In this thesis, we investigate the pathwise regularity of partial sum process of general orthogonal series, and prove that the partial sum process is a geometric 2-rough process under the same condition as in Menshov-Rademacher Theorem. For Fourier series, the condition can be improved, and an equivalent condition on the limit function is identified.

The main contribution of the present thesis is in two aspects. The first one, which is the heart of the thesis, is to explore the fundamental relation between rough paths and their signatures. Our main goal is to give a geometric characterization of the kernel of the signature map in different situations. In Chapter Two, we start by establishing a general fact that a continuous Jordan curve on a Riemannian manifold can be arbitrarily well approximated by piecewise minimizing geodesic interpolations which are again Jordan. This result enables us to prove a generalized version of Green’s theorem for planar Jordan curves with finite p-variation 1 &le; p < 2, and to prove that two such Jordan curves have the same signature if and only if they are equal up to reparametrization. In Chapter Three, we investigate the problem for general weakly geometric rough paths. In particular, we show that a weakly geometric rough path has trivial signature if and only if it is tree-like in the sense we will define later on. In Chapter Four, we study the problem in the probabilistic setting. In particular, we show that for a class of stochastic processes, with probability one the sample paths are determined by their signatures up to reparametrization. A fundamental example is Gaussian processes including fractional Brownian motion with Hurst parameter H > 1/4, the Ornstein-Uhlenbeck process and the Brownian bridge. The second one is an application of rough path theory to the study of nonlinear diffusions on manifolds under the framework of nonlinear expectations. In Chapter Five, we begin by studying the geometric rough path nature of G-Brownian motion. This enables us to introduce rough differential equations driven by G-Brownian motion from a pathwise point of view. Next we establish the fundamental relation between rough (pathwise theory) and stochastic (L²-theory) differential equations driven by G-Brownian motion. This is a crucial point of understanding nonlinear diffusions and their generating heat flows on manifolds from an intrinsic point of view. Finally, from the pathwise point of view we construct G-Brownian motion on a compact Riemannian manifold and establish its generating heat flow for a class of G-functions under orthogonal invariance. As an independent interest, we also develop the Euler-Maruyama scheme for stochastic differential equations driven by G-Brownian motion.

Doctor of Philosophy / Department of Horticulture, Forestry, and Recreation Resources / Jack Fry and Megan Kennelly / Rough bluegrass (RBG, Poa trivialis L.) is a difficult-to-control weed that commonly infests cool-season turfgrass swards after movement of vegetative propagules or contamination from seed lots. Rough bluegrass is less tolerant of heat stress than desirable cool-season species such as tall fescue (TF, Festuca arundinacea Schreb. Syn [italicize]Schedonorus [italicize]arundinaceus Schreb.), and often declines during mid-summer due to biotic or abiotic stresses. The objectives of these 2011-2013 controlled environment and field experiments were to: 1) observe growth and physiological differences between ‘Laser’ and ‘Pulsar’ RBG and TF; 2) differentiate between physiological and pathological contributors to RBG decline; 3) determine the effects of TF seeding rate and mowing height on TF/RBG establishment when RBG is a seed contaminant; 4) evaluate herbicide combinations for selective RBG control; and 5) evaluate seasonal timing of glyphosate for nonselective RBG control. Tall fescue was less affected by elevated temperature than RBG. At 35°C, Laser and Pulsar experienced similar reductions in quality, gross photosynthesis (Pg), shoot and root biomass, and root length density compared to when grown at 23°C, but maximum electrolyte leakage was greater for Pulsar (63%) than for Laser (49%). Cell membrane thermostability could contribute to the better heat tolerance of Laser RBG. Evaluation of RBG foliage and roots did not reveal a fungal pathogen associated with RBG decline. Still, repeated applications of azoxystrobin (610 g a.i. ha⁻¹) or pyraclostrobin (556 g a.i. ha⁻¹) increased RBG quality, cover, and Pg during summer compared to untreated RBG, possibly due to poorly understood non-target physiological effects of the fungicides. Mowing TF at 7.6 or 11.4 cm reduced RBG incidence up to 57% compared to mowing at 3.8 cm. Tall fescue seeding rate had no effect on RBG incidence. Several herbicides and herbicide combinations resulted in some RBG injury in the field, but bispyribac-sodium was the only treatment that provided RBG control (16 to 92%) in Manhattan, KS; Hutchinson, KS; and Mead, NE. Spring-applied glyphosate resulted in the lowest RBG coverage (1 to 31%) among field studies in Manhattan and Mead, followed by late-summer applications (6 to 58%), and mid-summer applications (9 to 86%).

