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Manhattan Converter Family: Partial Power Processing, Module Stacking with Linear Complexity, Efficiency and Power Density, in DC and AC ApplicationsJahnes, Matthew January 2024 (has links)
A modularized three-dimensional power electronics environment will become increasingly necessary as power converters are more intertwined with the dynamic desires of modern society. This is driven by ever-changing requirements, combined with the desire for quick design cycles, and then further compounded by the increased penetration of electrified technologies. The high demand for various power converters presents a design, manufacturing, and validation burden which can be lessened with a three-dimensional power electronics environment, where power converters of any arbitrary set of voltage, current, or quantity of independent input/outpt requirements can be assembled from a grouping of pre-existing converter modules. This, however, has drawbacks when compared with bespoke power converter designs. Modularization can be complex, lossy, and large, and the resulting converter's overall efficiency and power density will then suffer. To compensate for these costs of modularization, the individual modules must be first be power dense and efficient, and then the framework for grouping modules together must be simple.
This dissertation first proposes a high performance Power Conversion Unit (PCU) which is achieved through a unique combination of techniques. The first of these techniques is modification to the ubiqutioius buck converter topology in a form of an adjustment to its output filter. This topological modification results in decreased current ripple handling requirements of the filter, which can be used to reduce its volume. The second topological technique is an additional capacitance placed across the drain-source terminals of each FET, which is used to reduce their turn-off switching energy at the expense of their turn-on switching energy. A variable frequency soft-switching scheme is utitlized to prevent the converter from incurring turn-on losses, and a duty cycle compensation scheme is developed to mitigate the distortions caused by this increased drain-source capacitance. Finally, a process for balancing the PCU design parameters that results in a Pareto frontier of efficiency-power density optimal points is defined, one selected, and a protoype PCU constructed and tested in a three-phase inverter configuration.
A framework for the vertical stacking of PCUs is then shown. This framework, named the Manhattan Topology, is a multilevel power converter topology which is defined by a set of series stacked capacitances where there exists a method to transfer power between capacitances. This framework has linear complexity and switching device stress scaling with the number of levels, which yields a simple methodology for grouping modules together in the vertical dimension. Furthermore, it exhibits Partial Power Processing (PPP) characteristics as the power processed internally to the overall converter is less than its output power. This framework is validated for both DC/DC and AC/DC applications and control and conversion of voltages greater than the rating of any individual component within the converter is experimentally demonstrated. Lastly, another three-phase inverter is built using this topological framework and the performance of this vertically-modularized inverter is compared with the non-modularized inverter. It is shown that the three-dimensional modular power electronics environment with optimized PCUs, despite the costs of modularization, is still performance-competitive with the non-modular power electronics environment.
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[en] DESIGN OF A CONTACLESS VOLTMETER FOR ALTERNATING ELECTRICAL VOLTAGES IN 60 HZ / [pt] PROJETO DE UM VOLTÍMETRO POR APROXIMAÇÃO PARA TENSÕES ELÉTRICAS ALTERNADAS EM 60 HZANDRE RIBEIRO GOMES 12 November 2024 (has links)
[pt] O objetivo desta dissertação de mestrado foi projetar um voltímetro utilizando a
técnica de acoplamento capacitivo para medições de tensão. O design proposto do
voltímetro oferece uma alternativa simples e econômica aos métodos tradicionais de
medição de tensão. Ao utilizar o acoplamento capacitivo, a necessidade de contato elétrico
direto entre o circuito de medição e a fonte de tensão é eliminada, permitindo medições de
forma não invasivas. O processo de desenvolvimento envolveu o projeto e a construção de
um circuito de acoplamento capacitivo, que possibilitou a transferência do sinal de tensão
para um circuito de medição. O circuito de medição incluiu componentes de
condicionamento de sinal e um conversor analógico-digital para permitir leituras de tensão
com confiabilidade metrológica. O sistema foi calibrado e testado usando uma fonte de
valor de tensão conhecido para garantir medições confiáveis e precisas. Os resultados
experimentais mostram que o voltímetro obteve desempenho satisfatório para a voltagem
usual de 127 V em corrente alternada (127 V CA) e uma distância máxima de 0,2 m do
ponto de interesse, mantendo um baixo nível de interferência de ruídos elétricos externos.
