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Last parution: n° 199, Fall 2012, special issue: Mathematical psychology
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| Title |
Between and mathematics. Different kinds of computational representations of music |
| Author |
ACOTTO Edoardo, ANDREATTA Moreno |
| Keywords |
Gamble, Conceptual space, Generative theory of tonal music, Mental representation, Music, Phenomenological structuralism, Sound object, Transformational analysis |
| Topic |
None |
| Abstract |
In this article we analyse different types of representations of music, both from a cognitive and a computational point of view. Whereas mental representations of music are the objects of the musical mind, and are therefore by definition a subject of cognitive psychology and philosophy, it can be argued that mathematical representations of music also have some cognitive correlates enabling the understanding of non-tonal music. Amongst the many typologies of mathematical representations of music, we will analyse in detail some examples belonging to the transformational paradigm, which is a formalized subfield of computational musicology coming from the American set-theoretical tradition. Transforma-tional music analysis also raises new questions about the cognitive and philosophical ramifications of algebraic and category-theory approaches in music theory, analysis and composition. |
| Number |
199, Fall 2012, special issue: Mathematical psychology |
| Language |
 English | Read the article
| Title |
Rating the diversity in sets of objects by referring to transormation as criteria |
| Author |
BURIGANA Luigi, VICOVARO Michele |
| Keywords |
Diversity, Inner transformation, Invariance |
| Topic |
None |
| Abstract |
The starting point of this study is the definition of two concepts expressing how a set of transformations acting within a domain may represent an upper or a lower bound of the diversity existing in any subset of that domain. The subject of analysis is then gradually expanded, by considering partitions (rather than subsets) of the domain, families of sets of transformations (rather than just one such set), and sets of objects indirectly related to the domain (rather than sets directly included in it). The main concepts defined in this study are explored in their formal properties and illustrated by examples. The introductory and concluding sections include comments on the motivation for the study and the possible merits of the method discussed. |
| Number |
199, Fall 2012, special issue: Mathematical psychology |
| Language |
English | Read the article
| Title |
Differential item functioning detection with logistic regression |
| Author |
CUEVAS Martha, CERVANTES Victor H. |
| Keywords |
Differential item functioning, Length of test, Logistic regression, Magnitude of DIF (Differential Item Functioning), Sample size, Sample size ratio |
| Topic |
None |
| Abstract |
Logistic regression has been used as a method for identifying differential item functioning (DIF) in different contexts. Some studies have shown that DIF detection through this procedure may be affected by variables such as sample size ratio, and sample size. It also seems related to specific item parameters like certain ranges of difficulty and discrimination [Herrera, 2005 ; Santana 2009]. We made a simulation study with four partially crossed independent variables which resulted in 270 conditions and simulated 200 replications for each experimental condition. McFadden’s distance R2 between models (R2∆) was used as an effect size measure and as a dependent variable in order to minimize type I and II errors that the statistical test would not have been able to control. We used linear models to define which variables affected the effect size measures : R2∆ for detecting items with uniform DIF (DRU) and for detecting items with non uniform DIF (DRN). The results show that manipulated variables and some of their interactions affect DRU and DRN differently. We also obtained cut-off points, both for DRU and DRN, for several levels of the variables that affect the R2∆ measures. |
| Number |
199, Fall 2012, special issue: Mathematical psychology |
| Language |
English | Read the article
| Title |
Recalling the list-before-last: a cautionary tale |
| Author |
LAMING Donald |
| Keywords |
Free recall, Memory, Recalling the list-before last, Retrieval, Shiffrin's experiment |
| Topic |
None |
| Abstract |
An unresolved question in memory research is: What cues free recall? An experiment by Shiffrin [1970], in which participants were instructed to recall the list-before-last, has been cited as evidence that retrieval in free recall experiments is (somehow) cued. The alternative is that retrieval is spontaneous and the words recalled are selected only in retrospect, after they have been retrieved. This article illustrates the difference between these two hypotheses and then compares Shiffrin’s published data with data from Murdock and Okada [1970], and with three other experiments, to argue that the rate of recall from the list-before-last is no greater than one should expect from a spontaneous retrieval that (potentially) addresses all preceding lists. The number of intrusions, when recall is requested from the ultimate list, corrected by an estimate of the proportion of unwanted retrievals that are suppressed, is sufficient to account for the number of words recalled from the list-before-last. |
| Number |
199, Fall 2012, special issue: Mathematical psychology |
| Language |
English | Read the article
| Title |
Compression mechanisms in working memory |
| Author |
LEMAIRE Benoît, ROBINET Vivien, PORTRAT Sophie |
| Keywords |
Human experiment, Information compression, Information Theory, Minimum description length, Simulations, Working memory |
| Topic |
None |
| Abstract |
Working memory capacity is limited and much work has been done for decades on estimating its value. However, if stimuli contain redundancies, compression mechanisms probably appear which change the point of view on that capacity. By means of a behavioral study and a computational simulation, we aim at showing that working memory is not just a fixed number of items. We first present a theoretical framework in the domain of information theory in order to analyse this point of view. Then, we show the results of an experiment studying the effects of some regularities on memory recall performance, as well as a simulation using a model of chunking and two different memory models. Our results show that it is probably wrong to consider working memory capacity as a fixed number of items. It is better to express it in terms of a quantity of information. |
| Number |
199, Fall 2012, special issue: Mathematical psychology |
| Language |
English | Read the article
| Title |
Power vs. logarithmic model of Fitts’ law: a mathematical analysis |
| Author |
RIOUL Olivier, GUIARD Yves |
| Keywords |
Fitt's law, Functional equations, Mathematical models in psychology, Pointing, Simple rapid aimed movement |
| Topic |
None |
| Abstract |
Whether Fitts’ law, a well-known model of human pointing movement, is a logarithmic law or a power law has remained unclear so far. In two widely cited papers, Meyer & al. have claimed that the power model they derived from their celebrated stochastic optimized submovement theory encompasses the logarithmic model as a limiting case, when the number of submovements grows large. We review the Meyer & al. submovement theory and show that this claim is questionable mathematically. Our analysis reveals that Meyer & al.’s theory implies in fact a quasi-logarithmic, rather than quasi-power model, the two models not being equivalent. Awareness that the two classes of candidate mathematical descriptions of Fitts’ law are not equivalent should stimulate experimental research in the field. |
| Number |
199, Fall 2012, special issue: Mathematical psychology |
| Language |
English | Read the article
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