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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
31

A Full Frequency-Dependent Cable Model for the Calculation of Fast Transients

Hoshmeh, Abdullah, Schmidt, Uwe 31 August 2017 (has links) (PDF)
The calculation of frequency-dependent cable parameters is essential for simulations of transient phenomena in electrical power systems. The simulation of transients is more complicated than the calculation of currents and voltages in the nominal frequency range. The model has to represent the frequency dependency and the wave propagation behavior of cable lines. The introduced model combines an improved subconductor method for the determination of the frequency-dependent parameters and a PI section wave propagation model. The subconductor method considers the skin and proximity effect in all conductors for frequency ranges up to few megahertz. The subconductor method method yields accurate results. The wave propagation part of the cable model is based on a cascaded PI section model. A modal transformation technique has been used for the calculation in the time domain. The frequency-dependent elements of the related modal transformation matrices have been fitted with rational functions. The frequency dependence of cable parameters has been reproduced using a vector fitting algorithm and has been implemented into an resistor-inductor-capacitor network (RLC network) for each PI section. The proposed full model has been validated with measured data.
32

Unconditionally stable finite difference time domain methods for frequency dependent media

Rouf, Hasan January 2010 (has links)
The efficiency of the conventional, explicit finite difference time domain (FDTD)method is constrained by the upper limit on the temporal discretization, imposed by the Courant–Friedrich–Lewy (CFL) stability condition. Therefore, there is a growing interest in overcoming this limitation by employing unconditionally stable FDTD methods for which time-step and space-step can be independently chosen. Unconditionally stable Crank Nicolson method has not been widely used in time domain electromagnetics despite its high accuracy and low anisotropy. There has been no work on the Crank Nicolson FDTD (CN–FDTD) method for frequency dependent medium. In this thesis a new three-dimensional frequency dependent CN–FDTD (FD–CN–FDTD) method is proposed. Frequency dependency of single–pole Debye materials is incorporated into the CN–FDTD method by means of an auxiliary differential formulation. In order to provide a convenient and straightforward algorithm, Mur’s first-order absorbing boundary conditions are used in the FD–CN–FDTD method. Numerical tests validate and confirm that the FD–CN–FDTD method is unconditionally stable beyond the CFL limit. The proposed method yields a sparse system of linear equations which can be solved by direct or iterative methods, but numerical experiments demonstrate that for large problems of practical importance iterative solvers are to be used. The FD–CN–FDTD sparse matrix is diagonally dominant when the time-stepis near the CFL limit but the diagonal dominance of the matrix deteriorates with the increase of the time-step, making the solution time longer. Selection of the matrix solver to handle the FD–CN–FDTD sparse system is crucial to fully harness the advantages of using larger time-step, because the computational costs associated with the solver must be kept as low as possible. Two best–known iterative solvers, Bi-Conjugate Gradient Stabilised (BiCGStab) and Generalised Minimal Residual (GMRES), are extensively studied in terms of the number of iteration requirements for convergence, CPU time and memory requirements. BiCGStab outperforms GMRES in every aspect. Many of these findings do not match with the existing literature on frequency–independent CN–FDTD method and the possible reasons for this are pointed out. The proposed method is coded in Fortran and major implementation techniques of the serial code as well as its parallel implementation in Open Multi-Processing (OpenMP) are presented. As an application, a simulation model of the human body is developed in the FD–CN–FDTD method and numerical simulation of the electromagnetic wave propagation inside the human head is shown. Finally, this thesis presents a new method modifying the frequency dependent alternating direction implicit FDTD (FD–ADI–FDTD) method. Although the ADI–FDTD method provides a computationally affordable approximation of the CN–FDTD method, it exhibits a loss of accuracy with respect to the CN-FDTD method which may become severe for some practical applications. The modified FD–ADI–FDTD method can improve the accuracy of the normal FD–ADI–FDTD method without significantly increasing the computational costs.
33

Preference minoritního fenotypu v pohlavním výběru u člověka / The role of minority type preference in human sexual selection

