A game theoretical approach to the algebraic counterpart of the Wagner hierarchy

La hiérarchie de Wagner constitue à ce jour la plus fine classification des langages ω-réguliers. Par ailleurs, l'approche algébrique de la théorie de langages formels montre que ces ensembles ω-réguliers correspondent précisément aux langages reconnaissables par des ω-semigroupes finis pointés. Ce travail s'inscrit dans ce contexte en fournissant une description complète de la contrepartie algébrique de la hiérarchie de Wagner, et ce par le biais de la théorie descriptive des jeux de Wadge. Plus précisément, nous montrons d'abord que le degré de Wagner d'un langage ω-régulier est effectivement un invariant syntaxique. Nous définissons ensuite une relation de réduction entre ω-semigroupes pointés par le biais d'un jeu infini de type Wadge. La collection de ces structures algébriques ordonnée par cette relation apparaît alors comme étant isomorphe à la hiérarchie de Wagner, soit un quasi bon ordre décidable de largeur 2 et de hauteur ω. Nous exposons par la suite une procédure de décidabilité de cette hiérarchie algébrique : on décrit une représentation graphique des ω-semigroupes finis pointés, puis un algorithme sur ces structures graphiques qui calcule le degré de Wagner de n'importe quel élément. Ainsi le degré de Wagner de tout langage ω-régulier peut être calculé de manière effective directement sur son image syntaxique. Nous montrons ensuite comment construire directement et inductivement une structure de n''importe quel degré. Nous terminons par une description détaillée des invariants algébriques qui caractérisent tous les degrés de cette hiérarchie. Abstract The Wagner hierarchy is known so far to be the most refined topological classification of ω-rational languages. Also, the algebraic study of formal languages shows that these ω-rational sets correspond precisely to the languages recognizable by finite pointed ω-semigroups. Within this framework, we provide a construction of the algebraic counterpart of the Wagner hierarchy. We adopt a hierarchical game approach, by translating the Wadge theory from the ω-rational language to the ω-semigroup context. More precisely, we first show that the Wagner degree is indeed a syntactic invariant. We then define a reduction relation on finite pointed ω-semigroups by means of a Wadge-like infinite two-player game. The collection of these algebraic structures ordered by this reduction is then proven to be isomorphic to the Wagner hierarchy, namely a well-founded and decidable partial ordering of width 2 and height $\omega^\omega$. We also describe a decidability procedure of this hierarchy: we introduce a graph representation of finite pointed ω-semigroups allowing to compute their precise Wagner degrees. The Wagner degree of every ω-rational language can therefore be computed directly on its syntactic image. We then show how to build a finite pointed ω-semigroup of any given Wagner degree. We finally describe the algebraic invariants characterizing every Wagner degree of this hierarchy.

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.

STACK OVERWRITING ATTACKS AND DEFENCES IN UNIX ENVIRONMENT

Työn tarkoituksena on tutkia pinon ylikirjoitukseen perustuvien hyökkäysten toimintaa ja osoittaa kokeellisesti nykyisten suojaustekniikoiden olevan riittämättömiä. Tutkimus suoritetaan testaamalla miten valitut tietoturvatuotteet toimivat eri testitilanteissa. Testatut tuotteet ovat Openwall, PaX, Libsafe 2.0 ja Immunix 6.2. Testaus suoritetaan pääasiassa RedHat 7.0 ympäristössä testiohjelman avulla. Testeissä mitataan sekä tuotteiden kyky havaita hyökkäyksiä että niiden nopeusvaikutukset. Myös erityyppisten hyökkäysten ja niitä vastaan kehitettyjen metodien toimintaperiaatteet esitellään seikkaperäisesti ja havainnollistetaan yksinkertaistetuilla esimerkeillä. Esitellyt tekniikat sisältävät puskurin ylivuodot, laittomat muotoiluparametrit, loppumerkittömät merkkijonot ja taulukoiden ylivuodot. Testit osoittavat, etteivät valitut tuotteet estä kaikkia hyökkäyksiä, joten lopuksi perehdytään myös vahinkojen minimointiin onnistuneiden hyökkäysten varalta.

