Temporal Magnitudes Research Articles

Measuring temporal bias in sequential numerosity comparison

While several methods have been proposed to assess the influence of continuous visual cues in parallel numerosity estimation, the impact of temporal magnitudes on sequential numerosity judgments has been largely ignored. To overcome this issue, we extend a recently proposed framework that makes it possible to separate the contribution of numerical and non-numerical information in numerosity comparison by introducing a novel stimulus space designed for sequential tasks. Our method systematically varies the temporal magnitudes embedded into event sequences through the orthogonal manipulation of numerosity and two latent factors, which we designate as “duration” and “temporal spacing”. This allows us to measure the contribution of finer-grained temporal features on numerosity judgments in several sensory modalities. We validate the proposed method on two different experiments in both visual and auditory modalities: results show that adult participants discriminated sequences primarily by relying on numerosity, with similar acuity in the visual and auditory modality. However, participants were similarly influenced by non-numerical cues, such as the total duration of the stimuli, suggesting that temporal cues can significantly bias numerical processing. Our findings highlight the need to carefully consider the continuous properties of numerical stimuli in a sequential mode of presentation as well, with particular relevance in multimodal and cross-modal investigations. We provide the complete code for creating sequential stimuli and analyzing participants’ responses.

Distinguishing the observational signatures of hot spots orbiting Reissner-Nordström spacetime*

Abstract This paper investigates observable signatures of hot spots orbiting Reissner-Nordström (RN) black holes and naked singularities. For an RN black hole, we find two discernible lensing image tracks in time integrated images, capturing a complete orbit of hot spots and a image shadow within the critical curve where photons with a small impact parameter fall into the event horizon. Conversely, in RN singularities, additional image tracks can be found within the critical curve, originating from photons reflected by the infinitely high effective potential well. Moreover, we find incomplete and converging tracks from the time integrated images of hot spot orbiting RN singularities that have no photon sphere. The presence of these additional image tracks significantly influences temporal magnitudes at their local maxima, enabling us to differentiate between RN black holes and RN naked singularities.

Observations of orbiting hot spots around naked singularities

Recently, it has been reported that photons can traverse naked singularitiesin the Janis-Newman-Winicour and Born-Infeld spacetimes when thesesingularities are appropriately regularized. In this paper, we investigateobservational signatures of hot spots orbiting these naked singularities,with a focus on discerning them from black holes. In contrast to Schwarzschildblack holes, we unveil the presence of multiple additional image trackswithin critical curves in time integrated images capturing a completeorbit of hot spots. Moreover, these new images manifest as a morepronounced second-highest peak in temporal magnitudes when observedat low inclinations.

Observations of orbiting hot spots around scalarized Reissner–Nordström black holes

This paper investigates the observational signatures of hot spots orbiting scalarized Reissner–Nordström black holes, which have been reported to possess multiple photon spheres. In contrast to the single-photon sphere case, hot spots orbiting black holes with two photon spheres produce additional image tracks in time integrated images capturing a complete orbit of hot spots. Notably, these newly observed patterns manifest as a distinct second-highest peak in temporal magnitudes when observed at low inclination angles. These findings offer promising observational probes for distinguishing black holes with multiple photon spheres from their single-photon sphere counterparts.

Investigating the relationships between temporal and spatial ratio estimation and magnitude discrimination using structural equation modeling: Evidence for a common ratio processing system.

Humans perceive ratios of spatial and temporal magnitudes, such as length and duration. Previous studies have shown that spatial ratios may be processed by a common ratio processing system. The aim of the current study was to determine whether ratio processing is a domain-general ability and consequently involves common processing of temporal and spatial magnitudes. Two hundred seventy-five participants completed a battery of spatial and temporal ratio estimation and magnitude discrimination tasks online. Structural equation modeling was used to analyze the relationship between ratio processing across domains while controlling for absolute magnitude discrimination ability. The four-factor higher order model, consisting of spatial and temporal magnitude and ratio processing latent variables, showed adequate local and global fit, χ²(44) = 41.41, p = .626, root mean square error of approximation = .000. We found a significant relationship (r = .63) between spatial and temporal ratio processing, suggesting that ratio processing may be a domain-general ability. Additionally, absolute magnitude processing explained a large part (60-66%) of the variance in both spatial and temporal ratio processing factors. Overall, findings suggest that representation of spatial and temporal ratios is highly related and points toward a common ratio processing mechanism across different types of magnitudes. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Dynamical System Scaling of a Thermocline Thermal Storage System in the Thermal Energy Distribution System (TEDS) Facility