O design proposto do voltímetro tem potencial para várias aplicações, especialmente em
cenários onde o contato elétrico direto com a fonte de tensão é indesejável ou impraticável.
Ele oferece uma solução confiável e eficiente para medições, sendo adequado tanto para
fins industriais quanto de pesquisa. / [en] The objective of this master s thesis was to develop a voltmeter using the capacitive coupling technique for voltage measurements. The proposed voltmeter design offers a simple and cost-effective alternative to traditional voltage measurement methods. By using capacitive coupling, the need for direct electrical contact between the measuring circuit and the voltage source is eliminated, allowing for non-invasive voltage measurements. The development process involved the design and construction of a capacitive coupling circuit, which enabled the transfer of the voltage signal to a measurement circuit. The measurement circuit included signal conditioning components and an analog-to-digital converter for accurate voltage readings. The system has been calibrated and tested using a known voltage source to ensure reliable and accurate measurements. The experimental results show that the voltmeter obtained satisfactory performance for the usual voltage of 127 V AC and a maximum distance of 0.2 m from the point of interest, maintaining a low level of interference from external electrical noises. The proposed voltmeter design has potential for several applications, especially in scenarios where direct electrical contact with the voltage source is undesirable or impractical. It offers a reliable and efficient solution for voltage measurements, being suitable for both industrial and research purposes.
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以BSRS5時序性追蹤資料探討居家服務老年人口自殺意念與精神病理暨個人特質之關聯分析郭熙宏, Kuo, Hsi Hong Unknown Date (has links)
近幾年來,國人自殺死亡率不斷提高,且自殺死亡從1997年起已連續多年列於國人十大死亡原因之一,所以自殺防治工作刻不容緩。本研究採用自殺防治中心在桃園縣六家居家服務單位(龍祥、中國、仁愛、紅十字、家輔及寬福)所做之問卷調查資料,目的在於找出何種特性者,BSRS5 (The Five-Item Brief Symptom Rating Scale)分數及自殺意念分數可能較高。本研究屬於時序性追蹤資料,自民國96年5月份起,由居服人員針對受測對象進行訪談,大約每隔兩週收集一次,總共進行四次。
針對問卷進行基本敘述性統計、單項排名分析以及交叉分析後發現,在人口特質方面,男女性比例相當,年齡層主要皆在65~84歲,教育程度以不識字及國小為主;在BSRS5五題排名方面,以第一題「睡眠困難(難以入睡或早醒)」的平均分數最高,第四題「覺得比不上別人」平均分數最低;由交叉分析的結果發現身體狀況為一個重要的變數,身體狀況差的人BSRS5總分6分以上或自殺意念2分以上明顯較多。
對資料配適廣義估計方程式及Alternating Logistic Regressions的結果,發現在反應變數為BSRS5總分時,女性、身體狀況差及曾經看過精神科者BSRS5分數達到6分以上的可能性較高。若反應變數為自殺意念時,無論是利用廣義估計方程式或Alternating Logistic Regressions,從模型配適的結果發現只有BSRS5的效應顯著。不管利用BSRS5總分或是各題分開來看,BSRS5對自殺意念是一個相當有效的檢測工具,BSRS5分數愈高則自殺意念2分以上的機會也愈高。此外利用多層結構分析方法配適廣義估計方程式,針對BSRS5與受測次數間的關聯性分析,發現與配適傳統unstructured相關性矩陣的估計結果差異不大,但是可以減少許多參數估計,並且在電腦計算時間上是較快速的。 / In Taiwan, suicide has been among the top ten causes of death since 1997, and suicide prevention has thus attracted much attention since. Using the data provided by Taiwan Suicide Prevention Center (TSPC), this study is aimed to find out possible personal characteristics that might have some impacts on the BSRS5 (the Five-Item Brief Symptom Rating Scale) and suicide ideation scores The data come from a longitudinal study in which subjects from six elderly home service centers in Taoyuan County, Taiwan were visited four times between May and July, 2007, about two weeks between each visit.
