We present an axiomatization of relational varieties, i.e., classes of relational structures closed under formation of products and retracts, by a certain class of first-order sentences. We apply this result to categorically equivalent algebras and primal algebras. We consider the relational varieties generated by structures with minimal clone, rigid structures and two-element structures.

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A clone is a set of finitary operations closed under composition and contain- ing all projections. We say it is finitely generated if there exist a finite subset {f1, . . . , fn} such that all the other operations can be expressed as compositions of f1, . . . , fn. We present examples of finitely and non-finitely genreated clones on finite sets. First, we demonstrate an explicit construction of operations in finitely generated clones. Secondly, we define relations such that the clones of compatible operations have restricted essential arity, and discuss several modifi- cations. Lastly, for every binary operation f which cannot be composed to yield an essentially ternary operation, we find a maximal clone of essentially at most binary operations containing f. 1

The research in this diploma thesis aims on the comparison of quantitative and qualitative characteristics of selected clones of variety Sauvignon blanc. For selected clones were compared phenological phases, uvological characteristics, analysis of grape must, wine analysis and sensory evaluation. The experiment was carried out in the vineyards of the company Ampelos a.s. It was observed eight clones of variety Sauvignon Blanc. It was observed phenological phases in the same conditions of given clones. It was then determined uvological characteristics of bunch of grapes which was aimed on the average weight of bunch of grapes, the average weight of berries, the average weight of berry, the average weight of stem, the average number of berries and the average size of bunch of grapes (length x width). In the grape must were measured the analytical values, such as the sugar content, the amount of titratable acid, pH, the assimilable nitrogen content. From the results, it was clear that clones from Czech selection are much better adapted to the Czech climatic conditions. It was also observed that not all clones from Czech selection achieved better results than clones from abroad. This was confirmed in the case of clone 29/68 which has got the worst results from the all observed clones. As an ideal option for producing high quality wines is a planting composed from multiple clones with different characteristics.