The purpose of this study was to develop a process to convert input signals from one facility into another by reflecting geometric and environmental settings. The Dynamic Energy Transport and Integration Laboratory (DETAIL) is one facility in development that aims to emulate the daily interactions among power production industry systems and be capable of receiving real-time data from those systems as inputs. To convert signals and ensure that the temporal sequences and magnitudes reflect the laboratory settings, the ability to scale and project data is essential. To demonstrate this ability, Dynamical System Scaling (a methodology that enables systems to scale and project or extrapolate datasets to desired environments while conserving the observed transient behavior based on first principles) was applied to DETAIL’s thermocline thermal storage system in the Thermal Energy Distribution System. The thermocline system was successfully scaled and a test case was conducted to generate a doubly accelerated energy charge and discharge in reference to past experimental data from the facility. The accelerated data were determined as able to conserve the amount of energy stored and the associated test boundary conditions were charge line maximum temperature, charge line velocity, and thermocline maximum temperature at 354 °C, 0.458 m/s, and 418 °C, respectively. The research results represented a case that required signals to be accelerated without altering the stored energy.

Variability of the Center of Mass in Trained Triathletes in Running After Cycling: A Preliminary Study Conducted in a Real-Life Setting.

While the sport of short-distance (Sprint) triathlon provides an opportunity to research the effect of the center of mass (CoM) when cycling and running, much remains to be done. The literature has failed to consistently or adequately report how changes to hand position influence subsequent running as inferred by the magnitude of CoM acceleration. The demands of cycle training in a drops and aerodynamic position followed by running remain unquantified in Sprint Distance triathlon. Thus, far data collected indicate that the cycle to run transition (T2) is important for overall race success. While many age-groupers participate in Sprint Distance triathlon, the lack of T2 based research make comparisons between cycle hand position and ensuing running difficult. The motion of the human body when cycling and running in triathlon can be described by the motion of its CoM in a local coordinate system. Unobtrusive wearable sensors have proven to be an informative resource to monitor the magnitude of CoM accelerations in running. However, the extent to which they are used in cycling is unclear. Therefore, the aim of the present study was to analyse the temporal magnitudes of CoM acceleration when cycling position and cadence is changed and to analyse these effects on running after cycling. Ten recreational triathletes completed two 20 km cycling trials at varied cadence in a drops position (parts of the handlebars that curve outward, CycleDrops) and an aerodynamic position (arms bent, forearms parallel to the ground, CycleAero) immediately followed by a 5 km run at self-selected pace. Torso kinematics by way of CoM acceleration magnitude were captured in a typical training setting using a triaxial accelerometer. CoM acceleration was quantified in m/s2 and variability was measured by the coefficient of variation (CV) and root mean square (RMS). Results from CycleAero indicated that acceleration of the CoM in longitudinal (CV = 1%) and mediolateral directions (CV = 3%) was significantly reduced (p < 0.001) compared to CycleDrops. As for rate of perceived exertion (RPE), a significant difference was observed with triathletes reporting higher values in CycleAero alongside a greater CoM acceleration magnitude in the anteroposterior direction. The CoM varied significantly from RunAero with less longitudinal (CV = 0.2, p < 0.001) and mediolateral acceleration observed (CV = 7.5%, p < 0.001) compared to RunDrops. Although greater longitudinal acceleration was observed in the initial 1 km epoch of RunAero, triathletes then seemingly adjusted their CoM trajectory to record lower magnitudes until completion of the 5 km run, completing the run quicker compared to RunDrops (22.56 min1 ± 0.2, 23.34 min1 ± 0.5, p < 0.001, CV = 1.3%). Coaches may look to use triaxial accelerometers to monitor performance in both cycling and running after cycling.