The total number of subjects is 1981. The proportions of male and female are nearly the same, the age range is from 65 to 84, and most of them have only an elementary school degree. Preliminary analyses indicate that among the five items in BSRS5, insomnia (the first item) is ranked the highest, and inferiority (the fourth item) is the lowest. In addition, health status is highly correlated to the BSRS5 and suicide ideation scores, the worse the health status, the higher the BSRS5 and suicide ideation scores.
Fitting the data with Generalized Estimating Equation (GEE) and Alternating Logistic Regressions models with respect to the BSRS5 score, we further find that female, those who have bad health status, and those who have ever consulted a psychiatrist have higher probability that the BSRS5 score is greater than 6. As far as the suicide ideation score is concerned, the BSRS5 score is the only covariate that is statistically significant, an indication that BSRS5 is a useful tool for screening subjects at risk of committing suicide. While the conclusions stay the same whether the data are analyzed through GEE with commonly used unstructured correlation structure or newly developed multiblock and multilayer correlation structure, the latter approach reduces the computer time significantly.
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Vers une méthode de restauration aveugle d’images hyperspectrales / Towards a blind restoration method of hyperspectral imagesZhang, Mo 06 December 2018 (has links)
Nous proposons dans cette thèse de développer une méthode de restauration aveugle d'images flouées et bruitées où aucune connaissance a priori n'est exigée. Ce manuscrit est composé de trois chapitres : le 1er chapitre est consacré aux travaux de l'état de l'art. Les approches d'optimisation pour la résolution du problème de restauration y sont d'abord discutées. Ensuite les principales méthodes de restauration, dites semi-aveugles car nécessitant un minimum de connaissance a priori sont analysées. Parmi ces méthodes, cinq sont retenues pour évaluation. Le 2ème chapitre est dédié à la comparaison des performances des méthodes retenues dans le chapitre précédent. Les principaux critères objectifs d'évaluation de la qualité des images restaurées sont présentés. Parmi ces critères, la norme L1 de l'erreur d'estimation est sélectionnée. L'étude comparative menée sur une banque d'images monochromes, dégradées artificiellement par deux fonctions floues de supports différents et trois niveaux de bruit a permis de mettre en évidence les deux méthodes les plus pertinentes. La première repose sur une approche alternée mono-échelle où la PSF et l'image sont estimées dans une seule étape. La seconde utilise une approche hybride multi-échelle qui consiste tout d'abord à estimer de manière alternée la PSF et une image latente, puis dans une étape suivante séquentielle, à restaurer l'image. Dans l'étude comparative conduite, l'avantage revient à cette dernière. Les performances de ces méthodes serviront de référence pour comparer ensuite la méthode développée. Le 3ème chapitre porte sur la méthode développée. Nous avons cherché à rendre aveugle l'approche hybride retenue dans le chapitre précédent tout en améliorant la qualité d'estimation de la PSF et de l'image restaurée. Les contributions ont porté sur plusieurs points. Une première série d'améliorations concerne la redéfinition des échelles, celle de l'initialisation de l'image latente à chaque niveau d'échelle, l'évolution des paramètres pour la sélection des contours pertinents servant de support à l'estimation de la PSF et enfin, la définition d'un critère d'arrêt aveugle. Une seconde série de contributions a porté sur l'estimation aveugle des deux paramètres de régularisation