Efficacy of brief interdisciplinary psychotherapeutic intervention for motor conversion disorder and nonepileptic attacks.

OBJECTIVE: The objective was to compare a brief interdisciplinary psychotherapeutic intervention to standard care as treatments for patients recently diagnosed with severe motor conversion disorder or nonepileptic attacks. METHODS: This randomized controlled trial of 23 consecutive patients compared (a) an interdisciplinary psychotherapeutic intervention group receiving four to six sessions by a consultation liaison psychiatrist, the first and last sessions adding a neurological consultation and a joint psychiatric and neurological consultation, and (b) a standard care group. After intervention, patients were assessed at 2, 6 and 12 months with the Somatoform Dissociation Questionnaire (SDQ-20), Clinical Global Impression scale, Rankin scale, use of medical care, global mental health [Montgomery and Asberg Depression Rating Scale, Beck Depression Inventory, mental health component of Short Form (SF)-36] and quality of life (SF-36). We calculated linear mixed models. RESULTS: Our intervention brought a statistically significant improvement of physical symptoms [as measured by the SDQ-20 (P<.02) and the Clinical Global Impression scale (P=.02)] and psychological symptoms [better scores on the mental health component of the SF-36 (P<.05) and on the Beck Depression Inventory (P<.05)] and a reduction in new hospital stays after intervention (P<.05). CONCLUSION: A brief psychotherapeutic intervention taking advantage of a close collaboration with neurology consultants in the setting of consultation liaison psychiatry appears effective.

Detection of denial of service attacks

This thesis studies techniques used for detection of distributed denial of service attacks which during last decade became one of the most serious network security threats. To evaluate different detection algorithms and further improve them we need to test their performance under conditions as close to real-life situations as possible. Currently the only feasible solution for large-scale tests is the simulated environment. The thesis describes implementation of recursive non-parametric CUSUM algorithm for detection of distributed denial of service attacks in ns-2 network simulator – a standard de-facto for network simulation.

"Efficacy of brief interdisciplinary psychotherapeutic intervention for moto conversion disorder and non-epileptic attacks"

Comparer une intervention psychothérapeutique interdisciplinaire brève à une prise en charge standard comme traitements pour des patients ayant récemment été diagnostiqués comme souffrant d'un trouble de conversion moteur sévère ou d'attaques non-épileptiques. Méthodes Cette étude randomisée contrôlée de 23 patients consécutifs a comparé a) un groupe d'intervention psychothérapeutique interdisciplinaire recevant 4-6 séances par un psychiatre de liaison, la première et dernière séance étant couplée à une consultation neurologique et à une consultation conjointe par le neurologue et le psychiatre; b) un groupe de prise en charge standard. Après l'intervention, les patients ont été évalués à 2, 6 et 12 mois par le questionnaire de dissociation somatoforme SDQ-20, l'échelle d'impression clinique globale, l'échelle de Rankin, l'utilisation des services de santé, la santé mentale en général (MADRS, échelle de dépression de Beck, composante de santé mentale du SF-36), la qualité de vie (SF-36). Nous avons calculé des modèles linéaires mixtes. Résultats Notre intervention a mené à une amélioration statistiquement significative ? des symptômes physiques (par une mesure du SDQ-20 (p<0.02), et par l'échelle de l'impression clinique globale (p=0.02)) ? des symptômes psychologiques (meilleurs scores à la composante de santé mentale du SF-36 (p<0.05) et à l'inventaire de dépression de Beck (p<0.05)) ? et à une réduction des nouvelles hospitalisations après l'intervention (p<0.05). Conclusion Une intervention psychothérapeutique interdisciplinaire brève en étroite collaboration avec des spécialistes en neurologie dans un cadre de psychiatrie de consultation et liaison a un effet statistiquement significatif sur l'amélioration de patients souffrant de trouble de conversion moteur et d'attaques non-épileptiques.