Quaternary glaciolacustrine deposits around a Triple Junction site: Paleolakes at the foot of the Northern Patagonian Ice field (Argentina and Chile)

The area involved by the triple junction between the South American, Nazca and Antarctic plates activity was affected by Quaternary glaciations. Before 12,800 yrs BP an extended ice field occupied the top of the Patagonian Andes, irradiating glaciers towards the east and the west dominantly. Towards the east, the ice melted in piedmont lakes; towards the west, fjords melted into the Pacific Ocean. The Upper-Pleistocene climate amelioration caused the recession of those glaciers. Some piedmont lakes reversed their Atlantic outflow towards to the Pacific Ocean. The glaciers retreat caused the fluvial reactivations along crustal former faults that were located below the ice. The Patagonian ice field became therefore split into present Northern and Southern fields. At the second largest lake of South America, the Buenos Aires-General Carrera Lake, the water level dropped from about 500 m over present mean sea level to 230 m. Several glaciolacustrine deposits from this area are indicating significant variations caused by climatic changes, volcanism and tectonics, differing in spatial and temporal magnitudes. The triple junction activity involved subduction of the Chile Ridge below the continental South American plate, volcanic activity and faulting. During the glacier melting the Baker River captured three eastern-moving glacial systems towards the southwest, towards the Pacific Ocean. This rapid event is thought to occur 12,800 yrs BP. The lowering of these glaciolacustrine systems should be also interpreted in terms of the tectonic activity in the region and considering other processes operating in the lakes and within the watersheds.

Parámetros y Magnitudes del Tiempo en la Obra One million years de On Kawara

On Kawara´s One million years exhibits enormous temporal magnitudes enumerations, with that, problematizes diverse ways of relation with time as representation and as experience possibility. However, time is apprehended in a sensitive way, therefore time is alienated from the means that try to contain it. But then, how can enumeration show temporary magnitudes in the piece? How can we record time? and how can art articulate time as a productive poetic? From this problem is proposed the following: time in One million years is addressed in three ways; enumeration, imagination and experience. These three modes of time problematize and exhibit the constant abandonment of time in the work of art. This study thinks over these time modes showed in Kawara´s work, contrasting them with artistic proposals that address similar temporalities, reflecting upon the paradoxes and contradictions that the pieces try to display.

Initial validation of the Multiple-Choice procedure for measuring video game playing

The inclusion of pathological gaming behavior in the most recent editions of the Diagnostic and Statistical Manual and the International Classification of Diseases highlights the need for increased research on this emerging topic of public health concern. Behavioral economic theories have informed conceptual and treatment models of addictive behaviors and may have a similar impact on our understanding of video gaming. The current study used an online version of the Multiple-Choice Procedure (MCP) to measure the relative reinforcing value of hypothetical video game playing for different temporal magnitudes (i.e., 10, 30, and 90 min during which to play a video game) relative to alternative monetary reinforcers available immediately or after a 1-week delay. Participants completed the MCP and the Video Game Dependency Scale (VGDS) to assess problems associated with internet gaming disorder. Similar to other addictive behaviors measured with the MCP, mean crossover points increased as temporal magnitudes increased and as delay was introduced to the alternative monetary reinforcer. MCP crossover points also added to the variance accounted for in VGDS scores. Being male was a significant predictor of VGDS scores, even after accounting for their higher frequency of video game playing. The current study is the first to investigate a behavioral economics model of video game playing. The findings strengthen the notion that similar behavioral mechanisms account for a wide range of addictive behavior. Future research is needed to assess the treatment utility of the MCP and other behavioral economic measures.

Cross-magnitude interactions across development: Longitudinal evidence for a general magnitude system.

There is general agreement that humans represent numerical, spatial, and temporal magnitudes from early in development. However, there is disagreement about whether different magnitudes converge within a general magnitude system and whether this system supports behavioral demonstrations of cross-magnitude interactions at different developmental time points. Using a longitudinal design, we found a relation between children's cross-magnitude interactions assessed at two developmental time points with different behavioral measures. More specifically, stronger cross-magnitude interactions in infancy (M = 9.3 months) predicted a stronger cross-magnitude congruity effect at preschool age (M = 44.2 months), even when controlling for performance on measures of inhibitory control, analogical reasoning, and verbal competence at preschool age. The results suggest a common mechanism for cross-magnitude interactions at different points in development as well as stability of the underlying individual differences. We argue that this mechanism reflects a nonverbal general magnitude system that is operational early in life and that displays continuity from infancy to preschool age.

