Sobre coincidências e pontos fixos de aplicações

Pós-graduação em Matemática Universitária - IGCE

Cercador documental amb lematització

Un cercador documental d'arxius locals, en diferents formats, que permet l'extracció i indexació de lemes en diferents idiomes (principalment català, castellà i anglès) en el que s'habilita la cerca a través d'una pàgina web allotjada en un servidor local.

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.

Classification supervisée multi-étiquette en actes de dialogue: analyse discriminante et transformations de Schoenberg

Abstract This work studies the multi-label classification of turns in simple English Wikipedia talk pages into dialog acts. The treated dataset was created and multi-labeled by (Ferschke et al., 2012). The first part analyses dependences between labels, in order to examine the annotation coherence and to determine a classification method. Then, a multi-label classification is computed, after transforming the problem into binary relevance. Regarding features, whereas (Ferschke et al., 2012) use features such as uni-, bi-, and trigrams, time distance between turns or the indentation level of the turn, other features are considered here: lemmas, part-of-speech tags and the meaning of verbs (according to WordNet). The dataset authors applied approaches such as Naive Bayes or Support Vector Machines. The present paper proposes, as an alternative, to use Schoenberg transformations which, following the example of kernel methods, transform original Euclidean distances into other Euclidean distances, in a space of high dimensionality. Résumé Ce travail étudie la classification supervisée multi-étiquette en actes de dialogue des tours de parole des contributeurs aux pages de discussion de Simple English Wikipedia (Wikipédia en anglais simple). Le jeu de données considéré a été créé et multi-étiqueté par (Ferschke et al., 2012). Une première partie analyse les relations entre les étiquettes pour examiner la cohérence des annotations et pour déterminer une méthode de classification. Ensuite, une classification supervisée multi-étiquette est effectuée, après recodage binaire des étiquettes. Concernant les variables, alors que (Ferschke et al., 2012) utilisent des caractéristiques telles que les uni-, bi- et trigrammes, le temps entre les tours de parole ou l'indentation d'un tour de parole, d'autres descripteurs sont considérés ici : les lemmes, les catégories morphosyntaxiques et le sens des verbes (selon WordNet). Les auteurs du jeu de données ont employé des approches telles que le Naive Bayes ou les Séparateurs à Vastes Marges (SVM) pour la classification. Cet article propose, de façon alternative, d'utiliser et d'étendre l'analyse discriminante linéaire aux transformations de Schoenberg qui, à l'instar des méthodes à noyau, transforment les distances euclidiennes originales en d'autres distances euclidiennes, dans un espace de haute dimensionnalité.

Tool-supported invariant-based programming

The development of correct programs is a core problem in computer science. Although formal verification methods for establishing correctness with mathematical rigor are available, programmers often find these difficult to put into practice. One hurdle is deriving the loop invariants and proving that the code maintains them. So called correct-by-construction methods aim to alleviate this issue by integrating verification into the programming workflow. Invariant-based programming is a practical correct-by-construction method in which the programmer first establishes the invariant structure, and then incrementally extends the program in steps of adding code and proving after each addition that the code is consistent with the invariants. In this way, the program is kept internally consistent throughout its development, and the construction of the correctness arguments (proofs) becomes an integral part of the programming workflow. A characteristic of the approach is that programs are described as invariant diagrams, a graphical notation similar to the state charts familiar to programmers. Invariant-based programming is a new method that has not been evaluated in large scale studies yet. The most important prerequisite for feasibility on a larger scale is a high degree of automation. The goal of the Socos project has been to build tools to assist the construction and verification of programs using the method. This thesis describes the implementation and evaluation of a prototype tool in the context of the Socos project. The tool supports the drawing of the diagrams, automatic derivation and discharging of verification conditions, and interactive proofs. It is used to develop programs that are correct by construction. The tool consists of a diagrammatic environment connected to a verification condition generator and an existing state-of-the-art theorem prover. Its core is a semantics for translating diagrams into verification conditions, which are sent to the underlying theorem prover. We describe a concrete method for 1) deriving sufficient conditions for total correctness of an invariant diagram; 2) sending the conditions to the theorem prover for simplification; and 3) reporting the results of the simplification to the programmer in a way that is consistent with the invariantbased programming workflow and that allows errors in the program specification to be efficiently detected. The tool uses an efficient automatic proof strategy to prove as many conditions as possible automatically and lets the remaining conditions be proved interactively. The tool is based on the verification system PVS and i uses the SMT (Satisfiability Modulo Theories) solver Yices as a catch-all decision procedure. Conditions that were not discharged automatically may be proved interactively using the PVS proof assistant. The programming workflow is very similar to the process by which a mathematical theory is developed inside a computer supported theorem prover environment such as PVS. The programmer reduces a large verification problem with the aid of the tool into a set of smaller problems (lemmas), and he can substantially improve the degree of proof automation by developing specialized background theories and proof strategies to support the specification and verification of a specific class of programs. We demonstrate this workflow by describing in detail the construction of a verified sorting algorithm. Tool-supported verification often has little to no presence in computer science (CS) curricula. Furthermore, program verification is frequently introduced as an advanced and purely theoretical topic that is not connected to the workflow taught in the early and practically oriented programming courses. Our hypothesis is that verification could be introduced early in the CS education, and that verification tools could be used in the classroom to support the teaching of formal methods. A prototype of Socos has been used in a course at Åbo Akademi University targeted at first and second year undergraduate students. We evaluate the use of Socos in the course as part of a case study carried out in 2007.

