Parametrised enumeration

In this thesis, we develop a framework of parametrised enumeration complexity. At first, we provide the reader with preliminary notions such as machine models and complexity classes besides proving them to be well-chosen. Then, we study the interplay and the landscape of these classes and present connections to classical enumeration classes. Afterwards, we translate the fundamental methods of kernelisation and self-reducibility into equivalent techniques in the setting of parametrised enumeration. Subsequently, we illustrate the introduced classes by investigating the parametrised enumeration complexity of Max-Ones-SAT and strong backdoor sets as well as sharpen the first result by presenting a dichotomy theorem for Max-Ones-SAT. After this, we extend the definitions of parametrised enumeration algorithms by allowing orders on the solution space. In this context, we study the relations ``order by size'' and ``lexicographic order'' for graph modification problems and observe a trade-off between enumeration delay and space requirements of enumeration algorithms. These results then yield an enumeration technique for generalised modification problems that is illustrated by applying this method to the problems closest string, weak and strong backdoor sets, and weighted satisfiability. Eventually, we consider the enumeration of satisfying teams of formulas of poor man's propositional dependence logic. There, we present an enumeration algorithm with FPT delay and exponential space which is one of the first enumeration complexity results of a problem in a team logic. Finally, we show how this algorithm can be modified such that only polynomial space is required, however, by increasing the delay to incremental FPT time.In diesem Werk begründen wir die Theorie der parametrisierten Enumeration, präsentieren die grundlegenden Definitionen und prüfen ihre Sinnhaftigkeit. Im nächsten Schritt, untersuchen wir das Zusammenspiel der eingeführten Komplexitätsklassen und zeigen Verbindungen zur klassischen Enumerationskomplexität auf. Anschließend übertragen wir die zwei fundamentalen Techniken der Kernelisierung und Selbstreduzierbarkeit in Entsprechungen in dem Gebiet der parametrisierten Enumeration. Schließlich untersuchen wir das Problem Max-Ones-SAT und das Problem der Aufzählung starker Backdoor-Mengen als typische Probleme in diesen Klassen. Die vorherigen Resultate zu Max-Ones-SAT werden anschließend in einem Dichotomie-Satz vervollständigt. Im nächsten Abschnitt erweitern wir die neuen Definitionen auf Ordnungen (auf dem Lösungsraum) und erforschen insbesondere die zwei Relationen \glqq Größenordnung\grqq\ und \glqq lexikographische Reihenfolge\grqq\ im Kontext von Graphen-Modifikationsproblemen. Hierbei scheint es, als müsste man zwischen Delay und Speicheranforderungen von Aufzählungsalgorithmen abwägen, wobei dies jedoch nicht abschließend gelöst werden kann. Aus den vorherigen Überlegungen wird schließlich ein generisches Enumerationsverfahren für allgemeine Modifikationsprobleme entwickelt und anhand der Probleme Closest String, schwacher und starker Backdoor-Mengen sowie gewichteter Erfüllbarkeit veranschaulicht. Im letzten Abschnitt betrachten wir die parametrisierte Enumerationskomplexität von Erfüllbarkeitsproblemen im Bereich der Poor Man's Propositional Dependence Logic und stellen einen Aufzählungsalgorithmus mit FPT Delay vor, der mit exponentiellem Platz arbeitet. Dies ist einer der ersten Aufzählungsalgorithmen im Bereich der Teamlogiken. Abschließend zeigen wir, wie dieser Algorithmus so modifiziert werden kann, dass nur polynomieller Speicherplatz benötigt wird, bezahlen jedoch diese Einsparung mit einem Anstieg des Delays auf inkrementelle FPT Zeit (IncFPT)

Roles of polymorphisms and expression of genes coding for chemokines CX3C ligand 1 and CXC ligand 16 and their receptors in the development and progression of multiple sclerosis in Serbia