Performance-informed EEG analysis reveals mixed evidence for EEG signatures unique to the processing of time

Certain EEG components (e.g., the contingent negative variation, CNV, or beta oscillations) have been linked to the perception of temporal magnitudes specifically. However, it is as of yet unclear whether these EEG components are really unique to time perception or reflect the perception of magnitudes in general. In the current study we recorded EEG while participants had to make judgments about duration (time condition) or numerosity (number condition) in a comparison task. This design allowed us to directly compare EEG signals between the processing of time and number. Stimuli consisted of a series of blue dots appearing and disappearing dynamically on a black screen. Each stimulus was characterized by its duration and the total number of dots that it consisted of. Because it is known that tasks like these elicit perceptual interference effects that we used a maximum-likelihood estimation (MLE) procedure to determine, for each participant and dimension separately, to what extent time and numerosity information were taken into account when making a judgement in an extensive post hoc analysis. This approach enabled us to capture individual differences in behavioral performance and, based on the MLE estimates, to select a subset of participants who suppressed task-irrelevant information. Even for this subset of participants, who showed no or only small interference effects and thus were thought to truly process temporal information in the time condition and numerosity information in the number condition, we found CNV patterns in the time-domain EEG signals for both tasks that was more pronounced in the time-task. We found no substantial evidence for differences between the processing of temporal and numerical information in the time–frequency domain.

Magnetic Mineralogical Variability along Deccan Trap Basalt Borehole (KBH07), Koyna Deep Continental Drilling Program, Western Maharashtra, India

ABSTRACT A 1248 m long core (KBH 07, 17°18'07" N; 73°47'28.2"E, 960m above msl) drilled up to basement in the Deccan traps from Koyna region was sampled at ∼10m interval for magnetic mineralogical studies. Analysis of routine rock magnetic parameters (mass specific magnetic susceptibility: χlf, frequency dependence of susceptibility: χfd, susceptibility of anhysteretic remanance: χARM, saturation isothermal remanance: SIRM, remanance coercivty: B(0)CR, SoftIRM, HardIRM, S-Ratio, SIRM/χlf, χARM/χlf) and density (σ, gm/ cc) depicted significant higher order temporal variation. The χlf varies between 13 and 309 x 10−8m3/kg and is independent of density variation. The χARM, B(0)CR and S-Ratios indicate majority of SD-PSD ferrimagnets with episodes of MD ferrimagnetic concentration and few hard coercivity components. The giant plagioclase lath bearing (GPB) horizons show highest variability of ferrimagnetic concentration marked by anomalous peaks. Overall the variability of rock magnetic parameters independent of lava flow units suggest that the changeover in magnetic mineral concentration, composition and domain size occur at major episodes in magma composition (e.g., primary source, crustal contamination and fractional crystallization). The studied parameters are therefore examined to mark intervals of (i) magma compositional changes, (ii) zones of oxidative conditions and (iii) rapid/slow cooling intervals demanding detailed petrologic studies. We identified one I order trend, four II order cycles and eight III order cycles for the purpose of correlation. Notable peak in χlf at 650-700m, the changeover in rock magnetic parameters at ∼930 m and ∼280 m can facilitate marker intervals while several higher order variations can be adopted for high resolution correlation to other boreholes in the region. The complex variation in rock magnetic parameters independent of flow units reflect temporal magnitudes of compositional variability, cooling and emplacement history that needs detailed petro-mineralogical attempts; and the present data is useful for high order inter-core correlations under the deep drilling program.

Learning About Spatial and Temporal Scale: Current Research, Psychological Processes, and Classroom Implications

ABSTRACT Geoscientists analyze and integrate spatial and temporal information at a range of scales to understand Earth processes. Despite this, the concept of scale is ill defined and taught unevenly across the K–16 continuum. This literature review focuses on two meanings of scale: one as the magnitude of the extent of a dimension and the other as a relationship between objects or events. We review 42 papers from science education and discipline-based education research (DBER) literature on students' conceptions related to one or both meanings of scale. Analysis of this prior work reveals a broader (though still limited) research base on domain general concepts of scale as magnitude and scant research on scale as a relationship. Learners begin reasoning about spatial and temporal magnitudes categorically by working with scales based on standard units and nonmetric values, such as body length. Concepts of scale magnitudes outside human experience are nonlinear. Facility with fractions and proportional reasoning are positively associated with the ability to reason about scale as a relationship. Two constructs from the psychological literature, structure mapping and the category adjustment model, offer theoretical accounts for these findings. We borrow a typology from the psychological literature to frame common geoscience instructional models in the context of spatial and temporal scale and suggest how instructors might facilitate students' reasoning about scale models. We identify a number of avenues for possible future research, including a critical need to understand how conceptual understanding of scale develops across the K–16 continuum.