impliqués pour éviter d'avoir à les fixer empiriquement. Chaque paramètre est associé à une fonction coût distincte l'une pour l'estimation de la PSF et la seconde pour l'estimation d'une image latente. Dans l'étape séquentielle qui suit, nous avons cherché à affiner le support de la PSF estimée dans l'étape alternée, avant de l'exploiter dans le processus de restauration de l'image. A ce niveau, la seule connaissance a priori nécessaire est une borne supérieure du support de la PSF. Les différentes évaluations conduites sur des images monochromes et hyperspectrales dégradées artificiellement par plusieurs flous de type mouvement, de supports différents, montrent une nette amélioration de la qualité de restauration obtenue par l'approche développée par rapport aux deux meilleures approches de l'état de l'art retenues. / We propose in this thesis manuscript to develop a blind restoration method of single component blurred and noisy images where no prior knowledge is required. This manuscript is composed of three chapters: the first chapter focuses on state-of-art works. The optimization approaches for resolving the restoration problem are discussed first. Then, the main methods of restoration, so-called semi-blind ones because requiring a minimum of a priori knowledge are analysed. Five of these methods are selected for evaluation. The second chapter is devoted to comparing the performance of the methods selected in the previous chapter. The main objective criteria for evaluating the quality of the restored images are presented. Of these criteria, the l1 norm for the estimation error is selected. The comparative study conducted on a database of monochromatic images, artificially degraded by two blurred functions with different support size and three levels of noise, revealed the most two relevant methods. The first one is based on a single-scale alternating approach where both the PSF and the image are estimated alternatively. The second one uses a multi-scale hybrid approach, which consists first of alternatingly estimating the PSF and a latent image, then in a sequential next step, restoring the image. In the comparative study performed, the benefit goes to the latter. The performance of both these methods will be used as references to then compare the newly designed method. The third chapter deals with the developed method. We have sought to make the hybrid approach retained in the previous chapter as blind as possible while improving the quality of estimation of both the PSF and the restored image. The contributions covers a number of points. A first series concerns the redefinition of the scales that of the initialization of the latent image at each scale level, the evolution of the parameters for the selection of the relevant contours supporting the estimation of the PSF and finally the definition of a blind stop criterion. A second series of contributions concentrates on the blind estimation of the two regularization parameters involved in order to avoid having to fix them empirically. Each parameter is associated with a separate cost function either for the PSF estimation or for the estimation of a latent image. In the sequential step that follows, we refine the estimation of the support of the PSF estimated in the previous alternated step, before exploiting it in the process of restoring the image. At this level, the only a priori knowledge necessary is a higher bound of the support of the PSF. The different evaluations performed on monochromatic and hyperspectral images artificially degraded by several motion-type blurs with different support sizes, show a clear improvement in the quality of restoration obtained by the newly designed method in comparison to the best two state-of-the-art methods retained.