Many valued algebraic structures as measures of comparison

This thesis studies the properties and usability of operators called t-norms, t-conorms, uninorms, as well as many valued implications and equivalences. Into these operators, weights and a generalized mean are embedded for aggregation, and they are used for comparison tasks and for this reason they are referred to as comparison measures. The thesis illustrates how these operators can be weighted with a differential evolution and aggregated with a generalized mean, and the kinds of measures of comparison that can be achieved from this procedure. New operators suitable for comparison measures are suggested. These operators are combination measures based on the use of t-norms and t-conorms, the generalized 3_-uninorm and pseudo equivalence measures based on S-type implications. The empirical part of this thesis demonstrates how these new comparison measures work in the field of classification, for example, in the classification of medical data. The second application area is from the field of sports medicine and it represents an expert system for defining an athlete's aerobic and anaerobic thresholds. The core of this thesis offers definitions for comparison measures and illustrates that there is no actual difference in the results achieved in comparison tasks, by the use of comparison measures based on distance, versus comparison measures based on many valued logical structures. The approach has been highly practical in this thesis and all usage of the measures has been validated mainly by practical testing. In general, many different types of operators suitable for comparison tasks have been presented in fuzzy logic literature and there has been little or no experimental work with these operators.

$E_{1}$-Formality of complex algebraic varieties

Let $X$ be a smooth complex algebraic variety. Morgan showed that the rational homotopy type of $X$ is a formal consequence of the differential graded algebra defined by the first term $E_{1}(X,W)$ of its weight spectral sequence. In the present work, we generalize this result to arbitrary nilpotent complex algebraic varieties (possibly singular and/or non-compact) and to algebraic morphisms between them. In particular, our results generalize the formality theorem of Deligne, Griffiths, Morgan and Sullivan for morphisms of compact Kähler varieties, filling a gap in Morgan"s theory concerning functoriality over the rationals. As an application, we study the Hopf invariant of certain algebraic morphisms using intersection theory.

Fuzzy subgroups, algebraic and topological points of view and complex analysis

Fuzzy subsets and fuzzy subgroups are basic concepts in fuzzy mathematics. We shall concentrate on fuzzy subgroups dealing with some of their algebraic, topological and complex analytical properties. Explorations are theoretical belonging to pure mathematics. One of our ideas is to show how widely fuzzy subgroups can be used in mathematics, which brings out the wealth of this concept. In complex analysis we focus on Möbius transformations, combining them with fuzzy subgroups in the algebraic and topological sense. We also survey MV spaces with or without a link to fuzzy subgroups. Spectral space is known in MV algebra. We are interested in its topological properties in MV-semilinear space. Later on, we shall study MV algebras in connection with Riemann surfaces. In fact, the Riemann surface as a concept belongs to complex analysis. On the other hand, Möbius transformations form a part of the theory of Riemann surfaces. In general, this work gives a good understanding how it is possible to fit together different fields of mathematics.

Remarks on an algebraic semantics for paraconsistent Nelson's logic

In the paper Busaniche and Cignoli (2009) we presented a quasivariety of commutative residuated lattices, called NPc-lattices, that serves as an algebraic semantics for paraconsistent Nelson's logic. In the present paper we show that NPc-lattices form a subvariety of the variety of commutative residuated lattices, we study congruences of NPc-lattices and some subvarieties of NPc-lattices.