One of the problems associated with automatic thesaurus construction is with determining the semantic relationship between word pairs. Quasi-synonyms provide a type of equivalence relationship: words are similar only for purposes of information retrieval. Determining such relationships in a thesaurus is hard to achieve automatically. The term vector space model and an inverse term frequency similarity function can provide a way to automatically determine the similarity between words in thesaurus. A thesaurus constructed using this method can also improve precision and recall in information retrieval, when the thesaurus is constructed in conjunction with fuzzy rough set algorithms and used with tight upper approximation query expansion. This dissertation presents a method that combines fuzzy rough sets and a word weighting and inverse term frequency similarity function as a technique for automatic thesaurus construction.

This study focuses on numerical modeling of fluid flow and solute transport in rough-walled rock fractures and fracture-matrix systems, with the main aim to investigate the impacts of fracture surface roughness on flow and transport processes in rock fractures. Both 2D and 3D fracture models were built from laser-scanned surface tomography of a real granite rock sample, to consider realistic features of surface tomography and potential asperity contacts. The flow was simulated by directly solving the Navier-Stokes equations (NSE) and the transport was modeled by solving the advection-dispersion equation (ADE) in the entire domain of fracture-matrix system, including matrix diffusion process. Such direct simulations provided detailed flow and concentration fields for quantitatively analysis of flow and transport behavior. The detailed analysis of surface roughness decomposition, complex flow patterns (i.e., channeling, transverse and eddy flows), effective advective flow apertures, effective transmissivity, effective dispersivity, residence time, transport resistance and specific surface area demonstrated significant impacts of realistic fracture surface roughness on fluid flow and solute transport processes in rock fractures. The results show that the surface roughness and shear displacement caused asperity contacts significantly enhance nonlinearity and complexity of flow and transport processes in rough-walled fractures and fracture-matrix systems. The surface roughness also causes invasion flows in intersected fractures which enhance solute mixing at fracture intersections. Therefore, the fracture surface roughness is an important source of uncertainty in application of such simplified models like cubic law (CL) for fluid flow and analytical solutions for solute transport in rock fractures. The research conducted advances our understanding of realistic flow and transport processes in natural fractured rocks. The results are useful for model validation/extension, uncertainty analysis/quantification and laboratory experiments design in the context of various applications related to fracture flow and transport. / Denna studie fokuserar på numerisk modellering av vätskeflöde och transport av lösta ämnen i frakturer med ojämna väggar samt fraktur-matrissystem, med det huvudsakliga syftet att undersöka effekterna av frakturernas ytjämnhet på flödes- och transportprocesser i bergsfrakturer. Både 2D och 3D modeller skapades utifrån laser skannad tomografi av ett verkligt bergartsprov av granit, för att överväga de realistiska egenskaperna hos ytan och potentiell skrovlighet. Flödet simulerades genom att lösa Navier-Stokes ekvationer (NSE) och transporten modellerades genom att lösa advektion-dispersion ekvation (ADE) i hela domänen av fraktur-matrissystemet, inklusive diffusions process i matrisen. Sådana direkta simuleringar resulterade i detaljerade flödes- och koncentrationsfält för att kvantitativt kunna analysera flödet och transportbeteendet. En detaljerad analys av upplösningen av ytjämnhet, komplexa flödesmönster (dvs kanalisering, tvärgående och virvelströmmar), effektiv advektiv flödesöppning, effektiv transmissivitet, effektiv dispersivitet, uppehållstid, transport motstånd och specifik yta visade signifikanta effekter av realistiska ojämna frakturväggar på vätskeflöde och lösta transportprocesser i bergssprickor. Resultaten visar att ytjämnhet och skjuvningssystemsorsakade asperitetskontakter avsevärt förbättrar olinjäritet och komplexitet av flödes- och transportprocesser i frakturer med ojämna väggar samt fraktur-matrissystem. Ytråheten orsakar också intrång av flöde i tvärgående frakturer vilket ökar blandingen av lösta ämnen i korsningarna. Därför är ytjämnhet av frakturerna en viktig källa till osäkerhet i tillämpningen av sådana förenklade modeller som kubisk lag (CL) för vätskeflöde och analytiska lösningar för transport av lösta ämnen i bergsfrakturer. Studien har ökat förståelsen för realistiska flödes- och transportprocesser i naturligt sprucket berg. Resultaten är användbara för modellvalidering/förlängning, osäkerhetsanalys/kvantifiering och design av laboratorieexperiment i samband med olika tillämpningar av flöde och transport i bergsfrakturer. / <p>QC 20161010</p>