Construing Temporal Magnitudes: Implications for Event Conceptualisation

The paper investigates the effect of alternating construals of temporal magnitudes on individuals’ reasoning about events that are explicitly embedded in time. Specifically, I analyse the meaning-making potential of “cumulative” and “fractional” construals, as in “30 minutes” and “half an hour”. Inspired by Cognitive Linguistics postulates, the hypothesis is that although these alternate constructions of time quantities are numerically equivalent, i.e. the objective time intervals designated are the same, they will differently prompt conceptualisation and reasoning about events they structure. This hypothesis is empirically tested with native and non-native speakers of English at four levels of time granularity, for seconds/minute, minutes/hour, weeks/month and months/year configurations. The findings show that there is a consistent major effect indicating a semantic-conceptual asymmetry between cumulative and fractional construals for the seconds/minute level, and a weaker, though analogous, effect for the months/year level, with the fractional construals ‘magnifying’ the quantity. Critically, the effect is found to hold in the case of conceptualisers for whom English, in which stimuli were presented, was their L2 while English native speakers appear to be ‘immune’. I discuss the potential motivation behind those patterns as well as the effect’s theoretical and practical implications. Finally, the findings are then related to a study on individuals’ intuitive predictions about meaning-making implications of alternating between cumulative and fractional construals of time.

Influence of linear chirp on the output characteristics of cross polarized wave with saturated power density

Ultra-short and ultra-intense laser is one of the hottest research spot of laser technology and strong field physics, due to its challenging and the frontier application research. As the key specification of ultrafast ultrahigh intensity laser pulse, the contrast ratio is very influential on the effect of laser-matter interaction. To perform the laser-matter interaction experiments at a high power level, the contrast is required to be as high as 1010 to prevent preplasma dynamics. To solve these problems, one has proposed many methods to improve the contrast of ultrafast laser, such as using the saturable absorbers, double chirped pulse amplification, plasma mirrors and the cross-polarized wave (XPW) generation. The XPW technology can not only enhance the contrast of the pulse by 3-4 orders of magnitude without introducing any space dispersion, but also extend the output spectrum to support shorter pulse duration. The XPW is a nonlinear filter technique in third-order nonlinear crystal with anisotropic susceptibility. Because of its simple and all-solid-state structure, the XPW technique has become one of the most effective methods to enhance the temporal pulse contrast and deliver shorter pulse duration in the field of high peak-power ultrafast lasers. This method has been used in many large laser facilities under construction or upgrades, such as the Apollon and ELI, the contrast ratio as high as 1010 has been achieved. It is known that the conversion efficiency and spectral characteristics of XPW have a strong dependence on the spatial and temporal magnitudes of the input driving pulse. In our experiment, it is found that the various changes of the driven pulse properties have different influences on the characteristics of XPW pulses. The relationship between the linear dispersion of driven pulse and temporal property of XPW is investigated theoretically. In addition, an experiment on verifying the theory is conducted by taking advantage of a programmable acousto-optic dispersion filter. The experimental results fit well to the theoretical results while some new phenomena emerge when the intensity in the BaF2 crystal reaches a saturation threshold. The spectral broadening capability of XPW becomes stronger and exceeds a theoretical upper limit. The pulse width can also be compressed to shorter than the theoretical limit. It is found that there are significant differences in spectral shape and conversion efficiency between the XPW signals by applying the opposite linear chirps to the driving pulse. A further analysis and theoretical explanation of these new phenomena are also presented.

Do Indonesian Children’s Experiences with Large Currency Units Facilitate Magnitude Estimation of Long Temporal Periods?