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Procedurellt minne hos universitetsstuderande med dyslexiPierre, Janina, Toreheim, Josefine January 2014 (has links)
Dyslexi är en form av läs- och skrivsvårighet som inte kan förklaras av t.ex. bristfällig undervisning, låg begåvning eller synproblem. Orsaken till dyslexi anses vanligen vara nedsatt förmåga av fonologiskt processande. Flera studier har dock visat att dyslexi även är förknippat med språkliga, kognitiva och motoriska svårigheter som inte kan förklaras av nedsatt förmåga av fonologiskt processande. Det procedurella minnessystemet engageras vid inlärning, processande och konsolidering av kognitiva och motoriska färdigheter. Enligt the procedural deficit hypothesis (PDH) orsakas de svårigheter förekommande vid dyslexi av en nedsättning i detta minnessystem. Forskningen inom området är inte entydig då det har rapporterats om både intakt och nedsatt procedurellt minne hos personer med dyslexi. Föreliggande studie var den första att undersöka procedurellt minne hos svenska universitetsstuderande med dyslexi. Syftet var att testa PDH med hjälp av alternating serial reaction time task (ASRT), samt att undersöka relationen mellan procedurellt minne, närmare bestämt implicit sekvensinlärning, och läsförmåga samt aspekter av språklig/fonologisk förmåga. I studien deltog totalt 37 universitetsstuderande, 11 med dyslexi och 26 utan dyslexi. Resultatet indikerade att förmågan till inlärning och konsolidering i det procedurella minnet inte skilde sig åt mellan grupperna. Resultatet ger således inte stöd åt PDH. Vidare kunde inga signifikanta korrelationer påvisas, vilket tyder på att det inte föreligger något samband mellan procedurellt minne och respektive läsförmåga, fonologisk medvetenhet och snabb benämning (rapid automatized naming, RAN). / Developmental dyslexia is characterized by reading and writing difficulties that do not derive from poor education, low intelligence or visual impairment. The disorder is commonly explained as a result of an underlying phonological deficit. However, studies have shown that dyslexia is also associated with linguistic, cognitive, and motor impairments that can not be explained by a specific phonological deficit. The procedural memory underlies learning, processing and consolidation of motor and cognitive skills. The procedural deficit hypothesis (PDH) suggests that an impairment of procedural memory is the underlying cause of developmental dyslexia. Previous research has yielded inconsistent results as studies have reported intact as well as impaired procedural memory in dyslexics. This study was the first to examine procedural memory in Swedish university students. The aim was to test the PDH, by using an alternating serial reaction time task (ASRT), and to examine the correlation between procedural memory and reading ability as well as aspects of linguistic/phonological ability. In this study there was a total of 37 university students, 11 dyslexics and 26 nondyslexics. The result showed learning and consolidation of the procedural memory in both groups and there was no significant difference between the groups. Thus, the results do not support the PDH. No significant correlations were found, which indicates that there is no association between procedural memory and reading ability, phonological awareness or rapid automatized naming (RAN).
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Minimum Cost Distributed Computing using Sparse Matrix Factorization / Minsta-kostnads Distribuerade Beräkningar genom Gles MatrisfaktoriseringHussein, Seif January 2023 (has links)
Distributed computing is an approach where computationally heavy problems are broken down into more manageable sub-tasks, which can then be distributed across a number of different computers or servers, allowing for increased efficiency through parallelization. This thesis explores an established distributed computing setting, in which the computationally heavy task involves a number of users requesting a linearly separable function to be computed across several servers. This setting results in a condition for feasible computation and communication that can be described by a matrix factorization problem. Moreover, the associated costs with computation and communication are directly related to the number of nonzero elements of the matrix factors, making sparse factors desirable for minimal costs. The Alternating Direction Method of Multipliers (ADMM) is explored as a possible method of solving the sparse matrix factorization problem. To obtain convergence results, extensive convex analysis is conducted on the ADMM iterates, resulting in a theorem that characterizes the limiting points of the iterates as KKT points for the sparse matrix factorization problem. Using the results of the analysis, an algorithm is devised from the ADMM iterates, which can be applied to the sparse matrix factorization problem. Furthermore, an additional implementation is considered for a noisy scenario, in which existing theoretical results are used to justify convergence. Finally, numerical implementations of the devised algorithms are used to perform sparse matrix factorization. / Distribuerad beräkning är en metod där beräkningstunga problem bryts ner i hanterbara deluppgifter, som sedan kan distribueras över ett antal olika beräkningsenheter eller servrar, vilket möjliggör ökad effektivitet genom parallelisering. Denna avhandling undersöker en etablerad distribuerad beräkningssmiljö, där den beräkningstunga uppgiften involverar ett antal användare som begär en linjärt separabel funktion som beräknas över flera servrar. Denna miljö resulterar i ett villkor för tillåten beräkning och kommunikation som kan beskrivas genom ett matrisfaktoriseringsproblem. Dessutom är det möjligt att relatera kostanderna associerade med beräkning och kommunikation till antalet nollskilda element i matrisfaktorerna, vilket gör glesa matrisfaktorer önskvärda. Alternating Direction Method of Multipliers (ADMM) undersöks som en möjlig metod för att lösa det glesa matrisfaktoriseringsproblemet. För att erhålla konvergensresultat genomförs omfattande konvex analys på ADMM-iterationerna, vilket resulterar i ett teorem som karakteriserar de begränsande punkterna för iterationerna som KKT-punkter för det glesa matrisfaktoriseringsproblemet. Med hjälp av resultaten från analysen utformas en algoritm från ADMM-iterationerna, vilken kan appliceras på det glesa matrisfaktoriseringsproblemet. Dessutom övervägs en ytterligare implementering för ett brusigt scenario, där befintliga teoretiska resultat används för att motivera konvergens. Slutligen används numeriska implementeringar av de framtagna algoritmerna för att utföra gles matrisfaktorisering.