Pokorný, Šimon January 2016 (has links)
Minority phenotype preference, or the negative frequency-dependent selection is a type of selection, where a feature is more preferred, the lower it's frequency is in the population. Even a weak effect in other-preference based sexual selection can result in a sustainable polymorphism. This study reviews the phenomenon in the context of human visual facial features. Common trends in attractiveness shape the morphology of the human face towards uniformity. Individual recognition however, as a condition for most social relations, uses the wast variability of different features. This variability could be formed and maintained by minority phenotype preference. In our study we tested the effect of minority phenotype preference in the selection for rare hair and eye colors. In 120 unique sets, each containing six photographs, we experimentally manipulated the frequency of each color type. These sets were then shown to 226 human raters. We tested whether the relative frequency of each color type affected the rating of individual stimuli. In hair color, significant effect of minority phenotype preference was detected when females rated the photographs of men. When males rated the photographs of females, the effect was significant in eye color only. Key words: face perception, sexual selection,...
34

Evoluce a význam barvy duhovky u člověka, její biologická role a mezikulturni percepce / The Evolution and Functional Role of the Colour of Iris in Humans, Its Biological Role, and Cross-Cultural Perception

Kočnar, Tomáš January 2021 (has links)
The human eye is a conspicuous and unique component of facial appearance. From other mammalian eyes it is set apart mainly by its unusual shape, visible white sclera, and a wide range of iris colours, which is something unique within a single species. Whether alone or in the context of the face as a whole, eye colour is an underexplored area within research into the perception of various personality traits. In this thesis, the author first reviews the physiological factors connected with eye colour and reported correlations between eye colour and different psychological and behavioural conditions. This is followed by an investigation of a possible relationship between eye colour and perceived dominance and attractiveness. The first and second study examines whether and to what extent eye colour is associated with facial morphology responsible for perceived dominance. The results are ambiguous. A cross-cultural comparison in the third study revealed that faces with blue eyes are judged as more attractive only in populations where individuals with darker eyes predominate. It is thus discussed whether this population-specific pattern is the consequence of a negative frequency-dependent selection that may have contributed to the present-day eye colour diversity. In short, the aim of this thesis was to...
35

Selection Dynamics in Heliconius Hybrid Zones and the Origin of Adaptive Variation

Shaak, Steven Grant 11 December 2015 (has links)
There is repeated evidence that hybridization is a major contributor to the production of adaptive diversity; however, the evolutionary fate of hybrids in natural populations remains poorly understood. In Heliconius butterflies, hybridization is common and responsible for generating a variety of warning color patterns across the genus. Predator avoidance of warning colorations appears to largely be learned, which drives strong positive frequency-dependent selection. This creates a paradox for hybrid lineages: how do novel hybrid forms manage to establish and persist under such strong selection? In this dissertation, I present a series of studies centered on the selection dynamics of Heliconius hybrid zones, to elucidate how novel adaptive traits establish in nature. Clines across hybrid zones have often been analyzed to estimate selection on ecologically important loci. Here, warning color clines were characterized and compared across multiple transects along a Heliconius hybrid zone in the Guiana Shield. Furthermore, a mark-resight experiment and communal roost observations were completed near the center of this hybrid zone to determine the survival and likelihood of establishment of native and foreign forms. These studies reveal similar survivorship of hybrid and pure color patterns, and specifically demonstrate that a rare putative hybrid form can survive and establish within a hybrid zone. Both hybrids and pure color patterns showed comparable life expectancies in the mark-resight experiment and similar patterns of presence at nocturnal roosts. These results suggest that selection on warning color pattern is relatively weak within the hybrid zone. Analyses of color pattern clines uncovered strong selection bounding the hybrid zone in bi-race areas, while weaker selection was estimated for a tri-race area. In fact, the tri-race area was three times wider than the bi-race areas. Collectively, these studies suggest that the selection dynamics across hybrid zones may play an integral role in the establishment of new adaptive traits, and offers a route by which a reputed hybrid race may have arisen. The investigations within this dissertation also provide a new view of hybrid zone dynamics, and improve our understanding of how hybridization and selection shapes the evolution of biodiversity.
36

Pollinators, Enemies, Drought, and the Evolution of Reproductive Traits in Primula farinosa

