A mathematical study of fuzzy logic; an algebraic approach

Fuzzy set theory and Fuzzy logic is studied from a mathematical point of view. The main goal is to investigatecommon mathematical structures in various fuzzy logical inference systems and to establish a general mathematical basis for fuzzy logic when considered as multi-valued logic. The study is composed of six distinct publications. The first paper deals with Mattila'sLPC+Ch Calculus. THis fuzzy inference system is an attempt to introduce linguistic objects to mathematical logic without defining these objects mathematically.LPC+Ch Calculus is analyzed from algebraic point of view and it is demonstratedthat suitable factorization of the set of well formed formulae (in fact, Lindenbaum algebra) leads to a structure called ET-algebra and introduced in the beginning of the paper. On its basis, all the theorems presented by Mattila and many others can be proved in a simple way which is demonstrated in the Lemmas 1 and 2and Propositions 1-3. The conclusion critically discusses some other issues of LPC+Ch Calculus, specially that no formal semantics for it is given.In the second paper the characterization of solvability of the relational equation RoX=T, where R, X, T are fuzzy relations, X the unknown one, and o the minimum-induced composition by Sanchez, is extended to compositions induced by more general products in the general value lattice. Moreover, the procedure also applies to systemsof equations. In the third publication common features in various fuzzy logicalsystems are investigated. It turns out that adjoint couples and residuated lattices are very often present, though not always explicitly expressed. Some minor new results are also proved.The fourth study concerns Novak's paper, in which Novak introduced first-order fuzzy logic and proved, among other things, the semantico-syntactical completeness of this logic. He also demonstrated that the algebra of his logic is a generalized residuated lattice. In proving that the examination of Novak's logic can be reduced to the examination of locally finite MV-algebras.In the fifth paper a multi-valued sentential logic with values of truth in an injective MV-algebra is introduced and the axiomatizability of this logic is proved. The paper developes some ideas of Goguen and generalizes the results of Pavelka on the unit interval. Our proof for the completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if, and only if the algebra of the valuesof truth is a complete MV-algebra. The Compactness Theorem holds in our well-defined fuzzy sentential logic, while the Deduction Theorem and the Finiteness Theorem do not. Because of its generality and good-behaviour, MV-valued logic can be regarded as a mathematical basis of fuzzy reasoning. The last paper is a continuation of the fifth study. The semantics and syntax of fuzzy predicate logic with values of truth in ana injective MV-algerba are introduced, and a list of universally valid sentences is established. The system is proved to be semanticallycomplete. This proof is based on an idea utilizing some elementary properties of injective MV-algebras and MV-homomorphisms, and is purely algebraic.

Periodontal Diseases in Tanzania

Tutkimuksen tavoitteena oli kuvata hampaiden kiinnityskudossairauksien esiintyvyyttä ja suuhygieniatottumuksia Tansaniassa. Viiden eri tutkimuksen avulla kartoitettiin suuhygieniatottumuksia, kiinnityskudosten tilaa, kiinnityskudossairauksien riskitekijöitä ja hoidon tarvetta (CPITN) sekä ienvetäymiä. Tutkimukset toteutettiin eri paikkakunnilla vuosien 1987 ja 2003 välillä. Tutkittavat valittiin satunnaisesti tai harkitusti; tutkittavien määrä vaihteli 201:stä 1764:ään. Aineistot kerättiin kysymyslomakkeilla ja kliinisten tutkimusten avulla. Kliinisesti mitattiin plakin, hammaskiven ja ienten verenvuodon määrä, ientaskujen syvyys, ienvetäymien laajuus ja puuttuvien hampaiden lukumäärä. Tutkimusvälineinä käytettiin peiliä, Williamsin ja WHO:n ientaskumittareita. Muoviharjaksista hammasharjaa ilmoitti käyttävänsä 51,5-97,8% tutkituista. Ns. harjaustikun käyttö vaihteli paljon: 0,9-32,0 %. Plakkia löydettiin 65-100 %:lla tutkituista. Hammaskiveä oli suurimmalla osalla tutkituista. Myös ienverenvuotoa löytyi valtaosalta (79-100%). Ienverenvuotoa oli enemmän miehillä kuin naisilla sekä alhaisemman koulutustason omaavilla. Neljäkymmentä vuotta täyttäneiltä löydettiin 4–5 mm:n syvyisiä ientaskuja 82,1 %:lta ja ≥ 6 mm:n taskuja 43,8 %:lta. Suun terveystottumusten ohjaamiseen oli tarvetta yli 90 %:lla, hammaskiven poistoon ja juurten pinnan tasoitukseen yli 80%:lla. Yleisimmät riskitekijät kiinnityskudossairauksille olivat ikä (≥ 35 vuotta), miessukupuoli, alhainen koulutustaso, plakin, hammaskiven ja ientulehduksen määrä sekä asuminen maaseudulla. Ienvetäymiä (≥ 4 mm) löytyi noin 54%:lla tutkituista. Ienvetäymiä oli useammin miehillä kuin naisilla ja ne olivat yhteydessä ikään sekä hammaskiven ja ienverenvuodon esiintymiseen. Suuhygieniataso tutkituilla henkilöillä oli huono ja ienvetäymien esiintyvyys korkea. Syviä ientaskuja löytyi kuitenkin harvoilta tutkituilta. Riskitekijät kiinnityskudossairauksille olivat ikä, miessukupuoli, alhainen koulutustaso, plakin, hammaskiven ja ientulehduksen määrä sekä asuminen maaseudulla. Ienvetäymien riskit olivat ikä, miessukupuoli, hammaskivi ja ienverenvuoto

