C Mathematical and Quantitative Methods
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Institute
My thesis focused on the predictions of the activation-based model of Lewis and Vasishth (2005) to investigate the evidence for the use of the memory system in the formation of non-local dependencies in sentence comprehension.
The activation-based model, which follows the Adaptive Control of Thought-Rational framework (ACT-R; Anderson et al., 2004), has been used to explain locality effects and similarity-based interference by assuming that dependencies are resolved by a cue-based retrieval mechanism, and that the retrieval mechanism is affected by decay and interference.
Both locality effects and (inhibitory) similarity-based interference cause increased difficulty (e.g., longer reading times) at the site of the dependency completion where a retrieval is assumed: (I) Locality effects are attributed to the increased difficulty in the retrieval of a dependent when the distance from its retrieval site is increased. (II) Similarity-based interference is attributed to the retrieval being affected by the presence of items which have similar features as the dependent that needs to be retrieved.
In this dissertation, I investigated some findings problematic to the activation-based model, namely, facilitation where locality effects are expected (e.g., Levy, 2008), and the lack of similarity-based interference from the number feature in grammatical sentences (e.g., Wagers et al., 2009). In addition, I used individual differences in working memory capacity and reading fluency as a way to validate the theories investigated (Underwood, 1975), and computational modeling to achieve a more precise account of the phenomena.
Regarding locality effects, by using self-paced reading and eye-tracking-while reading methods with Spanish and German data, this dissertation yielded two main findings: (I) Locality effects seem to be modulated by working memory capacity, with high-capacity participants showing expectation-driven facilitation. (II) Once expectations and other potential confounds are controlled using baselines, with increased distance, high-capacity readers can show a slow-down (i.e., locality effects) and low-capacity readers can show a speedup. While the locality effects are compatible with the activation-based model, simulations show that the speedup of low-capacity readers can only be accounted for by changing some of the assumptions of the activation-based model.
Regarding similarity-based interference, two relatively high-powered self-paced reading experiments in German using grammatical sentences yielded a slowdown at the verb as predicted by the activation-based model. This provides evidence in favor of dependency creation via cue-based retrieval, and in contrast with the view that cue-based retrieval is a reanalysis mechanism (Wagers et al., 2009).
Finally, the same experimental results that showed inhibitory interference from the number feature are used for a finer grain evaluation of the retrieval process. Besides Lewis and Vasishth’s (2005) activation-based model, also McElree’s (2000) direct-access model can account for inhibitory interference. These two models assume a cue-based retrieval mechanism to build dependencies, but they are based on different assumptions. I present a computational evaluation of the predictions of these two theories of retrieval. The models were compared by implementing them in a Bayesian hierarchical framework. The evaluation of the models reveals that some aspects of the data fit better under the direct access model than under the activation-based model. However, a simple extension of the activation-based model provides a comparable fit to the direct access model. This serves as a proof of concept showing potential ways to improve the original activation-based model.
In conclusion, this thesis adds to the body of evidence that argues for the use of the general memory system in dependency resolution, and in particular for a cue-based retrieval mechanism. However, it also shows that some of the default assumptions inherited from ACT-R in the activation-based model need to be revised.
Solar-like stars maintain their magnetic fields thanks to a dynamo mechanism. The Babcock-Leighton dynamo is one possible dynamo that has the particularity to require magnetic flux tubes. Magnetic flux tubes are assumed to form at the bottom of the convective zone and rise buoyantly to the surface. A delayed dynamo model has been suggested, where the delay accounts for the rise time of the magnetic flux tubes; a time, that has been ignored by former studies.
The present thesis aims to study the applicability of the flux tube/Babcock-Leighton dynamo to other stars. To do so, we attempt to constrain the rise time of magnetic flux tubes thanks to the first fully compressible MHD simulations of rising magnetic flux tubes in stratified rotating spherical shells.
Such simulations are limited to an unrealistic parameter space, therefore, a scaling relation is required to scale the results to realistic physical regimes. We extended earlier works on 2D scaling relations and derived a general scaling law valid for both 2D and 3D. We then carried out two large series of numerical experiments and verified that the scaling law we have derived indeed applies to the fully non-linear case. It allowed us to extract a constraint for the rise time of magnetic flux tubes that is valid for any solar-like star. We finally introduced this constraint to a delayed dynamo model.
By carrying out simulations of a mean-field, delayed, flux tube/Babcock-Leighton dynamo, we were able to identify a new dynamo regime resulting from the delay. This regime requires delays about an entire cycle and exhibits subequipartition magnetic activity. Revealing this new regime shows that even for long delays the flux tube/Babcock-Leighton dynamo can still deliver non-decaying solutions and remains a good candidate for a wide range of solar-like stars.