Toräng, Per January 2007 (has links)
In this thesis, I combined comparative and experimental approaches to examine selection on reproductive traits and population differentiation in the insect-pollinated, self-incompatible, perennial herb Primula farinosa. More specifically, I (1) determined whether the effects of floral display and interactions with pollinators and seed predators, and plant reproductive success were frequency-dependent and affected by surrounding vegetation context, (2) examined the consequences of intermittent drought years on population dynamics using numerical simulations based on demographic data collected over seven years, (3) analyzed among-population differentiation in flowering phenology and reproductive allocation, and its relationship to soil-depth at the site of origin. A field experiment suggested that conspicuous plants facilitate inconspicuous plants in terms of pollinator attraction, and that the facilitation effect is contingent on the height of the surrounding vegetation. Further experiments revealed that both mutualistic and antagonistic interactions can result in frequency-dependent selection on floral display. Among inconspicuous plants, both fruit initiation, and damage from seed predators increased with the proportion of the conspicuous morph. The relative strength of these effects, and therefore their net outcome on the relationship between morph ratio and seed production varied among years. I combined information on vital rates and their relation to environmental conditions in simulations to predict future population viability in changing environments. Simulated stochastic population growth rate decreased with increasing frequency of drought years. Reproductive allocation varied significantly among populations both in the field and in a common-garden experiment, but was correlated with soil depth at the site of origin only in the field. The results suggest that among-population variation in reproductive effort in the field mainly reflects plastic responses to environmental conditions, and that this plasticity may be adaptive. The common-garden experiment suggested that the study populations have diverged genetically in flowering time.
37

L'influence de la sélection fréquence-dépendante sur le choix de partenaire chez le diamant mandarin (Taeniopygia guttata)

Hébert-Brassard, Cynthia 09 1900 (has links)
La sélection fréquence-dépendante est un mécanisme d’évolution selon lequel l’aptitude d'un type varie en fonction de sa fréquence dans la population. Ce mécanisme joue un rôle important dans de nombreuses interactions autant interspécifiques (parasitisme, prédation, compétition), qu'intra-spécifiques entre les différents phénotypes d'une même espèce. La sélection fréquence-dépendante peut être positive ou négative et favoriser alors les phénotypes communs ou rares, respectivement. Elle a été mise en évidence dans le contexte du choix de partenaire chez plusieurs espèces, notamment chez certaines espèces d'insectes (ex.: demoiselles, drosophiles, cantharide de Pennsylvanie) et de poissons (ex.: guppys, xiphos), mais elle a été aussi récemment découverte chez l’humain. L'importance de la sélection fréquence-dépendante dans le choix de partenaire chez les espèces monogames reste tout de même peu explorée et cette étude vise à combler cette lacune en utilisant le diamant mandarin, un passereau monogame, comme modèle biologique. Nous avons étudié l'importance de ce mécanisme lorsqu'un trait est neutre et lorsque celui-ci constitue un indicateur de qualité. De plus, nous avons tenté de déterminer si la présence de rivales peut modifier la préférence initiale des femelles pour les phénotypes rares ou communs. / Frequency-dependant selection is an evolution mechanism in which the fitness of a type depend of its frequency in the population. This mechanism play an important role in several interspecific (parasitism, predation, competition) and intraspecific interactions within different phenotypes of a same species. Frequency-dependant selection can be positive or negative and favor, respectively, either common or rare phenotype. This selection has been found in context of mated choice of several species, especially in insects (damselfly, drosophila, soldier beetle) and fishes (guppy, swordtail) and it has even been recently discover in humans. The significance of frequency-dependent selection in mated choice of monogamous species is still less explored and this study used the zebra finches (a monogamous passerine) in order to explored this field. We studied the significance of this mechanism when a character is neutral and when it is rather a quality cue. Also, we attempt to establish if rivals' presence affect or modify the initial preference of females for common or rare phenotypes.
38

Evolution expérimentale et spécialisation dans le paysage adaptatif d'un gradient environnemental / Experimental evolution and specialization in the adaptive landscape of an environmental gradient

