Random Number Generation Task Research Articles

A comparative evaluation of measures to assess randomness in human-generated sequences

Whether and how well people can behave randomly is of interest in many areas of psychological research. The ability to generate randomness is often investigated using random number generation (RNG) tasks, in which participants are asked to generate a sequence of numbers that is as random as possible. However, there is no consensus on how best to quantify the randomness of responses in human-generated sequences. Traditionally, psychologists have used measures of randomness that directly assess specific features of human behavior in RNG tasks, such as the tendency to avoid repetition or to systematically generate numbers that have not been generated in the recent choice history, a behavior known as cycling. Other disciplines have proposed measures of randomness that are based on a more rigorous mathematical foundation and are less restricted to specific features of randomness, such as algorithmic complexity. More recently, variants of these measures have been proposed to assess systematic patterns in short sequences. We report the first large-scale integrative study to compare measures of specific aspects of randomness with entropy-derived measures based on information theory and measures based on algorithmic complexity. We compare the ability of the different measures to discriminate between human-generated sequences and truly random sequences based on atmospheric noise, and provide a systematic analysis of how the usefulness of randomness measures is affected by sequence length. We conclude with recommendations that can guide the selection of appropriate measures of randomness in psychological research.

Three-phase temporal dynamics in random number generation.

"Inhibition of return" (IOR) was originally described in the field of spatial attention, but it has also been observed in random number generation tasks. Subjects showed a tendency of "repetition avoidance," which can be considered as equivalent to IOR in another cognitive domain. As temporal factors have been suspected to play an important role in random number generation, we aimed to examine how such factors might influence regularities such as repetition avoidance in random number generation tasks. Participants were instructed to verbally generate a sequence of numbers at a certain pace, that is, with either 0.5, 1.5, 3 or 4 s between each response. Each number in the sequence should have the same probability of appearance and should be independent from the others. However, it was observed that the human-generated sequences differed drastically from computer-simulated pseudo-random sequences. The distribution of the repetition gap, which indicates how many different numbers are reported between two identical numbers in the generated sequences, showed a "three-phase" characteristic: a phase of avoidance of the same number, an oscillatory component for coming back to the same number, and finally an exponential decay of number selection frequencies. This three-phase characteristic was independent of the time interval between responses. These observations indicate an item-based process in random number generation, making a time-based control in this task rather unlikely as has been hypothetically assumed.

Exploring randomness in autism.

The fast, intuitive and autonomous system 1 along with the slow, analytical and more logical system 2 constitute the dual system processing model of decision making. Whether acting independently or influencing each other both systems would, to an extent, rely on randomness in order to reach a decision. The role of randomness, however, would be more pronounced when arbitrary choices need to be made, typically engaging system 1. The present exploratory study aims to capture the expression of a possible innate randomness mechanism, as proposed by the authors, by trying to isolate system 1 and examine arbitrary decision making in autistic participants with high functioning Autism Spectrum Disorders (ASD). Autistic participants withhigh functioning ASD and an age and gender matched comparison group performed the random number generation task. The task was modified to limit the contribution of working memory and allow any innate randomness mechanisms expressed through system 1, to emerge. Utilizing a standard analyses approach, the random number sequences produced by autistic individuals and the comparison group did not differ in their randomness characteristics. No significant differences were identified when the sequences were examined using a moving window approach. When machine learning was used, random sequences' features could discriminate the groups with relatively high accuracy. Our findings indicate the possibility that individual patterns during random sequence production could be consistent enough between groups to allow for an accurate discrimination between the autistic and the comparison group. In order to draw firm conclusions around innate randomness and further validate our experiment, our findings need to be replicated in a bigger sample.

A time-series perspective on executive functioning: The benefits of a dynamic approach to random number generation.

Executive functioning (EF) is a key topic in neuropsychology. A multitude of underlying processes and constructs have been suggested to explain EF, which are measured by at least as many different neuropsychological tests. However, these tests often refer to summary statistics to quantify the construct under study, failing to capture the dynamic nature of EF. An alternative to these summary statistics is a time-series approach that quantifies all the available temporal information. We used recurrence quantification analysis (RQA) to quantify the characteristics of any temporal pattern in random number generation data and we compared RQA to the traditional and static analysis of random number sequences. The traditional measures yield inconsistent results with increasing sequences length, both for computer-generated and human-generated sequences, whereas the RQA measures do not. The results suggest that a time-series approach does a better job at modelling what is happening on different time-scales, and, therefore, is better at explaining how EF is changing in the course of the random number generation task. We argue that it is likely that these findings also apply to other neuropsychological EF tests, and that a time-series approach is an important addition to the study of EF.