Scheduling of guarded command based models

Formal methods provide a means of reasoning about computer programs in order to prove correctness criteria. One subtype of formal methods is based on the weakest precondition predicate transformer semantics and uses guarded commands as the basic modelling construct. Examples of such formalisms are Action Systems and Event-B. Guarded commands can intuitively be understood as actions that may be triggered when an associated guard condition holds. Guarded commands whose guards hold are nondeterministically chosen for execution, but no further control flow is present by default. Such a modelling approach is convenient for proving correctness, and the Refinement Calculus allows for a stepwise development method. It also has a parallel interpretation facilitating development of concurrent software, and it is suitable for describing event-driven scenarios. However, for many application areas, the execution paradigm traditionally used comprises more explicit control flow, which constitutes an obstacle for using the above mentioned formal methods. In this thesis, we study how guarded command based modelling approaches can be conveniently and efficiently scheduled in different scenarios. We first focus on the modelling of trust for transactions in a social networking setting. Due to the event-based nature of the scenario, the use of guarded commands turns out to be relatively straightforward. We continue by studying modelling of concurrent software, with particular focus on compute-intensive scenarios. We go from theoretical considerations to the feasibility of implementation by evaluating the performance and scalability of executing a case study model in parallel using automatic scheduling performed by a dedicated scheduler. Finally, we propose a more explicit and non-centralised approach in which the flow of each task is controlled by a schedule of its own. The schedules are expressed in a dedicated scheduling language, and patterns assist the developer in proving correctness of the scheduled model with respect to the original one.

Pregnancy and periodontium. A clinical, microbiological, and enzymological approach via a longitudinal study

The mechanisms leading to an enhanced susceptibility to gingivitis in pregnant women have not yet been completely described. Therefore, the current study series were performed to investigate longitudinally the influence of pregnancy on periodontal tissues, and to evaluate microbial and host response factors related to pregnancy gingivitis formation. Pregnancy-related periodontal changes were analysed in 30 generally healthy women (24- 35 years old) once per trimester, till the end of lactation. Matched non-pregnant women (n=24) served as the controls, and were examined three times, once per following month. Pregnancy-related gingival inflammation was observed as enhanced tendency towards gingival bleeding and pseudopocket formation with a concomitant decrease in plaque levels. Gingivitis reached its peak during mid-pregnancy and then decreased transiently visit by visit. After lactation, no differences in periodontal status were seen between the study and control populations. In contrast to previous studies reporting increased levels of Prevotella intermedia, a specific aim was to analyse phenotypically two identical species, P. intermedia and Prevotella nigrescens, separately using a 16S ribosomal DNA-based PCR. As a result, the increased levels of P. nigrescens were related to pregnancy gingivitis. Matrix metalloproteinases (MMPs) are involved in periodontal destruction. However, their role in pregnancy gingivitis is not well studied. Therefore, neutrophilic enzymes and proteinases, such as MMP and myeloperoxidase (MPO) levels were analysed from saliva and gingival crevicular fluid (GCF) samples during the follow-up. Despite increased inflammation and microbial shift towards anaerobes, the host response did not activate the MMP, elastase and MPO secretion during pregnancy. These results demonstrate that during pregnancy gingival inflammation is enhanced especially during the second trimester, when P. nigrescens levels in subgingival plaque were increased, whereas the neutrophilic enzymes and proteinase levels in both saliva and GCF remained low. These findings could explain, at least in part, why pregnancy gingivitis itself does not predispose or proceed to periodontitis.

Värispekrien eron laskenta

Olemassa olevat spektrieromittarit eivät vastaa riittävästi CIEDE2000-värieroa. Tämän työn tavoitteena oli toteuttaa menetelmä, joka laskee värispektrien eron siten, että tulos vastaa CIEDE2000-värieroa. Kehitystyön tuloksena syntyi menetelmä, joka perustuu ennalta laskettuihin eroihin tunnettujen spektrien välillä ja niiden perusteella johdettuihin laskentaparametreihin. menetelmällä pystyy laskemaan spektrieroja vain niiden spektrien välillä, jotka saadaan sekoittamalla tunnettuja spektrejä. Laskentaparametrien laskenta on työläs prosessi ja siksi menetelmään toteutettiin hajautus usealle tietokoneelle. Menetelmä saatiin vastaamaan hyvin CIEDE2000:ia suurimmalle osalle spektrejä harvoja poikkeuksia lukuunottamatta. Ongelmat johtuvat mallissa olevasta matemaattisesta ominaisuudesta. Spektrieromittari näyttää metameerisille spektreille nollasta poikkeavan arvon, vaikka CIEDE2000 näyttää nollaa. Tämä osoittaa spektrieromittarin oikeamman toiminnan CIEDE2000-värieroon verrattuna.