Ideas about temporal (and spatial) scale impact students’ understanding across science disciplines. Learners have difficulty comprehending the long time periods associated with natural processes because they have no referent for the magnitudes involved. When people have a good “feel” for quantity, they estimate cardinal number magnitude linearly. Magnitude estimation errors can be explained by confusion about the structure of the decimal number system, particularly in terms of how powers of ten are related to one another. Indonesian children regularly use large currency units. This study investigated if they estimate long time periods accurately and if they estimate those time periods the same way they estimate analogous currency units. Thirty-nine children from a private International Baccalaureate school estimated temporal magnitudes up to 10,000,000,000 years in a two-part study. Artifacts children created were compared to theoretical model predictions previously used in number magnitude estimation studies as reported by Landy et al. (Cognitive Science 37:775–799, 2013). Over one third estimated the magnitude of time periods up to 10,000,000,000 years linearly, exceeding what would be expected based upon prior research with children this age who lack daily experience with large quantities. About half treated successive powers of ten as a count sequence instead of multiplicatively related when estimating magnitudes of time periods. Children generally estimated the magnitudes of long time periods and familiar, analogous currency units the same way. Implications for ways to improve the teaching and learning of this crosscutting concept/overarching idea are discussed.

Impacts of emerging contaminants on surrounding aquatic environment from a youth festival.

The youth festival as we refer to Spring Scream, a large-scale pop music festival, is notorious for the problems of drug abuse and addiction. The origin, temporal magnitudes, potential risks and mass inputs of emerging contaminants (ECs) were investigated. Thirty targeted ECs were analyzed by solid-phase extraction and liquid chromatography coupled to tandem mass spectrometry (SPE-LC-MS/MS). Sampling strategy was designed to characterize EC behavior in different stages (before and after the youth festival), based on multivariate data analysis to explore the contributions of contaminants from normal condition to the youth festival. Wastewater influents and effluents were collected during the youth festival (approximately 600 000 pop music fans and youth participated). Surrounding river waters are also sampled to illustrate the touristic impacts during peak season and off-season. Seasonal variations were observed, with the highest concentrations in April (Spring Scream) and the lowest in October (off-season). Acetaminophen, diclofenac, codeine, ampicillin, tetracycline, erythromycin-H2O, and gemfibrozil have significant pollution risk quotients (RQs > 1), indicating ecotoxicological concerns. Principal component analysis (PCA) and weekly patterns provide a perspective in assessing the touristic impacts and address the dramatic changes in visitor population and drug consumption. The highest mass loads discharged into the aquatic ecosystem corresponded to illicit drugs/controlled substances such as ketamine and MDMA, indicating the high consumption of ecstasy during Spring Scream.

Relational congruence facilitates neural mapping of spatial and temporal magnitudes in preverbal infants

Mental representations of space, time, and number are fundamental to our understanding of the world around us. It should come as no surprise that representations of each are functional early in human development, appear to share a common format, and may be maintained by overlapping cortical structures. The consequences of these similarities for early learning and behavior are poorly understood. We investigated this issue by assessing neurophysiological processing of audio-visual temporal and spatial magnitude pairs using event-related potentials (ERPs) with young infants. We observed differential early processing and later enhanced attentional processing for pairings of spatial and temporal magnitudes that were relationally congruent (short visual character paired with a short auditory tone or long visual character paired with a long auditory tone) compared to the same stimuli paired in a relationally incongruent manner (short visual character with the long auditory tone or long visual character with a short tone). Unlike previous studies, these results were not dependent on a redundancy of information between the senses or an alignment of congruent magnitude properties within a single sense modality. Rather, these results demonstrate that mental representations of space and time interact to bias learning before formal instruction or the acquisition of spatial language.

Magnitude Representations in Williams Syndrome: Differential Acuity in Time, Space and Number Processing

For some authors, the human sensitivity to numerosities would be grounded in our ability to process non-numerical magnitudes. In the present study, the developmental relationships between non numerical and numerical magnitude processing are examined in people with Williams syndrome (WS), a genetic disorder known to associate visuo-spatial and math learning disabilities. Twenty patients with WS and 40 typically developing children matched on verbal or non-verbal abilities were administered three comparison tasks in which they had to compare numerosities, lengths or durations. Participants with WS showed lower acuity (manifested by a higher Weber fraction) than their verbal matched peers when processing numerical and spatial but not temporal magnitudes, indicating that they do not present a domain-general dysfunction of all magnitude processing. Conversely, they do not differ from non-verbal matched participants in any of the three tasks. Finally, correlational analyses revealed that non-numerical and numerical acuity indexes were both related to the first mathematical acquisitions but not with later arithmetical skills.