Robust fault detection using consistency techniques for uncertainty handling

Often practical performance of analytical redundancy for fault detection and diagnosis is decreased by uncertainties prevailing not only in the system model, but also in the measurements. In this paper, the problem of fault detection is stated as a constraint satisfaction problem over continuous domains with a big number of variables and constraints. This problem can be solved using modal interval analysis and consistency techniques. Consistency techniques are then shown to be particularly efficient to check the consistency of the analytical redundancy relations (ARRs), dealing with uncertain measurements and parameters. Through the work presented in this paper, it can be observed that consistency techniques can be used to increase the performance of a robust fault detection tool, which is based on interval arithmetic. The proposed method is illustrated using a nonlinear dynamic model of a hydraulic system

Estimating parameters for generalized mass action models using constraint propagation.

As modern molecular biology moves towards the analysis of biological systems as opposed to their individual components, the need for appropriate mathematical and computational techniques for understanding the dynamics and structure of such systems is becoming more pressing. For example, the modeling of biochemical systems using ordinary differential equations (ODEs) based on high-throughput, time-dense profiles is becoming more common-place, which is necessitating the development of improved techniques to estimate model parameters from such data. Due to the high dimensionality of this estimation problem, straight-forward optimization strategies rarely produce correct parameter values, and hence current methods tend to utilize genetic/evolutionary algorithms to perform non-linear parameter fitting. Here, we describe a completely deterministic approach, which is based on interval analysis. This allows us to examine entire sets of parameters, and thus to exhaust the global search within a finite number of steps. In particular, we show how our method may be applied to a generic class of ODEs used for modeling biochemical systems called Generalized Mass Action Models (GMAs). In addition, we show that for GMAs our method is amenable to the technique in interval arithmetic called constraint propagation, which allows great improvement of its efficiency. To illustrate the applicability of our method we apply it to some networks of biochemical reactions appearing in the literature, showing in particular that, in addition to estimating system parameters in the absence of noise, our method may also be used to recover the topology of these networks.

Memristive Computing

Memristive computing refers to the utilization of the memristor, the fourth fundamental passive circuit element, in computational tasks. The existence of the memristor was theoretically predicted in 1971 by Leon O. Chua, but experimentally validated only in 2008 by HP Labs. A memristor is essentially a nonvolatile nanoscale programmable resistor — indeed, memory resistor — whose resistance, or memristance to be precise, is changed by applying a voltage across, or current through, the device. Memristive computing is a new area of research, and many of its fundamental questions still remain open. For example, it is yet unclear which applications would benefit the most from the inherent nonlinear dynamics of memristors. In any case, these dynamics should be exploited to allow memristors to perform computation in a natural way instead of attempting to emulate existing technologies such as CMOS logic. Examples of such methods of computation presented in this thesis are memristive stateful logic operations, memristive multiplication based on the translinear principle, and the exploitation of nonlinear dynamics to construct chaotic memristive circuits. This thesis considers memristive computing at various levels of abstraction. The first part of the thesis analyses the physical properties and the current-voltage behaviour of a single device. The middle part presents memristor programming methods, and describes microcircuits for logic and analog operations. The final chapters discuss memristive computing in largescale applications. In particular, cellular neural networks, and associative memory architectures are proposed as applications that significantly benefit from memristive implementation. The work presents several new results on memristor modeling and programming, memristive logic, analog arithmetic operations on memristors, and applications of memristors. The main conclusion of this thesis is that memristive computing will be advantageous in large-scale, highly parallel mixed-mode processing architectures. This can be justified by the following two arguments. First, since processing can be performed directly within memristive memory architectures, the required circuitry, processing time, and possibly also power consumption can be reduced compared to a conventional CMOS implementation. Second, intrachip communication can be naturally implemented by a memristive crossbar structure.