Load-Dependent Prefrontal Cortex Activation Assessed by Continuous-Wave Near-Infrared Spectroscopy during Two Executive Tasks with Three Cognitive Loads in Young Adults.

The present study examined the evolution of the behavioral performance, subjectively perceived difficulty, and hemodynamic activity of the prefrontal cortex as a function of cognitive load during two different cognitive tasks tapping executive functions. Additionally, it investigated the relationships between these behavioral, subjective, and neuroimaging data. Nineteen right-handed young adults (18-22 years) were scanned using continuous-wave functional near-infrared spectroscopy during the performance of n-back and random number generation tasks in three cognitive load conditions. Four emitter and four receptor optodes were fixed bilaterally over the ventrolateral and dorsolateral prefrontal cortices to record the hemodynamic changes. A self-reported scale measured the perceived difficulty. The findings of this study showed that an increasing cognitive load deteriorated the behavioral performance and increased the perceived difficulty. The hemodynamic activity increased parametrically for the three cognitive loads of the random number generation task and in a two-back and three-back compared to a one-back condition. In addition, the hemodynamic activity was specifically greater in the ventrolateral prefrontal cortex than in the dorsolateral prefrontal cortex for both cognitive tasks (random number generation and n-back tasks). Finally, the results highlighted some links between cerebral oxygenation and the behavioral performance, but not the subjectively perceived difficulty. Our results suggest that cognitive load affects the executive performance and perceived difficulty and that fNIRS can be used to specify the prefrontal cortex's implications for executive tasks involving inhibition and working memory updating.

Random walk: Random number generation during backward and forward walking- the role of aging.

Deficits in executive function, visuospatial abilities, and cognitive embodiment may impair gait performance. This study aimed to investigate the effect of age on random number generation (RNG) performance during forward and backward locomotion to assess cognitive flexibility and cognitive embodiment during walking. Another aim was to examine the effect of age on the associations of RNG performance during walking with stride time variability (STV), the percentage of double support (DS%), and visuospatial abilities as measured by a spatial orientation test (SOT). Twenty old (age 68.8 ± 5.3, 65% female) and 20 young (age 25.2 ± 2.2, 45% female) adults generated random numbers during backward walking (BW) and forward walking (FW) over-ground and over a treadmill with an internal focus of attention and visual-attentive distraction; six walking conditions in total. To assess cognitive flexibility, sample entropy was calculated for each RNG sequence. The average of the first 5 numbers in each RNG task was calculated to assess the relationship between small/large numbers and movement direction. STV and DS% were recorded using inertial measurement units, and spatial orientation was measured using a computerized test. The older subjects had less flexibility in generating random numbers in three of the six walking conditions. A negative correlation between RNG flexibility and STV was found in older adults during treadmill BW with visual-attentive distraction and forward over-ground walking, whereas no correlations were demonstrated in the young group. The spatial orientation score (a higher value means a worse outcome) correlated positively with RNG flexibility in the older group under all walking conditions, suggesting that older adults with better visuospatial orientation have lower cognitive flexibility, and vice versa. There was no correlation between small/large numbers and direction of motion in either group. The correlation between RNG flexibility and STV may indicate similar executive control of verbal and gait rhythmicity in old adults. Conversely, our results suggest that cognitive flexibility and visuospatial ability may decline differently.

Is there a relationship between cardiorespiratory fitness and executive performance as function of mental workload in young adults?

In the current study, we have decided to investigate the relationship between cardiorespiratory fitness and executive functions in young adults as a function of mental workload. To achieve our objectives, we have solicited 29 young adults (18–25 years; 12 women) who have first realized the Random Number Generation (RNG) task with two levels of complexity. After each level of complexity, the participants were asked to report on their perceived difficulty. Secondly, participants performed the RABIT® test, during which oxygen consumption was measured through the Metamax 3B-R2. The results showed that executive performance and perceived difficulty deteriorate with increasing task complexity. Additionally, oxygen consumption increased significantly to reach a peak during the hardest phase of the RABIT® test. Finally, as in previous studies, we could not observe a correlation between cardiorespiratory fitness and executive functions. Our findings support the lack of a direct relationship between cardiorespiratory fitness and executive functions. Future studies should explore the relationship between the composite measure of executive function, hemodynamic activity, and cardiorespiratory fitness in healthy youth and their peers with cardiovascular disease. This will examine an indirect effect of Cardiorespiratory fitness (CRF) on Executive functions (EFs) through brain activity.