Multipla skleroza je hroniĉna inflamatorna, autoimunska, demijelinizaciona i neurodegenerativna bolest centralnog nervnog sistema (CNS-a). Hemokini i njihovi receptori predstavljaju znaĉajne medijatore inflamacije koji uĉestvuju u patogenezi odreĊenih hroniĉnih inflamatornih i autoimunskih bolesti meĊu kojima je i multipla skleroza. Ciljni hemokini u ovoj studiji, CX3C ligand 1 (CX3CL1) i CXC ligand 16 (CXCL16), specifiĉni su po tome što postoje u dve forme - kao transmembranski adhezivni molekuli i kao solubilni hemoatraktanti koji nastaju nakon proteolitiĉkog seĉenja vanćelijskih hemokinskih domena njihovih transmembranskih formi. U toku inflamatornog odgovora, na membrani endotelnih vaskularnih ćelija eksprimirani su CX3CL1 i CXCL16, a na membrani leukocita receptori za CX3CL1 (CX3CR1) i CXCL16 (CXCR6), te ovi hemokini i njihovi receptori posreduju u prodiranju leukocita iz krvi u tkivo zahvaćeno inflamacijom, podsticanjem hemotaksije i adhezije leukocita za aktivirani endotel krvnog suda. Ova studija obuhvata genetsko-epidemiološku analizu polimorfizama zamena pojedinaĉnih nukleotida u kodirajućim regionima gena, koje rezultuju zamenama aminokiselina. To su polimorfizmi V249I i T280M u genu za CX3CR1, i I123T i A181V u genu za CXCL16. U prethodnim studijama je pokazano da ovi genski polimorfizmi menjaju funkcionalna svojstva CX3CR1 i CXCL16, kao i da su asocirani sa patogenezom odreĊenih hroniĉnih inflamatornih bolesti. Uzimajući to u obzir, ova studija je imala za cilj da po prvi put ispita asocijaciju navedenih polimorfizama u genima za CX3CR1 i CXCL16 sa nastankom i progresijom multiple skleroze. Primenom alel-specifiĉne PCR metode i PIRA PCR-RFLP metode detektovani su genotipovi polimorfizama V249I i T280M u genu za CX3CR1, kod zdravih kontrola i pacijenata sa multiplom sklerozom. UtvrĊeno je da haplotip I249T280 u genu za CX3CR1 ima znaĉajno veću uĉestalost kod pacijenata sa relapsno-remitentnom (RR) formom, u odnosu na pacijente sa sekundarno-progresivnom (SP) formom multiple skleroze, što znaĉi da ovaj haplotip ima protektivni efekat na progresiju RR u SP formu bolesti...Multiple sclerosis is a chronic inflammatory, autoimmune, demyelinating and neurodegenerative disease of the central nervous system (CNS). Chemokines and their receptors are important mediators of inflammation, which are involved in pathogenesis of certain chronic inflammatory and autoimmune diseases including multiple sclerosis. Chemokines of interest in this study, CX3C ligand 1 (CX3CL1) and CXC ligand 16 (CXCL16), are specific in that they can exist either as transmembrane adhesion molecules or soluble chemoattractants being generated by proteolytic cleavage of their transmembrane forms’ extracellular domains. During the inflammatory response, CX3CL1 and CXCL16 are expressed on the surface of vascular endothelium, while the leukocytes produce membrane receptors for CX3CL1 (CX3CR1) and CXCL16 (CXCR6). Therefore, these chemokines and their receptors mediate the infiltration of leukocytes from blood into the inflamed tissue areas, by stimulation of both chemotaxis and adhesion of leukocytes to the activated endothelium of blood vessels. This study is based on genetic epidemiological analysis of single nucleotide polymorphisms, which are located in the coding regions of genes and result in amino acids’ substitutions. These are V249I and T280M substitutions in the gene coding for CX3CR1, and I123T and A181V substitutions in the gene coding for CXCL16. In previous studies these polymorphisms have been associated with the functional properties of CX3CR1 and CXCL16 as well as the pathogenesis of certain chronic inflammatory diseases. Therefore, this study aimed to investigate the association of the polymorphisms in CX3CR1 and CXCL16 genes with the development and progression of multiple sclerosis. Using the allele-specific PCR and PIRA PCR-RFLP methods, genotypes of CX3CR1 V249I and T280M polymorphisms were detected in healthy controls and patients with multiple sclerosis. Following statistical analysis showed significantly higher frequency of CX3CR1 I249T280 haplotype in patients with relapsingremitting (RR) form, compared to patients with secondary-progressive (SP) form of multiple sclerosis, so this haplotype had a protective effect on progression of RR to SP form of the disease..