Harmand, Noémie 21 June 2017 (has links)
De nos jours plus que jamais, il est nécessaire d’anticiper et de comprendre les réponses évolutives des organismes vivants, face à des habitats instables et hétérogènes. Mais à quel point cela est-il possible ? Reproduire l’ensemble du déroulé d’une trajectoire évolutive nécessite de pouvoir décrire, d’une part, le « matériel » disponible pour s’adapter (c’est-à-dire les effets phénotypiques associés à la variabilité génétique produite), d’autre part, comment agissent les forces évolutives, associées à un contexte écologique, pour aboutir à un certain « assemblage » de ce matériel. Dans sa version la plus simple, ce processus évolutif peut-être décrit par plusieurs cycles d’évènements de mutations-sélection conduisant à l’adaptation d’une population à son environnement. Cette dynamique correspond assez bien à celle qui est décrite par les populations bactériennes dans les expériences d’évolution contrôlées en laboratoire. Parallèlement, les modèles de paysages adaptatifs (phénotypiques), et en particulier le modèle géométrique de Fisher, sont des outils très puissants pour formuler des prédictions générales et quantitativement testables sur ces trajectoires évolutives. Cependant, ils restent très théoriques et ont été largement pensés dans un contexte écologique simplifié. Au cours de cette thèse, nous avons identifié les déterminants (mutationnels et sélectifs) des trajectoires évolutives à long terme de populations bactériennes s’adaptant dans différents contextes environnementaux. Une première partie des résultats est mise en lumière par la validation expérimentale et la reconstruction de la topographie du paysage adaptatif généré par différentes doses d’un antibiotique, le long d’un gradient. Une deuxième partie expérimentale vise à intégrer une composante biotique (une autre bactérie) à ce même contexte environnemental. Les processus évolutifs intervenant au cours d’une coévolution à long terme maintenue par sélection fréquence-dépendante, y sont étudiés. / Today more than ever, it is crucial to anticipate and understand the evolutionary responses of living organisms faced with heterogeneous and unstable habitats. But to what extent is this possible? To reproduce an entire evolutionary trajectory, we must first describe the “material” available for adaptation (e.g. the phenotypic effects associated with the existing and novel genetic variability), and second describe the way evolutionary forces, shaped by the ecological context, result in specific “assemblies” of this material. At its simplest, this evolutionary process can be described by several cycles of mutation-selection events, leading to the adaptation of a population to an environment. This process is reflected in the evolutionary trajectories of bacterial lineages undergoing controlled experimental evolution in the lab. Concurrently, adaptive (phenotypic) landscape models, and especially Fisher’s geometrical model of adaptation, are powerful tools to formulate general predictions, which can then be tested on such evolutionary trajectories. However, they remain highly theoretical, and are widely conceived in a simple ecological context. In this thesis, we identified the (mutational and selective) determinants of the evolutionary trajectories of bacterial lines adapting to various environmental contexts. A first set of results regards evolution along a gradient of antibiotic doses, and their relevance is highlighted by experimental validation and by the reconstruction of the underlying adaptive landscape. A second experimental part integrates a biotic component (another bacteria) to the same environmental context. The evolutionary processes acting throughout the resulting long-term coevolution – maintained by frequency-dependent selection – are studied.
39

Variabilidade comportamental e a seleção de uma sequência de baixa probabilidade inicial: comparando dois procedimentos

