The spatial association of numbers and mathematical symbols

The "SNARC effect" refers to the finding that people respond faster to small numbers with the left hand and to large numbers with the right hand. This effect is often explained by hypothesizing that numbers are represented from left to right in ascending order (Mental Number Line). However, the SNARC effect may not depend on quantitative information, but on other factors such as the order in which numbers are often represented from left to right in our culture. Four experiments were performed to test this hypothesis. In the first experiment, the concept of spatial association was extended to nonnumeric mathematical symbols: the minus and plus symbols. These symbols were presented as fixation points in a spatial compatibility paradigm. The results demonstrated an opposite influence of the two symbols on the target stimulus: the minus symbol tends to favor the target presented on the left, while the plus symbol the target presented on the right, demonstrating that spatial association can emerge in the absence of a numerical context. In the last three experiments, the relationship between quantity and order was evaluated using normal numbers and mirror numbers. Although mirror numbers denote quantity, they are not encountered in a left-to-right spatial organization. In Experiments 1 and 2, participants performed a magnitude classification task with mirror and normal numbers presented together (Experiment 1) or separately (Experiment 2). In Experiment 3, participants performed a new task in which quantity information processing was not required: the mirror judgment task. The results show that participants access the quantity of both normal and mirror numbers, but only the normal numbers are spatially organized from left to right. In addition, the physical similarity between the numbers, used as a predictor variable in the last three experiments, showed that the physical characteristics of numbers influenced participants' reaction times.

New indicators of star cluster dynamical evolution

This thesis presents a study of globular clusters (GCs), based on analysis of Monte Carlo simulations of globular clusters (GCs) with the aim to define new empirical parameters measurable from observations and able to trace the different phases of their dynamical evolution history. During their long term dynamical evolution, due to mass segregation and and dynamical friction, massive stars transfer kinetic energy to lower-mass objects, causing them to sink toward the cluster center. This continuous transfer of kinetic energy from the core to the outskirts triggers the runaway contraction of the core, known as "core collapse" (CC), followed by episodes of expansion and contraction called gravothermal oscillations. Clearly, such an internal dynamical evolution corresponds to significant variations also of the structure of the system. Determining the dynamical age of a cluster can be challenging as it depends on various internal and external properties. The traditional classification of GCs as CC or post-CC systems relies on detecting a steep power-law cusp in the central density profile, which may not always be reliable due to post-CC oscillations or other processes. In this thesis, based on the normalized cumulative radial distribution (nCRD) within a fraction of the half-mass radius is analyzed, and three diagnostics (A5, P5, and S2.5) are defined. These diagnostics show sensitivity to dynamical evolution and can distinguish pre-CC clusters from post-CC clusters.The analysis performed using multiple simulations with different initial conditions, including varying binary fractions and the presence of dark remnants showed the time variations of the diagnostics follow distinct patterns depending on the binary fraction and the retention or ejection of black holes. This analysis is extended to a larger set of simulations matching the observed properties of Galactic GCs, and the parameters show a potential to distinguish the dynamical stages of the observed clusters as well.