methods proposed earlier in a faster and more reliable way. Proposed system was tested on some records to prove its error rate. Results of tests are not very good but some possible improvements are proposed.
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