Bitondi, Fernanda Rizzi 25 May 2012 (has links)
Made available in DSpace on 2016-04-29T13:17:45Z (GMT). No. of bitstreams: 1 Fernanda Rizzi Bitondi.pdf: 1390449 bytes, checksum: c3d88238b2946cc2655e04fd9337cc96 (MD5) Previous issue date: 2012-05-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The aim of this study was to evaluate the effectiveness of two procedures, Discrete Trial (DT) and Discrete Trial with Interresponse Interval (DT/IRI), on the production of behavioral variability in different conditions (directly reinforced and induced) and determine what condition, in each procedure, would facilitate the selection of an initial sequence of low probability. Were selected 18 college students with baseline performance measured by U-valeu, that was equal or less than 0,5. They were divided into the two procedures and subdivided into three groups with three participants (VAR, YOKE and CON). The task was to form images on the computer screen by pressing two keys (left and right) on lateral keyboards. The unit was four responses to the keys. In both procedures, a piece of the image, a tone and 0,5 seconds was used to reinforce sequences that attended the contingency s criterion, and a timeout of 1,0 second, if not. Only the DT/IRI had a 0,5 second interval after the first three responses of the sequence. The experiment had three phases. In Phase I, baseline, sequences was continuous reinforced (CRF). For two groups (DT- VAR and DT/IRI-VAR) in Phase 2, variability was direct reinforced on 15 sequences, mean that the less frequent and less recent sequence had more probability of been reinforced than the others, and a target sequence (less frequent sequence at baseline) was reinforced in CRF. In Phase 3, the distribution of reinforcement of the prior phase was yoked for the 15 sequences and another target sequence was reinforced in CRF. For the groups DT-YOKE and DT/IRI-YOKE, the phase s exposure was reversed, whereas in Phase 2 the distribution of reinforcement was yoked to the performance of the VAR groups. In groups DT-CON and DT/IRI-CON, only the target sequence was reinforced in both phases. The results showed that variability increased in the first session of Phase 2 for all participants. The DT-YOKE group showed the highest levels of variability within this procedure. In the DT/IRI procedure, this was true for the group DT/IRI-VAR. With regard to the selection of the target sequence the groups that had higher percentages of selection in all sessions were DT-CON and DT/IRI-VAR, respectively within each procedure. It was noted that both procedures produced the selection of the target sequence, but is seems that the use of IRI produced a more variable performance, when it was directly reinforced, allowing the selection of the target sequence to occur more rapidly / O objetivo do estudo foi avaliar a efetividade de dois procedimentos, Tentativa Discreta (TD) e Tentativa Discreta com Intervalo entre as Respostas (TD/IRI), na produção da variabilidade comportamental em diferentes condições (diretamente reforçada e induzida) e averiguar que condição, em cada procedimento, mais facilitaria a seleção de uma sequência de baixa probabilidade inicial. Selecionou-se 18 universitários com um desempenho na linha de base, medido pelo índice U, igual ou inferior a 0,5. Estes foram divididos nos dois procedimentos e subdivididos em três grupos com três participantes (VAR, ACO e CON). A tarefa consistia em formar figuras na tela do computador pressionando duas teclas (direita e esquerda) de teclados laterais. A unidade comportamental era quatro respostas às teclas. Nos dois procedimentos apresentava-se um pedaço da figura, um tom e 0,5 segundo, caso a sequência fosse passível de reforço, e um timeout de 1,0 segundo, caso não fosse. Somente no TD/IRI havia um IRI de 0,5 segundo após as três primeiras respostas da sequência. O experimento continha três fases. Na Fase 1, linha de base, vigorava o reforçamento contínuo (CRF) das 16 sequências. Para dois grupos (TD-VAR e TD/IRI-VAR) na Fase 2 havia o reforçamento direto da variabilidade, para 15 sequências, no qual a sequência menos frequente e menos recente teria maior probabilidade de ser reforçada, e CRF de uma sequência alvo (sequência menos frequente na linha de base). Na Fase 3, havia a distribuição acoplada dos reforços da fase anterior para as 15 sequências e CRF de outra sequência alvo. Para os grupos TD-ACO e TD/IRI-ACO a ordem de exposição às fases foi inversa, visto que na Fase 2 a distribuição de reforços foi acoplada ao desempenho dos participantes dos grupos VAR. Nos grupos TD-CON e TD/IRI-CON havia somente o CRF da sequência alvo nas duas fases. Os resultados mostraram que a variabilidade aumentou na primeira sessão da Fase 2 para todos os participantes. O grupo TD-ACO foi o que apresentou maior índices de variabilidade dentro deste procedimento. Já no TD/IRI, isto foi verdadeiro para o grupo TD/IRI-VAR. Com relação à seleção da sequência alvo, os grupos que apresentaram maiores porcentagens de seleção em todas as sessões foram TD-CON e TD/IRI-VAR, respectivamente dentro de cada procedimento. Notou-se que os dois procedimentos produziram seleção da sequência alvo, mas parece que o uso do IRI produziu um responder mais variável, quando este foi diretamente reforçado, o que possibilitou que a seleção da sequência alvo ocorresse mais rapidamente
40

Efeitos das contingências de reforçamento LAG e RDF sobre a variabilidade comportamental de crianças autistas / Effects of reinforcement contingencies LAG and RDF on behavioral variability of autistic children