Evaluating DNA damage response (DDR) activation in human prostate cancer

Introduction: Au Canada, le cancer de la prostate est le cancer le plus fréquemment diagnostiqué chez les hommes et le plus mortel après les cancers du poumon et du côlon. Il y a place à optimiser le traitement du cancer de la prostate de manière à mettre en œuvre une médecine personnalisée qui s’adapte aux caractéristiques de la maladie de chaque patient de façon individuelle. Dans ce mémoire, nous avons évalué la réponse aux dommages de l’ADN (RDA) comme biomarqueur potentiel du cancer de la prostate. Les lésions potentiellement oncogènes de l'ADN déclenche une cascade de signalisation favorisant la réparation de l'ADN et l’activation des points de contrôle du cycle cellulaire pour préserver l’intégrité du génome. La RDA est un mécanisme central de suppression tumorale chez l’homme. La RDA joue un rôle important dans l’arrêt de la prolifération des cellules dont les génomes sont compromis, et donc, prévient la progression du cancer en agissant comme une barrière. Cette réponse cellulaire détermine également comment les cellules normales et cancéreuses réagissent aux agents utilisés pour endommager l'ADN lors du traitement du cancer comme la radiothérapie ou la chimiothérapie, en plus la présence d,un certain niveau de RDA dans les cellules du cancer de la prostate peuvent également influer sur l'issue de ces traitements. L’activation des signaux de la RDA peut agir comme un frein au cancer dans plusieurs lésions pré-néoplasiques de l'homme, y compris le cancer de la prostate. Il a été démontré que la RDA est augmentée dans les cellules de néoplasie intra- épithéliale (PIN) comparativement aux cellules prostatiques normales. Toutefois, le devient de la RDA entre le PIN et l’adénocarcinome est encore mal documenté et aucune corrélation n'a été réalisée avec les données cliniques des patients. Notre hypothèse est que les niveaux d’activation de la RDA seront variables selon les différents grades et agressivité du cancer de la prostate. Ces niveaux pourront être corrélés et possiblement prédire les réponses cliniques aux traitements des patients et aider à définir une stratégie plus efficace et de nouveaux biomarqueurs pour prédire les résultats du traitement et personnaliser les traitements en conséquence. Nos objectifs sont de caractériser l'activation de la RDA dans le carcinome de la prostate et corréler ses données avec les résultats cliniques. Méthodes : Nous avons utilisé des micro-étalages de tissus (tissue microarrays- TMAs) de 300 patients ayant subi une prostatectomie radicale pour un cancer de la prostate et déterminé le niveau d’expression de protéines de RDA dans le compartiment stromal et épithélial des tissus normaux et cancéreux. Les niveaux d’expression de 53BP1, p-H2AX, p65 et p-CHK2 ont été quantifiés par immunofluorescence (IF) et par un logiciel automatisé. Ces marqueurs de RDA ont d’abord été validés sur des TMAs-cellule constitués de cellules de fibroblastes normales ou irradiées (pour induire une activation du RDA). Les données ont été quantifiées à l'aide de couches binaires couramment utilisées pour classer les pixels d'une image pour que l’analyse se fasse de manière indépendante permettant la détection de plusieurs régions morphologiques tels que le noyau, l'épithélium et le stroma. Des opérations arithmétiques ont ensuite été réalisées pour obtenir des valeurs correspondant à l'activation de la RDA qui ont ensuite été corrélées à la récidive biochimique et l'apparition de métastases osseuses. Résultats : De faibles niveaux d'expression de la protéine p65 dans le compartiment nucléaire épithélial du tissu normal de la prostate sont associés à un faible risque de récidive biochimique. Par ailleurs, nous avons aussi observé que de faibles niveaux d'expression de la protéine 53BP1 dans le compartiment nucléaire épithéliale du tissu prostatique normal et cancéreux ont été associés à une plus faible incidence de métastases osseuses. Conclusion: Ces résultats confirment que p65 a une valeur pronostique chez les patients présentant un adénocarcinome de la prostate. Ces résultats suggèrent également que le marqueur 53BP1 peut aussi avoir une valeur pronostique chez les patients avec le cancer de la prostate. La validation d'autres marqueurs de RDA pourront également être corrélés aux résultats cliniques. De plus, avec un suivi des patients plus long, il se peut que ces résultats se traduisent par une corrélation avec la survie. Les niveaux d'activité de la RDA pourront éventuellement être utilisés en clinique dans le cadre du profil du patient comme le sont actuellement l’antigène prostatique spécifique (APS) ou le Gleason afin de personnaliser le traitement.