Les propriétés de surface, particulièrement microgéométriques, jouent un rôle essentiel dans tous les systèmes tribologiques. L’analyse de la répartition des efforts de contact dans l’interface entre surfaces rugueuses est indispensable à la prédiction du frottement, de l'usure, de l'adhérence, des résistances de contact électrique et thermique… De nombreux modèles ont été proposés ces dernières décennies pour prédire les efforts entre aspérités de surfaces rugueuses. Parmi ces modèles, les modèles statistiques sont majoritairement développés en considérant le contact ente une surface rugueuse équivalente, la surface somme - qui tient compte des microgéométries des deux surfaces en contact ainsi que de leur matériau - et un plan lisse. Cependant la validité de cette modélisation n’a pas été clairement démontrée. L’objectif de notre étude a été de développer un modèle statistique de contact entre deux surfaces rugueuses isotropes aléatoires puis de comparer les résultats obtenus pour ces deux surfaces avec ceux obtenus en considérant la surface somme définie classiquement à partir des deux surfaces rugueuses et un plan lisse. Les différences entre les résultats nous ont amenés à proposer une nouvelle modélisation de la surface somme. / Surface properties, particularly micro-geometry, play a key role in all tribological systems. The analysis of the distribution of contact forces in the interface between rough surfaces is essential for the prediction of friction, wear, adhesion, electrical and thermal contact resistance... Many models have been proposed during the last decades to predict the forces between asperities of rough surfaces. Among these models, statistical models are mainly based on the contact between an equivalent rough surface, the sum surface - which combines micro-geometry of the two surfaces in contact and their material - and a smooth plane. However, the validity of this model has not been clearly demonstrated. The aim of our study was to develop a statistical model of the contact between two random isotropic rough surfaces and then compare the results with those obtained by considering the classical sum surface. The differences between the results have led us to propose a new definition for the sum surface.

[pt] Em terrenos acidentados é crítico para robôs móveis manter uma adequada tração nas rodas, pois um excessivo deslizamento das mesmas pode fazer o robô capotar ou desviar da rota desejada. Também, se uma força excessiva é aplicada sobre uma região do terreno, pode levar o mesmo a ceder deixando as rodas presas. Para se evitar os problemas acima citados e ainda otimizar o consumo de energia em terrenos planos, a presente dissertação desenvolveu um controle de tração para terrenos acidentados com o intuito de aplicá- lo ao Robô Ambiental Híbrido (RAH) da Petrobrás. O RAH é um robô móvel anfíbio que está em fase de desenvolvimento no Laboratório de Robótica do CENPES (Petrobras), que poderá ser comandado por um operador ou se deslocar autonomamente. Esse robô faz parte do projeto Cognitus, braço tecnológico do projeto Piatam (Potenciais Impactos e Riscos Ambientais da Indústria de Óleo e Gás na Amazônia), e será aplicado na monitoração e coleta de dados do meio ambiente de dois gasodutos da Petrobrás na região Amazônica, o gasoduto Urucu (AM)- Porto Velho (RO) e o gasoduto Coari (AM) - Manaus (AM). A técnica de controle de tração de veículos robóticos em terrenos acidentados desenvolvida visa controlar a velocidade ao mesmo tempo em que garante a estabilidade dinâmica, não deslizamento das rodas, evita a saturação dos motores, e em certas condições ainda permite minimizar a potência requerida através do conhecimento dos ângulos de contato entre as rodas e o terreno. Foram feitas duas modelagens independentes, uma considerando a suspensão do robô flexível e a outra considerando o veículo robótico como um corpo rígido, sendo ambas para o caso plano (2D).Foram realizadas simulações em terrenos suaves e acidentados, as quais comprovaram a eficácia das técnicas de controle propostas. / [en] Abstract Silva, Alexandre F. Barral Silva; Meggiolaro, Marco Antonio. Traction Control to Mobile Robotic Systems in Rough Terrain. Rio de Janeiro, 2004. 194 p. MSc. Thesis - Departamento de Engenharia Mecânica, Pontifícia Universidade Católica do Rio de Janeiro. In rough terrain it is critical for mobile robots to maintain adequate wheel traction, because excessive sliding could cause the robot to roll over or deviate from its intended path. Also, if an excessive force is applied onto the terrain, the soil may fail and trap the robot wheels. To avoid these problems, and also minimize the power consumption on even terrain, the present work develops a rough terrain traction control to be applied to the Hybrid Environmental Robot (HER) from Petrobras. The HER is an amphibious mobile robot developed by the Robotics Laboratory from CENPES (Petrobras). It can be commanded by an operator or autonomously. This robot is part of the Cognitus Project, technological branch of the Piatam project (Potential Impacts and Environmental Risks of the Oil and Gas Industry in the Amazon). It will be used for monitoring and environmental data collecting along two gas pipelines in the Amazon region, the Urucu (AM) - Porto Velho (RO) and the Coari (AM) - Manaus (AM). The developed traction control of robotic vehicles in rough terrain aims to control the speed at the same time that it guarantees dynamic stability, no slip of the wheels, prevents motor saturation, and under certain conditions it may also allow for the minimization of the required power. This control needs the knowledge of the current state of the robot, including the contact angles between its wheels and the terrain. Two independent 2D models have been proposed, one including the suspension compliance and one considering the robotic vehicle as a rigid body. Simulations have been performed in even and rough terrains, proving the effectiveness of the proposed control techniques.