Sélios, Talita Lopes 25 May 2012 (has links)
Made available in DSpace on 2016-04-29T13:17:46Z (GMT). No. of bitstreams: 1 Talita Lopes Selios.pdf: 2740314 bytes, checksum: bbf543faeed50b1b17909eb0128d1ebb (MD5) Previous issue date: 2012-05-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In order to verify the effects of the reinforcement contingencies LAG and RDF on the behavioral variability of autistic children, was established in the present research two different teaching procedures of variability one for the LAG contingency and other for the RDF that started with low variation requirement to obtain reinforcement and consisted of gradual increasing in the variability exigency. So, the objective was to investigate if (1) the two reinforcement procedures contingent to the vary LAG and RDF of motor responses of autistic children, with gradual increasing in the exigency of variation, would produce a variable responding in computer games; and (2) occurred extension of acquired variability in the taught task with the LAG and RDF contingencies for the other tasks not submitted to the direct reinforcement of vary task with response topographically similar and task with response topographically different from the task that composed the experimental task. The six participants realized three computer games. They were exposed a baseline phase with each one of the tree games and, then, four of them were submitted to the training phase with the variability contingency with the Game 1 considering that for two of them, the teaching of the variability was given with the LAG contingency (the reinforce was presented if a determined sequence completed differed from last n completed sequences), and, for the other two, with the threshold contingency or frequency dependent reinforcement RDF (the reinforce probability was greater as lower was the relative frequency and the recency of a sequence) and two passed to training with the yoked contingency with the Game 1 (the reinforce distribution obtained in the procedure in which the variability was directly reinforced established what completed sequences would produce reinforces; the release of the reinforce was, therefore, independent of the responding being varied). In the end of each level that composed the teaching of variability and the yoked and after the teaching of the last level, extension tests of variability were realized one to the task topographically similar to teaching task (Game 2) and other to the task topographically different (Game 3). The results showed that the reinforcement contingencies LAG and RDF produced variability. The procedures of gradual increasing of exigency of variation, for both contingencies, generate variable responding and, in general, the higher was the requirement of variation, higher the variability. Both contingencies produced, in the end of the teaching process, high and similar variability levels. The yoked contingency did not alter the variability, permitting conclude that the variable responding generated for the LAG and RDF contingencies was due to the reinforcement contingent to vary and not of the intermittency among the reinforces. It was also verified that occurred extension of variability only to the task topographically similar to that taught and it could already be observed during the teaching process / A fim de verificar os efeitos das contingências de reforçamento LAG e RDF sobre a variabilidade comportamental de crianças autistas, estabeleceu-se na presente pesquisa dois diferentes procedimentos de ensino da variabilidade um para a contingência LAG e outro para a RDF que iniciavam com baixo requerimento de variação para a obtenção do reforço e consistiam em aumentar gradualmente a exigência de variabilidade. Assim, objetivou-se investigar se (1) os dois procedimentos de reforçamento contingente ao variar - LAG e RDF - de respostas motoras de crianças autistas, com aumento gradual da exigência de variação, produziram um responder variável, em jogos de computador; e (2) ocorreu extensão da variabilidade adquirida na tarefa ensinada com as contingências LAG e RDF para outras tarefas não submetidas ao reforçamento direto do variar tarefa com resposta topograficamente semelhante e tarefa com resposta topograficamente diferente da que compôs a tarefa experimental. Os seis participantes realizaram três jogos de computador. Eles foram expostos a uma fase de linha de base com cada um dos três jogos e, em seguida, quatro deles foram submetidos à fase de treino com a contingência de variabilidade com o Jogo 1 sendo que, para dois deles, o ensino da variabilidade deu-se com a contingência LAG (o reforço era apresentado se uma determinada sequência completada diferisse da últimas n sequências completadas) e, para os outros dois, com a contingência limiar ou de reforçamento dependente da frequência - RDF (a probabilidade de reforço era maior quanto menor fosse a frequência relativa e a recência de uma sequência) e dois passaram pelo treino com a contingência de acoplamento com o Jogo 1 (a distribuição de reforços obtida no procedimento em que se reforçou diretamente a variabilidade estabeleceu quais sequências completadas produziriam reforços; a liberação do reforço era, portanto, independente do responder ser variado). Ao final de cada nível que compôs o ensino de variabilidade e o acoplamento e após o ensino do último nível, testes de extensão da variabilidade foram realizados um para tarefa topograficamente semelhante à tarefa ensinada (Jogo 2) e outro para tarefa topograficamente diferente (Jogo 3). Os resultados mostraram que as contingências de reforçamento LAG e RDF produziram variabilidade. Os procedimentos de aumento gradual da exigência de variação, para ambas as contingências, geraram responder variável e, de forma geral, quanto maior o requerimento de variação, maior a variabilidade. Ambas as contingências produziram, ao final do processo de ensino, altos e semelhantes níveis de variabilidade. A contingência acoplamento não alterou a variabilidade, permitindo concluir que o responder variável gerado pelas contingências LAG e RDF foi decorrente do reforçamento contingente ao variar e não da intermitência entre os reforços. Verificou-se, também, que ocorreu extensão da variabilidade apenas para a tarefa topograficamente semelhante à ensinada e esta já pôde ser observada durante o processo de ensino

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