Robust fault detection using consistency techniques for uncertainty handling

Often practical performance of analytical redundancy for fault detection and diagnosis is decreased by uncertainties prevailing not only in the system model, but also in the measurements. In this paper, the problem of fault detection is stated as a constraint satisfaction problem over continuous domains with a big number of variables and constraints. This problem can be solved using modal interval analysis and consistency techniques. Consistency techniques are then shown to be particularly efficient to check the consistency of the analytical redundancy relations (ARRs), dealing with uncertain measurements and parameters. Through the work presented in this paper, it can be observed that consistency techniques can be used to increase the performance of a robust fault detection tool, which is based on interval arithmetic. The proposed method is illustrated using a nonlinear dynamic model of a hydraulic system

Propriedades dos sistemas de numeração: uma sequência didática em uma abordagem histórica

This paper aims to describe the construction and validation of a notebook of activities whose content is a didactic sequence that makes use of the study of ancient numbering systems as compared to the object of our decimal positional numbering system Arabic. This is on the assumption that the comparison with a system different from our own might provide a better understanding of our own numbering system, but also help in the process of arithmetic operations of addition, subtraction and multiplication, since it will force us to think in ways that are not routinely object of our attention. The systems covered in the study were the Egyptian hieroglyphic system of numbering, the numbering system Greek alphabet and Roman numbering system, always compared to our numbering system. The following teachung is presented structured in the form of our activities, so-called exercise set and common tasks around a former same numbering system. In its final stage of preparation, the sequence with the participation of 26 primary school teachers of basic education

Geometria e arirmética numa visão multicultural: uma experiência pedagógica

This paper aims to build a notebook of activities that can help the teacher of elementary school mathematics. Topics covered are arithmetic and geometry and the activities proposed here were developed aiming print them a multicultural character. We take as a base line developed by Claudia Zaslavsky multiculturalism and reflected in his books "Games and activities worldwide" and "More games and activities worldwide." We structure our work around four themes: the symbol of the Olympic Games, the pyramids of Egypt, the Russian abacus abacus and Chinese. The first two themes allow you to explore basic concepts of geometry while the latter two themes allow us to explore numerical notation and arithmetic operations

Fast-forward/fast-backward substitutions on vector computers

This paper deals with approaches for sparse matrix substitutions using vector processing. Many publications have used the W-matrix method to solve the forward/backward substitutions on vector computer. Recently a different approach has been presented using dependency-based substitution algorithm (DBSA). In this paper the focus is on new algorithms able to explore the sparsity of the vectors. The efficiency is tested using linear systems from power systems with 118, 320, 725 and 1729 buses. The tests were performed on a CRAY Y MP2E/232. The speedups for a fast-forward/fast-backward using a 1729-bus system are near 19 and 14 for real and complex arithmetic operations, respectively. When forward/backward is employed the speedups are about 8 and 6 to perform the same simulations.

Especificação do tipo intervalar parametrizado em CASL

The interval datatype applications in several areas is important to construct a interval type reusable, i.e., a interval constructor can be applied to any datatype and get intervals this datatype. Since the interval is, of certain form, a set of elements limited for two bounds, left and right, with a order notions, then it s reasonable that interval constructor enclose datatypes with partial order. On the order hand, what we want is work with interval of any datatype like this we work with this datatype then. it s important to guarantee the properties of the datatype when maps to interval of this datatype. Thus, the interval constructor get a theory to parametrized interval type, i.e., a interval with generics parameters (for example rational, real, complex). Sometimes, the interval application in some algebras doesn t guarantee the mainutenance of their properties, for example, when we use interval of real, that satisfies the field properties, it doesn t guarantee the distributivity propertie. A form to surpass this problem Santiago introduced the local equality theory that weakened the notion of strong equality, and thus, allowing some properties are local keeped, what can be discard before. The interval arithmetic generalization aim to apply the interval constructor on ordered algebras weakened for local equality with the purpose of the keep their properties. How the intervals are important in applications with continuous data, it s interesting specify that theory using a specification language that supply a system development using intervals of form disciplined, trustworth and safe. Currently, the algebraic specification language, based in math models, have been use to that intention often. We choose CASL (Common Algebraic Specification Language) among others languages because CASL has several characteristics excellent to parametrized interval type, such as, provide parcialiy and parametrization

Análise praxeológica de conexões entre aritmética e álgebra no contexto do desenvolvimento profissional do professor de matemática