Virulence properties of Aggregatibacter actinomycetemcomitans biofilm and characterisation of its putative cytokine exploitation

Biofilms are surface-attached multispecies microbial communities that are embedded by their self-produced extracellular polymeric substances. This lifestyle enhances the survival of the bacteria and plays a major role in many chronic bacterial infections. For instance, periodontitis is initiated by multispecies biofilms. The phases of active periodontal tissue destruction and notably increased levels of proinflammatory mediators, such as the key inflammatory mediator interleukin (IL)-1beta, are typical of the disease. The opportunistic periodontal pathogen Aggregatibacter actinomycetemcomitans is usually abundant at sites of aggressive periodontitis. Despite potent host immune system responses to subgingival invaders, A. actinomycetemcomitans is able to resist clearance attempts. Moreover, some strains of A. actinomycetemcomitans can generate genetic diversity through natural transformation, which may improve the species’ adjustment tothe subgingival environment in the long term. Some biofilm forming species are known to bind and sense human cytokines. As a response to cytokines, bacteria may increase biofilm formation and alter their expression of virulence genes. Specific outer membrane receptors for interferon-γ or IL-1β have been characterised in two Gram-negative pathogens. Because little is known about periodontal pathogens’ ability to sense cytokines, we used A. actinomycetemcomitans as a model organism to investigate how the species responds to IL-1beta. The main aims of this thesis were to explore cytokine binding on single-species A. actinomycetemcomitans biofilms and to determine the effects of cytokines on the biofilm formation and metabolic activity of the species. Additionally, the cytokine’s putative internalisation and interaction with A. actinomycetemcomitans proteins were studied. The possible impact of biofilm IL-1beta sequestering on the proliferation and apoptosis of gingival keratinocyte cells was evaluated in an organotypic mucosa co-culture model. Finally, the role of the extramembranous domain of the outer membrane protein HofQ (emHofQ) in DNA binding linked to DNA uptake in A. actinomycetemcomitans was examined. Our main finding revealed that viable A. actinomycetemcomitans biofilms can bind and take up the IL-1β produced by gingival cells. At the sites of pathogen-host interaction, the proliferation and apoptosis of gingival keratinocytes decreased slightly. Notably, the exposure of biofilms to IL-1beta caused their metabolic activity to drop, which may be linked to the observed interaction of IL-1beta with the conserved intracellular proteins DNA binding protein HU and the trimeric form of ATP synthase subunit beta. A Pasteurellaceaespecific lipoprotein, which had no previously determined function, was characterized as an IL-1beta interacting membrane protein that was expressed in the biofilm cultures of all tested A. actinomycetemcomitans strains. The use of a subcellular localisation tool combined with experimental analyses suggested that the identified lipoprotein, bacterial interleukin receptor I (BilRI), may be associated with the outer membrane with a portion of the protein oriented towards the external milieu. The results of the emHofQ study indicated that emHofQ has both the structural and functional capability to bind DNA. This result implies that emHofQ plays a role in DNA assimilation. The results from the current study also demonstrate that the Gram-negative oral species appears to sense the central proinflammatory mediator IL-1beta.

Korkeapainevesisumusuuttimen virtaustekninen laadunhallinta

Tämä työ vastaa tarpeeseen hallita korkeapainevesisumusuuttimen laatua virtausmekaniikan työkalujen avulla. Työssä tutkitaan suutinten testidatan lisäksi virtauksen käyttäytymistä suuttimen sisällä CFD-laskennan avulla. Virtausmallinnus tehdään Navier-Stokes –pohjaisella laskentamenetelmällä. Työn teoriaosassa käsitellään virtaustekniikkaa ja sen kehitystä yleisesti. Lisäksi esitetään suuttimen laskennassa käytettävää perusteoriaa sekä teknisiä ratkaisuja. Teoriaosassa käydään myös läpi laskennalliseen virtausmekaniikkaan (CFD-laskenta) liittyvää perusteoriaa. Tutkimusosiossa esitetään käsitellyt suutintestitulokset sekä mallinnetaan suutinvirtausta ajasta riippumattomaan virtauslaskentaan perustuvalla laskentamenetelmällä. Virtauslaskennassa käytetään OpenFOAM-laskentaohjelmiston SIMPLE-virtausratkaisijaa sekä k-omega SST –turbulenssimallia. Tehtiin virtausmallinnus kaikilla paineilla, joita suuttimen testauksessa myös todellisuudessa käytetään. Lisäksi selvitettiin mahdolliset kavitaatiokohdat suuttimessa ja suunniteltiin kavitaatiota ehkäisevä suutingeometria. Todettiin myös lämpötilan ja epäpuhtauksien vaikuttavan kavitaatioon sekä mallinnettiin lämpötilan vaikutusta. Luotiin malli, jolla suuttimen suunnitteluun liittyviin haasteisiin voidaan vastata numeerisella laskennalla.