Many studies have investigated the association between numerical magnitude processing skills, as assessed by the numerical magnitude comparison task, and broader mathematical competence, e.g. counting, arithmetic, or algebra. Most correlations were positive but varied considerably in their strengths. It remains unclear whether and to what extent the strength of these associations differs systematically between non-symbolic and symbolic magnitude comparison tasks and whether age, magnitude comparison measures or mathematical competence measures are additional moderators. We investigated these questions by means of a meta-analysis. The literature search yielded 45 articles reporting 284 effect sizes found with 17,201 participants. Effect sizes were combined by means of a two-level random-effects regression model. The effect size was significantly higher for the symbolic (r = .302, 95% CI [.243, .361]) than for the non-symbolic (r = .241, 95% CI [.198, .284]) magnitude comparison task and decreased very slightly with age. The correlation was higher for solution rates and Weber fractions than for alternative measures of comparison proficiency. It was higher for mathematical competencies that rely more heavily on the processing of magnitudes (i.e. mental arithmetic and early mathematical abilities) than for others. The results support the view that magnitude processing is reliably associated with mathematical competence over the lifespan in a wide range of tasks, measures and mathematical subdomains. The association is stronger for symbolic than for non-symbolic numerical magnitude processing. So symbolic magnitude processing might be a more eligible candidate to be targeted by diagnostic screening instruments and interventions for school-aged children and for adults.

The number line estimation task is widely used to investigate mathematical learning and development. The present meta-analysis statistically synthesized the extensive evidence on the correlation between number line estimation and broader mathematical competence. Averaged over 263 effect sizes with 10,576 participants with sample mean ages from 4 to 14 years, this correlation was r = .443. The correlation increased with age, mainly because it was higher for fractions than for whole numbers. The correlation remained stable across a wide range of task variants and mathematical competence measures (i.e., counting, arithmetic, school achievement). These findings demonstrate that the task is a robust tool for diagnosing and predicting broader mathematical competence and should be further investigated in developmental and experimental training studies.

In daily life, signals from the different senses are often integrated to enhance multisensory perception. However, an important, yet currently still controversial, topic concerns the need for attention in this integration process. To investigate this question, we turned to the processing of multisensory distractors. Note that multisensory target processing is typically confounded with attention as people attend to the stimuli that they respond to. We therefore designed a multisensory flanker task in which the target and distractor stimuli were both multisensory and the congruency between the features (auditory and visual) was varied orthogonally. In addition, we manipulated whether distractor or target was within the focus of participants’ gaze (i.e., was overtly attended). Importantly, distractor congruency effects were modulated by this manipulation. Fixating the distractor led to crossmodal congruency effects between the visual and auditory feature dimensions (e.g., a visually incongruent distractor interfered more if it was also auditorily incongruent with the target), while congruency effects were independent of each other when the distractor was not fixated (i.e., visual interference was not modulated by auditory interference in this case). These results suggest that distractors outside the focus of overt attention are processed at the level of features whereas those distractors presented at fixation are processed as a configuration of features. Taken together, these results can be taken to suggest that the multisensory integration of irrelevant stimuli depends on the focus of spatial attention.

We here report on the implementation of a microwave lens for neutral polar molecules suitable to focus molecules both in low-field-seeking and in high-field-seeking states. By using the TE11m modes of a 12 cm long cylindrically symmetric microwave resonator, Stark-decelerated ammonia molecules are transversally confined. We investigate the focusing properties of this microwave lens as a function of the molecules' velocity, the detuning ∆ of the microwave frequency from the molecular resonance frequency, and the microwave power. Such a microwave lens can be seen as a first important step towards further microwave devices, such as decelerators and traps.

We report on the experimental realization of a microwave decelerator for neutral polar molecules, suitable for decelerating and focusing molecules in high-field-seeking states. The multistage decelerator consists of a cylindrical microwave cavity oscillating in the TE 11n mode, with n = 12 electric field maxima along the symmetry axis. By switching the microwave field on and off at the appropriate times, a beam of state-selected ammonia molecules with an incident mean velocity of 25 m/s is guided while being spatially focused in the transverse direction and bunched in the forward direction. Deceleration from 20.0 to 16.9 m/s and acceleration from 20.0 to 22.7 m/s are demonstrated.