Este trabalho é uma pesquisa narrativa autobiográfica, que expõe a análise das minhas praxeologias, no contexto do meu desenvolvimento profissional, como professor de matemática. O foco da análise recai sobre os diversos conflitos praxeológicos que vivi durante a elaboração e aplicação em sala de aula de uma proposta didática para ensinar operações polinomiais na sétima série (oitavo ano) do ensino fundamental. Com esta pesquisa pretendi responder a seguinte questão: Quais conexões entre aritmética e álgebra determinaram as minhas praxeologias durante a ampliação didática que desenvolvi, para ensinar adição, subtração, multiplicação e divisão de polinômios, na sétima série (oitavo ano) do ensino fundamental? Para analisar as minhas próprias praxeologias a partir da proposta didática que elaborei, assumi a Teoria Antropológica do Didático (TAD) de Yves Chevallard como referencial teórico principal. A análise que fiz das minhas próprias praxeologias envolveu sistema de numeração decimal, operações aritméticas fundamentais, operações polinomiais, tipos de tarefas e técnicas, universo cognitivo e equipamento praxeológico. Os resultados apontam que as minhas relações pessoais com tipos de objetos ostensivos e não ostensivos e tipos de tarefas e técnicas presentes ou não na proposta didática que elaborei, revelam quais praxeologias passadas e presentes compunham os diversos momentos do meu desenvolvimento profissional como professor de matemática. Assim, antes da graduação vivi as praxeologias de professor leigo, durante e após a especialização o meu universo cognitivo passou por conflitos praxeológicos, revelando que as sujeições institucionais conformavam as minhas praxeologias para ensinar as operações polinomiais.

Introdução à análise intervalar em níveis simples e extensão de Zadeh

Pós-graduação em Matemática - IBILCE

Educação de jovens e adultos: a construção das operações aritméticas em matemática

Working with adult students who attend literacy rooms has been set a challenge for educators, especially with regard to issues of learning mathematics. This work of course completion intention was to investigate the process of construction of arithmetic operations in mathematics from the perspective of the students themselves. Thus specific objectives were to investigate how these students face simple operations that can do this automatically on a daily basis, but not always systematized in the classroom; how these students think and communicate their ideas to the mental operation of the paper record. To this end we chose a qualitative research approach with characteristics of case study, conducted in a room of Youth and Adult participants with three ladies. The data collection occurred through the application of a semi-structured, audio recorded and later transcribed, which issues the verbalization sought and a description of how to give students the learning process of some mathematical content. The results showed that students bring with them skills, cultures and values to the classroom and that these are the basis for understanding the content. The teacher of adult education must take into consideration everything that the student brings to the classroom, their experiences, their history and culture, thus questioning the real world, so they can understand math in a way closer to their daily lives

Incerteza intervalar em otimização e controle

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Topologically correct intersection curves of tori and natural quadrics

This thesis provides efficient and robust algorithms for the computation of the intersection curve between a torus and a simple surface (e.g. a plane, a natural quadric or another torus), based on algebraic and numeric methods. The algebraic part includes the classification of the topological type of the intersection curve and the detection of degenerate situations like embedded conic sections and singularities. Moreover, reference points for each connected intersection curve component are determined. The required computations are realised efficiently by solving quartic polynomials at most and exactly by using exact arithmetic. The numeric part includes algorithms for the tracing of each intersection curve component, starting from the previously computed reference points. Using interval arithmetic, accidental incorrectness like jumping between branches or the skipping of parts are prevented. Furthermore, the environments of singularities are correctly treated. Our algorithms are complete in the sense that any kind of input can be handled including degenerate and singular configurations. They are verified, since the results are topologically correct and approximate the real intersection curve up to any arbitrary given error bound. The algorithms are robust, since no human intervention is required and they are efficient in the way that the treatment of algebraic equations of high degree is avoided.

When language of instruction and language of application differ: Cognitive costs of bilingual mathematics learning

Bilingual education programs implicitly assume that the acquired knowledge is represented in a language-independent way. This assumption, however, stands in strong contrast to research findings showing that information may be represented in a way closely tied to the specific language of instruction and learning. The present study aims to examine whether and to which extent cognitive costs appear during arithmetic learning when language of instruction and language of retrieving differ. Thirty-nine high school students participating in a bilingual education program underwent a four-day training on multiplication and subtraction problems in one language (German or French), followed by a test session in which they had to solve trained as well as untrained problems in both languages. We found that cognitive costs related to language switching appeared for both arithmetic operations. Implications of our findings are discussed with respect to bilingual education as well as to cognitive mechanisms underlying different arithmetic operations.