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Efficient algorithms for compressed sensing and matrix completionWei, Ke January 2014 (has links)
Compressed sensing and matrix completion are two new data acquisition techniques whose efficiency is achieved by exploring low dimensional structures in high dimensional data. Despite the combinatorial nature of compressed sensing and matrix completion, there has been significant development of computationally efficient algorithms which can produce accurate desired solutions to these problems. In this thesis, we are concerned with the development of low per iteration computational complexity algorithms for compressed sensing and matrix completion. First, we derive a locally optimal stepsize selection rule for the simplest iterative hard thresholding algorithm for matrix completion, and obtain a simple yet efficient algorithm. It is observed to have average case performance superior in some aspects to other matrix completion algorithms. To balance the fast convergence rates of more sophisticated recovery algorithms with the low per iteration computational cost of simple line-search algorithms, we introduce a family of conjugate gradient iterative hard thresholding algorithms for both compressed sensing and matrix completion. The theoretical results establish recovery guarantees for the restarted and projected variants of the algorithms, while the empirical performance comparisons establish significant computational advantages of the proposed methods over other hard thresholding algorithms. Finally, we introduce an alternating steepest descent method and a scaled variant especially designed for the matrix completion problem based on a simple factorization model of the low rank matrix. The computational efficacy of this method is achieved by reducing the high per iteration computational cost of the second order method and fully exploring the numerical linear algebra structure in the algorithm. Empirical evaluations establish the effectiveness of the proposed algorithms, compared with other state-of-the-art algorithms.
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Phase Retrieval with Sparsity ConstraintsLoock, Stefan 07 June 2016 (has links)
No description available.
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Investigating cognitive control in language switchingClapp, Amanda Louise January 2013 (has links)
How do bi/multilinguals switch between languages so effectively that there is no obvious intrusion from the alternatives? One can examine this by comparing language selection with task selection, or language switching with task switching. This is the approach adopted in the first of two strands of research presented in this thesis. In task switching, providing advance warning of the task typically leads to a reduction in the performance ‘switch cost’, suggesting top-down biasing of task selection. It is not clear whether the language switch cost also reduces with preparation, partly because there have been very few attempts to examine preparation for a language switch, and partly because these attempts suffered from non-trivial methodological drawbacks. In Experiments 1-3 I used an optimised picture naming paradigm in which language changed unpredictably and was specified by a language cue presented at different intervals before the picture. Experiment 1, conducted on ‘unbalanced’ bilinguals, revealed some evidence of reduction in the language switch cost for naming times with preparation, but only when cue duration was short. In an attempt to further optimise the paradigm, in Experiment 2 the cue-stimulus interval (which was varied from trial to trial in Experiment 1), was varied over blocks instead. Visual cues were replaced with auditory cues – the latter also enabled a comparison between semantically transparent word cues (the spoken names of the languages) and less transparent cues (fragments of national anthems). Experiment 2 revealed a reduction in switch cost with preparation for naming latencies, but only in the second language; the first language showed the reverse. To examine whether the increase in switch cost with preparation in the first language could be due to unbalanced bilinguals biasing processing towards L2, balanced bilinguals were tested in Experiment 3. This revealed a robust reduction in switch cost in naming latencies for both languages, which was driven primarily by the trials with the anthem cues. However, in the error rates the switch cost increased with preparation interval, thus complicating the interpretation of the reduction