[pt] O uso de robôs móveis para monitorar locais inacessíveis vem se tornando cada vez mais comum. Essas operações podem ser autônomas ou tripuladas e quando são feitas em terrenos irregulares é preciso garantir segurança na missão, pois muitas das vezes o resgate se torna inviável. O robô estudado nesta dissertação terá dificuldades para locomoção em certas localidades, como por exemplo: derrapagem em regiões alagadas, vencer atoleiro em regiões pantanosas e de brejos e capotagem nas regiões que apresentam aclives e declives. Diante deste quadro de problemas apresentados, garantir a estabilidade nas regiões de ladeiras é de grande valor nas operações, sejam elas tele-operadas ou autônomas. Visando contribuir para o sucesso da locomoção do robô, esta dissertação apresenta uma técnica de controle de estabilidade de um robô móvel para sensoreamento remoto em terrenos irregulares, incluindo projeto, simulação e construção de um protótipo funcional. Este controle visa garantir que as rodas do veículo não descolem do terreno, através da atuação nas forças de atrito entre as rodas e o solo variando os torques nos seus motores. / [en] The use of mobile robots to monitor non-accessible environments has become increasingly common in the recent years. These tasks can be either autonomous, remote-controlled, or passenger-operated. When performed in rough terrain, it is necessary to guarantee mission safety, since many times it is impossible to send a rescue party for recovery. The hybrid environmental robot presented in this thesis is a mobile robot that will face very challenging conditions, avoiding e.g. slippage in wet terrain, becoming trapped in muddy soil, and tipping over in regions with high slopes. Therefore, it is a challenging task to guarantee robot stability under such circumstances, either in autonomous or operated tasks. This thesis presents a stability control methodology for a mobile robot to perform remote sensing tasks in rough terrain. The model-based technique guarantees wheel-ground contact at all times, acting individually at the wheel motors to control the traction/friction forces. This work also addresses the design, simulation and construction aspects of a functional prototype of a mobile robot to validate the proposed approach.

