On the instability and constraints of the interaction between number representation and spatial attention in healthy humans. A concise review of the literature and new experimental evidence

.The relationship between number and space representation is still one of the most debated topics in studies of mathematical cognition. Here we offer a concise review of two important behavioral effects that have pointed out the use of a spatially left-to-right oriented mental number line (MNL) in healthy participants: the SNARC effect and the attentional SNARC effect (Att-SNARC). Following a brief summary of seminal investigations on the introspective properties of the MNL, we review recent empirical evidence and theories on the functional origin of the SNARC effect, where upon left/right response choices faster reaction times are found for small numbers with left-side responses and for large numbers with right-side responses. Then we offer a summary of the studies that have investigated whether the mere perception of visual Arabic numbers presented at central fixation can engender spatially congruent lateral shifts of attention, ie, leftward for small numbers and rightward for large ones, ie, the Att-SNARC effect. Finally, we summarize four experiments that tested whether the Att-SNARC depends on an active rather than passive processing of centrally presented digit cues. In line with other recent studies, these experiment do not replicate the original Att-SNARC and show that the mere perception of Arabic numerals does not trigger automatic shifts of attention. These shifts are instead found when the task requires the explicit left/right spatial coding of digit cues, ie, Spatial Att-SNARC (Fattorini et al., 2015b). Nonetheless, the reliability of the Spatial Att-SNARC effect seems not as strong as that of conventional SNARC effects where left/ right codes are mapped onto responses rather than directly mapped on digit cues. Comparing the magnitude of digits to a numerical reference, ie, "5," also produced a Magnitude Comparison Att-SNARC that was weaker than the spatial one. However, the reliability of this Magnitude Comparison Att-SNARC should be considered with caution because, like in a study by Zanolie and Pecher (2014), we recently failed to replicate this effect in a separate behavioral-eventrelated potentials study in preparation (Fattorini et al., 2015a). All together the results from the present series of experiments support the hypothesis that spatial coding is not an intrinsic part of number representation and that number-space interaction is determined by the use of stimulus-or response-related spatial codes in the task at han

Standard model anomalies: Lepton flavour non-universality and lepton g-2

We critically analyze the body of results that hints to the existence of New Physics from possible violations of lepton universality observed by the LHCb experiment in the $\mu/e$ ratios $R_{K}$ and $R_{K^*}$ to the $g-2$ lepton anomalies. The analysis begins with a theoretical, in depth, study of the $\mu/e$ ratios $R_{K}$ and $R_{K^*}$ as well as the process $B_s \rightarrow \mu^+ \mu^-$. Here we consider the impact of complex Wilson coefficients and derive constraints on their imaginary and real parts. We then move to a comprehensive comparison with experimental results. We show that, by fitting a single Wilson coefficient, the deviations from the Standard Model are at the $4.7\sigma$ level when including only the hadronic insensitive observables while it increases to $6.1\sigma$ when including also the hadronic sensitive ones. When switching on all relevant Wilson coefficients and combining both hadronic sensitive and insensitive data into the fit, the deviation from the Standard Model peaks at 7.2$\sigma$ and decreases at the $4.9\sigma$ level if we assume that the central values of $R_K$ and $R_K^{\ast}$ are taken to be unity. We further estimate the non-perturbative long distance hadronic contributions and show that their inclusion still requires New Physics to fit the data. We then introduce the $g-2$ lepton anomalies results. Different theoretical models are considered that can explain the discrepancies from the Standard Model. In the final part of our work we estimate the impact of the forthcoming data from LHCb (coming from LHC Run3) and Belle II, when it will have accumulated about $5~ab^{-1}$