Clinical features of panic patients sensitive to hyperventilation or breath-holding methods for inducing panic attacks

Our aim was to compare the clinical features of panic disorder (PD) patients sensitive to hyperventilation or breath-holding methods of inducing panic attacks. Eighty-five PD patients were submitted to both a hyperventilation challenge test and a breath-holding test. They were asked to hyperventilate (30 breaths/min) for 4 min and a week later to hold their breath for as long as possible, four times with a 2-min interval. Anxiety scales were applied before and after the tests. We selected the patients who responded with a panic attack to just one of the tests, i.e., those who had a panic attack after hyperventilating (HPA, N = 24, 16 females, 8 males, mean age ± SD = 38.5 ± 12.7 years) and those who had a panic attack after breath holding (BHPA, N = 20, 11 females, 9 males, mean age ± SD = 42.1 ± 10.6 years). Both groups had similar (chi² = 1.28, d.f. = 1, P = 0.672) respiratory symptoms (fear of dying, chest/pain disconfort, shortness of breath, paresthesias, and feelings of choking) during a panic attack. The criteria of Briggs et al. [British Journal of Psychiatry, 1993; 163: 201-209] for respiratory PD subtype were fulfilled by 18 (75.0%) HPA patients and by 14 (70.0%) BHPA patients. The HPA group had a later onset of the disease compared to BHPA patients (37.9 ± 11.0 vs 21.3 ± 12.9 years old, Mann-Whitney, P < 0.001), and had a higher family prevalence of PD (70.8 vs 25.0%, chi² = 19.65, d.f. = 1, P = 0.041). Our data suggest that these two groups - HPA and BHPA patients - may be specific subtypes of PD.

Effect of vitamin D therapy in addition to amitriptyline on migraine attacks in pediatric patients

The purpose of this study was to investigate the effect of supplementary vitamin D therapy in addition to amitriptyline on the frequency of migraine attacks in pediatric migraine patients. Fifty-three children 8-16 years of age and diagnosed with migraine following the International Headache Society 2005 definition, which includes childhood criteria, were enrolled. Patients were classified into four groups on the basis of their 25-hydroxyvitamin D [25(OH)D] levels. Group 1 had normal 25(OH)D levels and received amitriptyline therapy alone; group 2 had normal 25(OH)D levels and received vitamin D supplementation (400 IU/day) plus amitriptyline; group 3 had mildly deficient 25(OH)D levels and received amitriptyline plus vitamin D (800 IU/day); and group 4 had severely deficient 25(OH)D levels and was given amitriptyline plus vitamin D (5000 IU/day). All groups were monitored for 6 months, and the number of migraine attacks before and during treatment was determined. Calcium, phosphorus alkaline phosphatase, parathormone, and 25(OH)D levels were also determined before and during treatment. Results were compared between the groups. Data obtained from the groups were analyzed using one-way analysis of variance. The number of pretreatment attacks in groups 1 to 4 was 7±0.12, 6.8±0.2, 7.3±0.4, and 7.2±0.3 for 6 months, respectively (all P>0.05). The number of attacks during treatment was 3±0.25, 1.76±0.37 (P<0.05), 2.14±0.29 (P<0.05), and 1.15±0.15 (P<0.05), respectively. No statistically significant differences in calcium, phosphorus, alkaline phosphatase, or parathormone levels were observed (P>0.05). Vitamin D given in addition to anti-migraine treatment reduced the number of migraine attacks.

Is All Fair in Law and War? The Ambiguous Principle of Proportionality of Collateral Damage and the CIA Drone Attacks in Pakistan