Die „donor lymphocyte infusion“ (DLI) stellt eine wirksame Therapieoption für ein Rezidiv bei Patienten mit akuter myeloischer Leukämie (AML) nach allogener Stammzelltransplantation (SZT) dar. Jedoch ist die DLI oft mit einer „graft-versus-host disease” (GvHD) assoziiert, die auf einer proinflammatorischen, gegen den Empfänger gerichteten T-Zell-vermittelten Immunantwort beruht. Eine Strategie, den „graft-versus-leukemia” (GvL)-Effekt zu steigern und dabei das Risiko einer GvHD zu mindern, besteht in dem adoptiven Transfer hoch-avider CD8+ T-Zell-Klone, welche selektiv AML-assoziierte Antigene erkennen. Daher bestand das Ziel dieser Arbeit darin, eine neue Strategie zur Generierung hoch-avider CD8+ T-Zell-Klone, welche die Leukämie-assoziierten Antigene (LAAs) Wilms‘-Tumor-Antigen 1 (WT1), Proteinase 3 (PR3), Nucleophosmin 1 (NPM1) und Survivin als attraktive Ziele für spezifische Immuntherapien erkennen, zu entwickeln. Zunächst wurden mithilfe der innovativen Streptamer-Technologie die Frequenzen von CD8+ T-Zellen mit Reaktivität gegen WT1, PR3, NPM1 und Survivin im peripheren Blut von 10 gesunden HLA-A*02:01+ Spendern analysiert. Auf diese Weise konnten jedoch nur sehr geringe bis keine detektierbaren Frequenzen LAA-spezifischer CD8+ T-Lymphozyten nachgewiesen werden. Diese Beobachtungen führten zu dem Schluss, dass AML-Peptid-spezifische CD8+ T-Zellen im Gegensatz zu Virus-spezifischen T-Zellen aufgrund deutlich geringerer Frequenzen nicht direkt aus dem peripheren Blut isoliert werden können. Daher erfolgte die in vitro-Expansion der CD8+ T-Zellen mithilfe von autologen Monozyten-abgeleiteten dendritischen Zellen (MoDCs). DCs sind als professionelle Antigen-präsentierende Zellen in der Lage, Effektorzellen des adaptiven Immunsystems zu stimulieren sowie deren Expansion zu induzieren. Im Rahmen dieser Arbeit wurde ein geeignetes Protokoll für die Generierung von Fast-MoDCs etabliert. Diese zeichneten sich durch die ausgeprägte Expression kostimulatorischer und Antigen-präsentierender Moleküle, die Sekretion großer Mengen des proinflammatorischen Zytokins IL-12 sowie ein effizientes stimulatorisches Potenzial gegenüber CD4+ T-Zellen aus. Erneute Frequenzanalysen nach zweimaliger in vitro-Stimulation mit Peptid-beladenen Fast-MoDCs mittels ELISpot ergaben einen Anstieg der Frequenzen AML-Peptid-spezifischer CD8+ T-Zellen, insbesondere von WT1126-spezifischen CD8+ T-Zellen. Daraufhin erfolgte die Anreicherung der stimulierten CD8+ T-Zellen mit Spezifität für die vier untersuchten LAAs WT1, PR3, NPM1 und Survivin mittels Streptamer-Technologie. Dabei erzielte die Anreicherung WT1126-spezifischer CD8+ T-Lymphozyten deutlich höhere Reinheiten als die von CD8+ T-Zellen mit Reaktivität gegen die Peptide PR1169, NPM1283,mut A/D und Survivin95. Aus diesem Grund wurden die weiteren Untersuchungen auf WT1126 als das bisher vielversprechendste der untersuchten Peptide begrenzt. CD8+ T-Zellen von drei gesunden Spendern wurden mit bestrahlten T2-Zellen und Fast-MoDCs, welche mit dem HLA-A*02:01-restringierten Peptid WT1126 beladen waren, stimuliert. Anschließend erfolgte die Anreicherung WT1126-spezifischer CD8+ T-Zellen mittels Streptamer-Technologie. Bereits nach einmaliger Stimulation kam es zu einer deutlichen Anreicherung WT1126-spezifischer CD8+ T-Zellen, welche effektiv in der Lage waren, Peptid-beladene Zielzellen zu lysieren. Jedoch konnte nach zweimaliger Stimulation nochmals eine deutliche Steigerung in Reinheit und Ausbeute erzielt werden. Die angereicherten Zellen wurden als Effektor-Gedächtnis-T-Zellen charakterisiert. Ausgehend von den Streptamer-isolierten CD8+ T-Zellen eines Spenders erfolgte die Generierung WT1126-spezifischer CD8+ T-Zell-Klone. Im Rahmen der Klonierung wurden 32 WT1126-spezifische CD8+ T-Zell-Klone generiert. Drei vielversprechende Klone wurden genauer hinsichtlich ihrer funktionellen Eigenschaften charakterisiert. Diese exprimierten hoch-avide T-Zell-Rezeptoren und zeigten einen heterogenen Phänotyp von zentralen Gedächtnis-T-Zellen hin zu terminal differenzierten Effektor-Gedächtnis-T-Zellen. Zudem führten sie zu einer effizienten Lyse der HLA-A*02:01+ und WT1+ Zelllinien T2 und SET-2. Darüber hinaus wurde demonstriert, dass die untersuchten Klone auch HLA-A*02:01- und WT1-exprimierende primäre Blasten von AML-Patienten effektiv lysieren. Diese Ergebnisse zeigen, dass die Streptamer-basierte Anreicherung stimulierter Tumorpeptid-spezifischer CD8+ T-Zellen vor anschließender Klonierung eine geeignete Strategie für die Generierung hoch-avider CD8+ T-Zell-Klone mit anti-tumoraler Aktivität darstellt. So generierte CD8+ T-Zell-Klone mit Reaktivität gegen AML-assoziierte Antigene können für die Entwicklung neuer immuntherapeutischer Strategien zur Therapie eines Rezidivs bei AML-Patienten nach allogener SZT verwendet werden.

