A systematic investigation reveals that Ishihara et al.'s (2008) STEARC effect only emerges when time is directly assessed

The Spatial-TEmporal Association of Response Codes (STEARC) effect (Ishihara et al. in Cortex 44:454-461, 2008) is evidence that time is spatially coded along the horizontal axis. It consists in faster left-hand responses to early onset timing and faster right-hand responses to late onset timing. This effect has only been established using tasks that directly required to assess onset timing, while no studies investigated whether this association occurs automatically in the auditory modality. The current study investigated the occurrence of the STEARC effect by using a procedure similar to Ishihara and colleagues. Experiment 1 was a conceptual replication of the original study, in which participants directly discriminated the onset timing (early vs. late) of a target sound after listening to a sequence of auditory clicks. This experiment successfully replicated the STEARC effect and revealed that the onset timing is mapped categorically. In Experiments 2, 3a and 3b participants were asked to discriminate the timbre of the stimuli instead of directly assessing the onset timing. In these experiments, no STEARC effect was observed. This suggests that the auditory STEARC effect is only elicited when time is explicitly processed, thus questioning the automaticity of this phenomenon

Temporal speed prevails on interval duration in the SNARC-like effect for tempo

The Spatial-Numerical Association of Response Codes (SNARC) effect is evidence of an association between number magnitude and response position, with faster left-key responses to small numbers and faster right-key responses to large numbers. Similarly, recent studies revealed a SNARC-like effect for tempo, defined as the speed of an auditory sequence, with faster left-key responses to slow tempo and faster right-key responses to fast tempo. In order to address some methodological issues of previous studies, in the present study we designed an experiment to investigate the occurrence of a SNARC-like effect for tempo, employing a novel procedure in which only two auditory beats in sequence with a very short interstimulus interval were used. In the "temporal speed" condition, participants were required to judge the temporal speed (slow or fast) of the sequence. In the "interval duration" condition, participants were required to judge the duration of the interval between the two beats (short or long). The results revealed a consistent SNARC-like effect in both conditions, with faster left-hand responses to slow tempo and faster right-hand responses to fast tempo. Interestingly, the consistency of the results across the two conditions indicates that the direction of the SNARC-like effect was influenced by temporal speed even when participants were explicitly required to focus on interval duration. Overall, the current study extends previous findings by employing a new paradigm that addresses potential confounding factors and strengthens evidence for the SNARC-like effect for tempo

It’s SNARC o’ clock: manipulating the salience of the context in a conceptual replication of Bächtold et al.’s (1998) clockface study

The Spatial-Numerical Association of Response Codes (SNARC) effect consists in faster left-/right-key responses to small/large numbers. (Bächtold et al., Neuropsychologia 36:731–735, 1998) reported the reversal of this effect after eliciting the context of a clockface—where small numbers are represented on the right and large numbers on the left. The present study investigates how the salience of a particular spatial-numerical context, which reflects the level of activation of the context in working memory, can alter Spatial Numerical Associations (SNAs). Four experiments presented the clockface as context and gradually increased its salience using different tasks. In the first two experiments (low salience), the context was presented at the beginning of the experiment and its retrieval was not required to perform the tasks (i.e., random number generation in Experiment 1, magnitude classification and parity judgement in Experiment 2). Results revealed regular left-to-right SNAs, unaffected by the context. In Experiment 3 (medium salience), participants performed magnitude classification and parity judgement (primary task), and a Go/No-go (secondary task) which required the retrieval of the context. Neither the SNARC effect nor a reversed-SNARC emerged, suggesting that performance was affected by the context. Finally, in Experiment 4 (high salience), the primary task required participants to classify numbers based on their position on the clockface. Results revealed a reversed SNARC, as in (Bächtold et al., Neuropsychologia 36:731–735, 1998). In conclusion, SNARC is disrupted when the context is retrieved in a secondary task, but its reversal is observed only when the context is relevant for the primary task

Discrete Calculus - Methods for counting

This chapter is dedicated to counting partitions of sets and partitions of sets into cycles, and also introduces Stirling numbers and Bell numbers. As an application of the concepts discussed here we state Fa\ue0 di Bruno chain rule for the n-th derivative of a composite of n-times differentiable functions on R. In the last section we discuss Eulerian numbers and as an application we solve the famous problem of the Smith College diplomas, and we establish some notable identities like Worpitzky\u2019s formula

Stereoselective ring-opening metathesis polymerization of 7-tert-butoxy-bicyclo[2,2,1]hepta-2,5-diene by NHC-ruthenium catalysts

Ru complexes having N-heterocyclic carbene (NHC) ligands, differing in the bulkiness of N-aryl substituents and in the backbone substitution and/or configuration, are utilized in the ring-opening metathesis polymerization (ROMP) of 7-tert-butoxybicyclo[2,2,1]hepta-2,5-diene (7-TBONBD). The activity, regioselectivity, and stereoselectivity of the catalysts are investigated and rationalized considering the influence of the NHC ligand architectures of Ru complexes on the outcome of the polymerization. The reactivity order is influenced by bulky substituents at the nitrogen of the NHC ligand and by NHC-backbone substitution. All of the catalysts give rise to living polymerizations and show high selectivity, producing highly syndiotactic polymers with 100% of anti-units and, surprisingly, an elevated cis-content (up to 88%)