observed for response times. Experiment 4 investigated whether preparation for a language switch elicits the electrophysiological patterns commonly found during preparation for a task switch – a switch-induced positive polarity Event-Related Potential (ERP) with a posterior scalp distribution. Contrary to a recent report of the absence of the posterior positivity in language switching, it was clearly present in the present EEG data. As in task switching, the amplitude of the posterior positivity predicted performance. The electrophysiological data suggest that preparation for a language switch and preparation for a task switch rely on highly overlapping control mechanisms. The behavioural data suggest that advance control can be effective in language switching, but perhaps not as effective as in task switching. Experiments 1-3 also examined the effect of stimulus associative history – whether the language used on the previous encounter with a given stimulus influenced performance on the current trial). Having previously named a given picture in the same language benefited overall performance, but did not do so more for switches than repeats. Thus, stimulus associative history does not seem to contribute to the language switch cost. The second strand of my research asked whether bilinguals can set themselves independently for speech vs. comprehension. Previous research has examined the cost of switching the language in output tasks and in input tasks. But, it is not clear whether one can apply separate control settings for input and output selection. To investigate this, I used a paradigm that combined switching languages for speech production and comprehension. My reasoning was that, if there is cross-talk between the control settings for input vs. output, performance in one pathway should benefit if the language selected for the other pathway is the same relative to when it is different: a ‘language match effect’. Conversely, if there is no cross-talk, there should not be a language match effect. In Experiment 5 bilinguals alternated predictably between naming numbers in their first and second language (in runs of 3 trials), whilst also having to semantically categorise spoken words which occasionally (and unpredictably) replaced the numbers. The language of the categorisation ‘probes’ varied over blocks of ~17 naming runs, but was constant within a block. The results showed a clear match effect in the input task (categorisation), but not the output task (naming). To examine the potential role of proficiency, Experiment 6 used the same paradigm to test unbalanced and balanced bilinguals. The pattern of results was qualitatively similar in both groups to that observed in Experiment 5: a language match effect confined to the input task. These results suggest ‘leakage’ from the output control settings into the input control settings.
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The Kakimizu complex of a linkBanks, Jessica E. January 2012 (has links)
We study Seifert surfaces for links, and in particular the Kakimizu complex MS(L) of a link L, which is a simplicial complex that records the structure of the set of taut Seifert surfaces for L. First we study a connection between the reduced Alexander polynomial of a link and the uniqueness of taut Seifert surfaces. Specifically, we reprove and extend a particular case of a result of Juhasz, using very different methods, showing that if a non-split homogeneous link has a reduced Alexander polynomial whose constant term has modulus at most 3 then the link has a unique incompressible Seifert surface. More generally we see that this constant term controls the structure of any non-split homogeneous link. Next we give a complete proof of results stated by Hirasawa and Sakuma, describing explicitly the Kakimizu complex of any non-split, prime, special alternating link. We then calculate the form of the Kakimizu complex of a connected sum of two non-fibred links in terms of the Kakimizu complex of each of the two links. This has previously been done by Kakimizu when one of the two links is fibred. Finally, we address the question of when the Kakimizu complex is locally infinite. We show that if all the taut Seifert surfaces are connected then MS(L) can only be locally infinite when L is a satellite of a torus knot, a cable knot or a connected sum. Additionally we give examples of knots that exhibit this behaviour. We finish by showing that this picture is not complete when disconnected taut Seifert surfaces exist.
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