This report discusses clones with nullary operations and the corresponding relational clones, both defined on arbitrary non-empty sets. The relationship between such clones and clones in the usual sense, i.e. without nullary operations, is investigated, and in particular the latter type of clones is located in the lattice of all clones. By means of two pairs of kernel and closure operators, a framework is developed that allows to transfer statements about usual clones to statements about clones with nullary constants. In this respect, familiar operators and constructions from clone theory, like the operators Pol and Inv, the closure operators belonging to the clone lattices, and the different variants of local closure operators on sets of relations and operations, respectively, are translated from the usual setting to the more general one and vice versa. The applicability of the presented machinery is demonstrated using the example of the theorem characterising Galois closed sets w.r.t. Pol-Inv as local closures of clones and relational clones, respectively.

Implication is a logical connective corresponding to the rule of causality "if ... then ...". Implications allow one to organize knowledge of some field of application in an intuitive and convenient manner. This thesis explores possibilities of automatic construction of all valid implications (implicative theory) in a given field. As the main method for constructing implicative theories a robust active learning technique called Attribute Exploration was used. Attribute Exploration extracts knowledge from existing data and offers a possibility of refining this knowledge via providing counter-examples. In frames of the project implicative theories were constructed automatically for two mathematical domains: algebraic identities and parametrically expressible functions. This goal was achieved thanks both pragmatical approach of Attribute Exploration and discoveries in respective fields of application. The two diverse application fields favourably illustrate different possible usage patterns of Attribute Exploration for automatic construction of implicative theories.

This report discusses clones with nullary operations and the corresponding relational clones, both defined on arbitrary non-empty sets. The relationship between such clones and clones in the usual sense, i.e. without nullary operations, is investigated, and in particular the latter type of clones is located in the lattice of all clones. By means of two pairs of kernel and closure operators, a framework is developed that allows to transfer statements about usual clones to statements about clones with nullary constants. In this respect, familiar operators and constructions from clone theory, like the operators Pol and Inv, the closure operators belonging to the clone lattices, and the different variants of local closure operators on sets of relations and operations, respectively, are translated from the usual setting to the more general one and vice versa. The applicability of the presented machinery is demonstrated using the example of the theorem characterising Galois closed sets w.r.t. Pol-Inv as local closures of clones and relational clones, respectively.

Title: Relational Approach to Universal Algebra Author: Jakub Opršal Department: Department of Algebra Supervisor: doc. Libor Barto, Ph.D., Department of Algebra Abstract: We give some descriptions of certain algebraic properties using rela- tions and relational structures. In the first part, we focus on Neumann's lattice of interpretability types of varieties. First, we prove a characterization of vari- eties defined by linear identities, and we prove that some conditions cannot be characterized by linear identities. Next, we provide a partial result on Taylor's modularity conjecture, and we discuss several related problems. Namely, we show that the interpretability join of two idempotent varieties that are not congruence modular is not congruence modular either, and the analogue for idempotent va- rieties with a cube term. In the second part, we give a relational description of higher commutator operators, which were introduced by Bulatov, in varieties with a Mal'cev term. Furthermore, we use this result to prove that for every algebra with a Mal'cev term there exists a largest clone containing the Mal'cev operation and having the same congruence lattice and the same higher commu- tator operators as the original algebra, and to describe explicit (though infinite) set of identities describing supernilpotence...

This study focuses on the question of the epidemiology of resistance to antibiotics in Acinetobacter baumannii, which is nowadays one of the most problematic bacterial patho- gens associated with failing antimicrobial therapy. Its aim was to define population-genetic properties, epidemiology and the nature of multidrug resistance for a sample of the current population of A. baumannii from Czechia. A total of 55 isolates were collected in eight medi- cal facilities in central Bohemia from October 2016 to May 2018. The isolates were assessed for their identity at the species, clonal and strain levels as well as resistance phenotype and genotype; they were classified into five clonal groups, each of which encompassed isolates that were likely to be epidemiologically related. The 55 isolates studied belonged, nearly exclusively, to global clone ECII, with 53 % of them forming a genetically relatively homoge- neous group characterized by extensive resistance to antibiotics (susceptible only to col- istin), the presence of genes encoding ArmA a OXA-23 (resistance to all aminoglycosides and carbapenems) and spread in all locations. The in-depth epidemiological analysis of isolates from the city of Příbram and its vicinity indicated the regional spread of two strains, one of which belonged to the...