ONTIC: A Knowledge Representation System for Mathematics

Ontic is an interactive system for developing and verifying mathematics. Ontic's verification mechanism is capable of automatically finding and applying information from a library containing hundreds of mathematical facts. Starting with only the axioms of Zermelo-Fraenkel set theory, the Ontic system has been used to build a data base of definitions and lemmas leading to a proof of the Stone representation theorem for Boolean lattices. The Ontic system has been used to explore issues in knowledge representation, automated deduction, and the automatic use of large data bases.

El problema de Alhacén

El presente documento es un estudio detallado del problema conocido bajo el título de Problema de Alhacén. Este problema fue formulado en el siglo X por el filósofo y matemático árabe conocido en occidente bajo el nombre de Alhacén. El documento hace una breve presentación del filósofo y una breve reseña de su trascendental tratado de óptica Kitab al-Manazir. A continuación el documento se detiene a estudiar cuidadosamente los lemas requeridos para enfrentar el problema y se presentan las soluciones para el caso de los espejos esféricos (convexos y cóncavos), cilíndricos y cónicos. También se ofrece una conjetura que habría de explicar la lógica del descubrimiento implícita en la solución que ofreció Alhacén. Tanto los lemas como las soluciones se han modelado en los software de geometría dinámica Cabri II-Plus y Cabri 3-D. El lector interesado en seguir dichas modelaciones debe contar con los programas mencionados para adelantar la lectura de los archivos. En general, estas presentaciones constan de tres partes: (i) formulación del problema (se formula en forma concisa el problema); (ii) esquema general de la construcción (se presentan los pasos esenciales que conducen a la construcción solicitada y las construcciones auxiliares que demanda el problema), esta parte se puede seguir en los archivos de Cabri; y (iii) demostración (se ofrece la justificación detallada de la construcción requerida). Los archivos en Cabri II plus cuentan con botones numerados que pueden activarse haciendo “Click” sobre ellos. La numeración corresponde a la numeración presente en el documento. El lector puede desplazar a su antojo los puntos libres que pueden reconocerse porque ellos se distinguen con la siguiente marca (º). Los puntos restantes no pueden modificarse pues son el resultado de construcciones adelantadas y ajustadas a los protocolos recomendados en el esquema general.

Back to basics: how measures of lexical diversity can help discriminate between CEFR levels

This study contributes to ongoing discussions on how measures of lexical diversity (LD) can help discriminate between essays from second language learners of English, whose work has been assessed as belonging to levels B1 to C2 of the Common European Framework of Reference (CEFR). The focus is in particular on how different operationalisations of what constitutes a “different word” (type) impact on the LD measures themselves and on their ability to discriminate between CEFR levels. The results show that basic measures of LD, such as the number of different words, the TTR (Templin 1957) and the Index of Guiraud (Guiraud 1954) explain more variance in the CEFR levels than sophisticated measures, such as D (Malvern et al. 2004), HD-D (McCarthy and Jarvis 2007) and MTLD (McCarthy 2005) provided text length is kept constant across texts. A simple count of different words (defined as lemma’s and not as word families) was the best predictor of CEFR levels and explained 22 percent of the variance in overall scores on the Pearson Test of English Academic in essays written by 176 test takers.

Projeto de controladores robustos para sistemas sujeitos a falhas estruturais usando realimentação estática de saída

Pós-graduação em Engenharia Elétrica - FEIS

Controle de sistemas lineares incertos via realimentação derivativa utilizando Funções de Lyapunov dependentes de parâmetros

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Morfologia e anatomia de Paspalum L. (Poaceae, Poales) e suas implicações taxonômicas

Pós-graduação em Ciências Biológicas (Biologia Vegetal) - IBRC

On the Study of Complex Impulsive Systems

The article investigates complex impulsive systems in which the so-called controlling systems jumps effect emerges. In particular, this research includes the correctness of the solution to the impulsive control system and approximation lemmas. A 3D model example is provided which illustrates the relevance of the considered approach to the study of complex impulsive systems.

On the properness of an impulsive control extension of dynamic optimization problems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)