Tutkielma käsittelee Yhdysvaltain CIAn miehittämättömiä lennokki-iskuja Pakistanissa kansainvälisen humanitaarisen oikeuden suhteellisuusperiaatteen näkökulmasta. Suhteellisuusperiaatteen mukaan aseellisista iskuista saatavan sotilaallisen hyödyn tulee olla suhteellinen verrattuna siviileille aiheutuvaan haittaan. CIAn iskuja Pakistanissa on kritisoitu, että ne eivät täytä suhteellisuusperiaatteen asettamia vaatimuksia. Tutkielmassa perehdytään ensinnäkin selvittämään ne velvollisuudet, jotka suhteellisuusperiaate asettaa hyökkääjille. Sen jälkeen CIAn lennokki-iskuja tutkitaan näiden velvollisuuksien valossa. Tutkielmassa pyritään selvittämään antaako suhteellisuusperiaatteen luomat oikeudelliset velvollisuudet riittävää suojaa Pakistanin siviileille lennokki-iskujen tuhoja vastaan. Lisäksi pyritään selvittämään, onko lennokki-iskuissa viitteitä suhteellisuusperiaatteen vastaisista iskuista. Tutkimusmenetelmänä käytetään positivistista lainopin metodia, jonka avulla selvitetään voimassa olevaa kansainvälisen humanitaarisen tapaoikeuden suhteellisuusperiaatteen sisältöä. Oikeudellisina lähteinä käytetään pääasiassa humanitaarista tapaoikeutta, mutta tulkinnallisena apuna myös kansainvälisiä sopimuksia sekä oikeuden päätöksiä. Lisäksi oikeudellinen kirjallisuus on tutkimuksessa tärkeässä asemassa. Tutkimuksessa päädytään siihen, että suhteellisuusperiaatteen asettamat velvollisuudet hyökkääjälle ovat niin epämääräiset, että ne eivät anna riittävää suojaa siviileille. Ensinnäkin hyökkääjä voi määrittää sotilaallisen hyödyn omien päämääriensä mukaisesti suhteellisuusanalyysissä. Lisäksi kynnys sille, mikä katsotaan suhteellisuusperiaatteen vastaisuudeksi on hyvin epämääräinen ja korkea. Tämän vuoksi varotoimenpiteet iskujen suunnittelussa ovat hyvin tärkeässä asemassa myös suhteellisuusanalyysissä. Kuitenkin jos hyökkääjä edes jossain määrin osoittaa, että on tehnyt iskut hyvässä uskossa niiden laillisuudesta, iskujen katsotaan yleensä olevan suhteellisuusperiaatteen mukaisia. CIAn lennokki-iskuissa Pakistanissa on viitteitä suhteellisuusperiaatteen vastaisuudesta erityisesti ”tunnusmerkki-iskujen” osalta. ”Tunnusmerkki-iskut” johtavat yleensä vain vähäiseen sotilaalliseen hyötyyn aiheuttaen silti siviiliuhreja. Lisäksi erityisesti tunnusmerkki-iskuissa edellytetään korkeampaa tarkkuutta varotoimenpiteissä. Kuitenkin useat siviiliuhrit voivat merkitä sitä, että näitä varotoimenpiteitä ei ole noudatettu iskuissa.

An Abstract Algebraic Theory of L-Fuzzy Relations for Relational Databases

Classical relational databases lack proper ways to manage certain real-world situations including imprecise or uncertain data. Fuzzy databases overcome this limitation by allowing each entry in the table to be a fuzzy set where each element of the corresponding domain is assigned a membership degree from the real interval [0…1]. But this fuzzy mechanism becomes inappropriate in modelling scenarios where data might be incomparable. Therefore, we become interested in further generalization of fuzzy database into L-fuzzy database. In such a database, the characteristic function for a fuzzy set maps to an arbitrary complete Brouwerian lattice L. From the query language perspectives, the language of fuzzy database, FSQL extends the regular Structured Query Language (SQL) by adding fuzzy specific constructions. In addition to that, L-fuzzy query language LFSQL introduces appropriate linguistic operations to define and manipulate inexact data in an L-fuzzy database. This research mainly focuses on defining the semantics of LFSQL. However, it requires an abstract algebraic theory which can be used to prove all the properties of, and operations on, L-fuzzy relations. In our study, we show that the theory of arrow categories forms a suitable framework for that. Therefore, we define the semantics of LFSQL in the abstract notion of an arrow category. In addition, we implement the operations of L-fuzzy relations in Haskell and develop a parser that translates algebraic expressions into our implementation.