Selección de los componentes para el sistema de refrigeración

We approached the first question using functional imaging techniques in two steps: first, we investigated whether the two processes of subitizing and counting are implemented in separable regions in the brain using PET. The simple logic behind that study was that a different localisation would be quite a strong support for their dichotomy. Results from this first study indicated that no brain area is specific for subitizing or counting. On the contrary, we found activation in bilateral middle occipital and parietal areas for both subitizing and counting. This activation increases as the number of items in the visual array increases, reaching maximum peak and extent when counting 6-9 arranged items. This failure to measure an anatomical segregation between subitizing and counting, however, does not completely rule out the hypothesis of a different nature of the two processes. In fact, there was still the possibility that the two processes result from a qualitative different involvement of a common set of regions. In that study, due to the constraints of the techniques used (PET), the activity evoked by different numerosities could only be measured in two distinct blocks (numbers 1-4, and numbers above 4). This did not allow investigating whether the regions more active in counting showed a sudden, discontinuous engagement at a specific numerosity or

whether their activity increased linearly with each added item, even within the subitizing range. Moreover, with such block designs, it was not possible to obtain a trial-by-trial measure of the brain activity. Such a measure might be crucial if subjects’ reliance on subitizing versus counting is a probabilistic rather than deterministic process and shows a high degree of variability between subjects and trials, even for a fixed numerosity.

Therefore, in a second step, using event related fMRI, we investigated whether the two processes emerge from a qualitatively different recruitment of a set of previously individuated common brain regions. Results revealed that activation in regions of the parietal and prefrontal cortex increase non linearly as the number of objects increases. In particular, concentrating on activity of the posterior parietal cortex, we showed that such increase shows a strong discontinuity around the numerosity 3, the putative subitizing range. Activity showed very little or no increase from one to 3 objects, a sudden increase at 4, and a linear constant increase with number beyond 4. These results are in strong support for a qualitative difference between subitizing and counting. We further demonstrated the robustness of such subitizing/counting discontinuity by predicting the numerosity range (subitizing or counting) of the stimuli that subjects were presented at any given trial, by simply looking at the level of activity in such parietal regions. This way of reasoning, reversing the arrow of causality classically oriented from behaviour to brain imaging, has been proven particularly useful in this study. We took this logic further, showing that even at the fixed intermediate numerosity of 4, where often a mixture of subitizing and counting strategies were deployed, we were able to predict the subject’s strategy at the single trial level, therefore accounting for some of the otherwise unexplained inter-subject and inter-trial variability in performance.

In conclusion, with these studies on subitizing and counting we demonstrated that they emerge from a qualitatively different recruitment of a set of common brain regions related to both attention and language. While the activity of such cerebral network linearly increases with the number of objects in counting, there is no differential activation of such network with the number of objects in subitizing. Where, in the brain, the difference between a set containing one, two, three, or four items is coded, is still an open question, as we were not able to isolate a region responding differentially to different numerosity in subitizing. Moreover, as presented in the first

chapter, different models of subitizing have been proposed, some suggesting that it reflects a numerosity estimation process, other suggesting that it reflects a preattentive visual routine of grouping and/or pattern recognition. Our experiments do not allow us to select between those different models. More specific experiments should be envisaged in order to clarify the nature of subitizing.

1.2- Inferring cognitive processes from brain activation

In passing, we would like to remark that in our second experiment we used brain activity to shed light on cognitive processes involved in our quantification task, in particular to separate trials where a subitizing-parallel or a counting-serial strategy was used. Such logic of going from brain activity to the cognitive processes, reversing the usual direction of functional imaging experiments, was only very seldom previously applied, for example to infer motor behaviour using fMRI signals from motor cortex (Dehaene et al., 1998) or to separate trials where subjects imagined a face or a house using fMRI signals from the fusiform face area (FFA) and the parahippocampal place area (PPA) (O'Craven & Kanwisher, 2000). Here, we show that single-trial parietal activation can be used to sort out trials with or without serial attentive processing, and that this can capture some of the otherwise unexplained inter-subjects and inter-trial variability in behaviour. In the present thesis such logic was functional to a specific question related to subitizing and counting, but we think that such an approach could (and should) have much broader applications, whenever behavioural data are not sufficient to shed light on the processes underlying a given overt behavioural and/or even covert mental event.