Pouco se sabe sobre o efeito do substrato e a interação entre as leveduras selvagens e bactérias do gênero Lactobacillus na fermentação alcoólica, pois os estudos tem se concentrado na avaliação dos efeitos da contaminação por um ou outro contaminante separadamente. Diante disso, este trabalho teve como objetivos estudar o efeito do substrato e das condições de tratamento do fermento sobre as fermentações contaminadas com ambos os micro-organismos, leveduras S. cerevisiae selvagens (três linhagens apresentando colônias rugosas e células dispostas em pseudohifas) e Lactobacillus fermentum, tendo a linhagem industrial de S. cerevisiae PE-2 como levedura do processo. Foram realizadas fermentações em batelada em mosto de caldo e de melaço, sem reciclo e com reciclo celular, utilizando tanto a cultura pura da linhagem PE-2 quanto as culturas mistas com as linhagens rugosas e ou L. fermentum. Foram avaliadas modificações no tratamento ácido do fermento, visando o controle do crescimento dos contaminantes sem afetar a levedura do processo. Em seguida, foram conduzidas fermentações contaminadas e não contaminadas submetidas ao tratamento ácido combinado com adição de etanol, tanto em caldo quanto em melaço, utilizando-se PE-2, uma das linhagens rugosas e L. fermentum. A atividade da invertase extracelular foi também avaliada em ambos os substratos para os micro-organismos estudados, em condições de crescimento. Concluiu-se que o tipo de substrato de fermentação, caldo de cana ou melaço, influenciou o desempenho da linhagem industrial PE-2 assim como afetou o desenvolvimento das contaminações com as leveduras rugosas S. cerevisiae na presença ou ausência da bactéria L. fermentum, em fermentações sem reciclo celular. O efeito da contaminação foi mais evidente quando se utilizou caldo de cana do que melaço como substrato, no caso da contaminação com leveduras rugosas, e o inverso no caso da contaminação com L. fermentum. O efeito da contaminação sobre a eficiência fermentativa foi maior na presença da levedura rugosa do que com a bactéria, e a contaminação dupla (tanto com a levedura rugosa quanto com a bactéria) não teve efeito maior sobre a eficiência fermentativa do que a contaminação simples, por um ou por outro micro-organismo isoladamente, especialmente na fermentação em batelada com reciclo celular, independentemente do substrato. Nas fermentações com reciclo de células, o efeito do substrato foi menos evidente. O controle do crescimento das linhagens rugosas pode ser realizado modificando o tratamento ácido normalmente realizado na indústria, seja pela adição de etanol à solução ácida ou pelo abaixamento do pH, dependendo da linhagem rugosa. O tratamento combinado baixo pH (2,0) + 13% etanol afetou a fisiologia da linhagem industrial, trazendo prejuízos à fermentação com reciclo celular, com pequeno controle sobre o crescimento da levedura rugosa e causando morte celular à L. fermentum. A diferença na atividade invertásica entre as linhagens rugosas e industrial de S. cerevisiae pode ser a responsável pela fermentação lenta apresentada pelas linhagens rugosas quando presentes na fermentação, sendo não significativa a influência do substrato sobre a atividade dessa enzima. / A little is known about the effect of the substrate and the interaction among wild yeast strains and bacteria Lactobacillus in the alcoholic fermentation, because the studies have been concentrated in the evaluation of the contamination effects by one or another contaminant, separately. This work aimed to evaluate the effect of the substrate and the cell treatment conditions over the batch fermentations contaminated with both microorganisms, yeast wild strains of S. cerevisiae (three strains displaying rough colonies and pseudohyphal cell growth) and Lactobacillus fermentum, being the S. cerevisiae strain PE-2 as the starter yeast. Fermentations using sugarcane juice and molasses, without and with cell recycle, utilizing both the pure culture of PE-2 as the mixed cultures with rough yeast strains and or L. fermentum were carried out. Modifications in the acid cell treatment by the addition of ethanol to the acid solution and the lowering of pH of the acid solution or a treatment with potassium metabisulphite were evaluated, aiming the growth control of the contaminants without affecting the starter yeast. An acid treatment with the addition of 13% ethanol was applied in fermentation with cell recycle, both in sugarcane juice and molasses, utilizing PE-2, one of the rough yeast strains and L. fermentum. The extracellular invertase activity was also evaluated in both substrates for the microorganisms studied, in growing conditions. The type of substrate, sugarcane juice or molasses, influenced the performance of the PE-2 strain as well as affected the development of the contaminations with rough S. cerevisiae yeast strains with or without L. fermentum, in fermentations without cell recycle. The effect of the contamination was more remarkable when sugarcane juice was utilized, in fermentations contaminated with rough yeast strains, but the inverse was observed when L. fermentum was the contaminant. The contamination effect was more harmful with the rough yeast strain than with the bacteria, and the double contamination (with both rough yeast strain and bacteria) did not have a higher effect over the fermentative efficiency than the single contamination, by one or another microorganism in isolation, especially in the batch fermentation with cell recycle, regardless the substrate. In cell-recycled fermentations the effect of the substrate was less evident. The growth control of the rough yeast strains may be done by modifying the acid cell treatment carried out in the industry, both by the addition of ethanol to the acid solution or by the pH lowering, depending on the rough yeast strain. , The combined treatment (pH 2.0 + 13% ethanol) affected PE-2 physiology, bringing about loss in the cell-recycled fermentation, with low growth control of the rough yeast strain but causing cell death of L. fermentum. The difference in the invertase activity between the rough yeast strains and the starter yeast PE-2 may be responsible for the low fermentation rate displayed by the rough yeast strains, but a non significant effect of the substrate on the enzyme activity was observed.

No Aprendizado de Máquina Supervisionado---AM---o algoritmo de indução trabalha com um conjunto de exemplos de treinamento, no qual cada exemplo é constituído de um vetor com os valores dos atributos e as classes, e tem como tarefa induzir um classificador capaz de predizer a qual classe pertence um novo exemplo. Em geral, os algoritmos de indução baseiam-se nos exemplos de treinamento para a construção do classificador, sendo que uma representação inadequada desses exemplos, bem como inconsistências nos mesmos podem tornar a tarefa de aprendizado difícil. Um dos problemas centrais de AM é a Seleção de um Subconjunto de Atributos---SSA---cujo objetivo é diminuir o número de atributos utilizados na representação dos exemplos. São três as principais razões para a realização de SSA. A primeira razão é que a maioria dos algoritmos de AM, computacionalmente viáveis, não trabalham bem na presença de vários atributos. A segunda razão é que, com um número menor de atributos, o conceito induzido através do classificador pode ser melhor compreendido. E, a terceira razão é o alto custo para coletar e processar grande quantidade de informações. Basicamente, são três as abordagens para a SSA: embedded, filtro e wrapper. A Teoria de Rough Sets---RS---é uma abordagem matemática criada no início da década de 80, cuja principal funcionalidade são os redutos, e será tratada neste trabalho. Segundo essa abordagem, os redutos são subconjuntos mínimos de atributos que possuem a propriedade de preservar o poder de descrição do conceito relacionado ao conjunto de todos os atributos. Neste trabalho o enfoque esta na abordagem filtro para a realização da SSA utilizando como filtro os redutos calculados através de RS. São descritos vários experimentos sobre nove conjuntos de dados naturais utilizando redutos, bem como outros filtros para SSA. Feito isso, os atributos selecionados foram submetidos a dois algoritmos simbólicos de AM. Para cada conjunto de dados e indutor, foram realizadas várias medidas, tais como número de atributos selecionados, precisão e números de regras induzidas. Também, é descrito um estudo de caso sobre um conjunto de dados do mundo real proveniente da área médica. O objetivo desse estudo pode ser dividido em dois focos: comparar a precisão dos algoritmos de indução e avaliar o conhecimento extraído com a ajuda do especialista. Embora o conhecimento extraído não apresente surpresa, pôde-se confirmar algumas hipóteses feitas anteriormente pelo especialista utilizando outros métodos. Isso mostra que o Aprendizado de Máquina também pode ser visto como uma contribuição para outros campos científicos. / In Supervised Machine Learning---ML---an induction algorithm is typically presented with a set of training examples, where each example is described by a vector of feature values and a class label. The task of the induction algorithm is to induce a classifier that will be useful in classifying new cases. In general, the inductive-learning algorithms rely on existing provided data to build their classifiers. Inadequate representation of the examples through the description language as well as inconsistencies in the training examples can make the learning task hard. One of the main problems in ML is the Feature Subset Selection---FSS---problem, i.e. the learning algorithm is faced with the problem of selecting some subset of feature upon which to focus its attention, while ignoring the rest. There are three main reasons that justify doing FSS. The first reason is that most ML algorithms, that are computationally feasible, do not work well in the presence of many features. The second reason is that FSS may improve comprehensibility, when using less features to induce symbolic concepts. And, the third reason for doing FSS is the high cost in some domains for collecting data. Basically, there are three approaches in ML for FSS: embedded, filter and wrapper. The Rough Sets Theory---RS---is a mathematical approach developed in the early 1980\'s whose main functionality are the reducts, and will be treated in this work. According to this approach, the reducts are minimal subsets of features capable to preserve the same concept description related to the entire set of features. In this work we focus on the filter approach for FSS using as filter the reducts obtained through the RS approach. We describe a series of FSS experiments on nine natural datasets using RS reducts as well as other filters. Afterwards we submit the selected features to two symbolic ML algorithms. For each dataset, various measures are taken to compare inducers performance, such as number of selected features, accuracy and number of induced rules. We also present a case study on a real world dataset from the medical area. The aim of this case study is twofold: comparing the induction algorithms performance as well as evaluating the extracted knowledge with the aid of the specialist. Although the induced knowledge lacks surprising, it allows us to confirm some hypothesis already made by the specialist using other methods. This shows that Machine Learning can also be viewed as a contribution to other scientific fields.