Giving Ideas Some Legs or Legs Some Ideas? Children's Motor Creativity Is Enhanced by Physical Activity Enrichment: Direct and Mediated Paths.

Approaches to foster motor creativity differ according to whether creative movements are assumed to be enacted creative ideas, or solutions to emerging motor problems that arise from task and environmental constraints. The twofold aim of the current study was to investigate whether (1) an enriched physical education (PE) intervention delivered with a joint constraints-led and cognitive stimulation approach fosters motor creativity, and the responsiveness to the intervention is moderated by baseline motor and cognitive skills and sex; (2) the intervention may benefit motor creativity through gains in motor coordination, executive function, and creative thinking. Ninety-five children, aged 6–9 years, participated in a 6-month group randomized trial with specialist-led enriched PE vs. generalist-led conventional PE. Before and after the intervention, Bertsch’s Test of Motor Creativity, Movement Assessment Battery for Children, Random Number Generation task and Torrance Test of Creative Thinking were administered. Linear mixed models were run accounting for the random effects of data clusters. Multiple mediation analysis was performed to assess whether motor coordination, executive function and creative thinking mediated any improvement of motor creativity. Results showed that (1) specialist-led enriched PE, compared to generalist-led conventional practice, elicited a more pronounced improvement in all motor creativity dimensions (fluency, flexibility, and originality) independently of baseline levels of motor and cognitive skills and sex; and (2) improved motor creativity was partially mediated by improved motor coordination and, as regards motor flexibility, also by improved inhibitory ability. In conclusion, enriching PE with tailored manipulations of constraints and variability may enhance the ability to create multiple and original task-pertinent movements both directly and through indirect paths. The results are discussed extending to motor creativity a theoretical framework that distinguishes different creativity modes. The intervention may have fostered the generation of creative movements directly through the exposure to variation in constraints, activating the sensorimotor ‘flow’ mode of creativity that bypasses higher-order cognition, but also indirectly through a systematic and conscious convergence on solutions, activating the ‘deliberate’ mode of creativity that relies on inhibition to reject common or task-inappropriate movement categories.

Neuromuscular Diseases Affect Number Representation and Processing: An Exploratory Study.

Spinal muscular atrophy (SMA) and Duchenne muscular dystrophy (DMD) both are rare genetic neuromuscular diseases with progressive loss of motor ability. The neuromotor developmental course of those diseases is well documented. In contrast, there is only little evidence about characteristics of general and specific cognitive development. In both conditions the final motor outcome is characterized by an inability to move autonomously: children with SMA never accomplish independent motoric exploration of their environment, while children with DMD do but later lose this ability again. These profound differences in developmental pathways might affect cognitive development of SMA vs. DMD children, as cognition is shaped by individual motor experiences. DMD patients show impaired executive functions, working memory, and verbal IQ, whereas only motor ability seems to be impaired in SMA. Advanced cognitive capacity in SMA may serve as a compensatory mechanism for achieving in education, career progression, and social satisfaction. This study aimed to relate differences in basic numerical concepts and arithmetic achievement in SMA and DMD patients to differences in their motor development and resulting sensorimotor and environmental experiences. Horizontal and vertical spatial-numerical associations were explored in SMA/DMD children ranging between 6 and 12 years through the random number generation task. Furthermore, arithmetic skills as well as general cognitive ability were assessed. Groups differed in spatial number processing as well as in arithmetic and domain-general cognitive functions. Children with SMA showed no horizontal and even reversed vertical spatial-numerical associations. Children with DMD on the other hand revealed patterns in spatial numerical associations comparable to healthy developing children. From the embodied Cognition perspective, early sensorimotor experience does play a role in development of mental number representations. However, it remains open whether and how this becomes relevant for the acquisition of higher order cognitive and arithmetic skills.

RandseqR: An R Package for Describing Performance on the Random Number Generation Task.

The Random Number Generation (RNG) task has a long history in neuropsychology as an assessment procedure for executive functioning. In recent years, understanding of human (executive) behavior has gradually changed from reflecting a static to a dynamic process and this shift in thinking about behavior gives a new angle to interpret test results. However, this shift also asks for different methods to process random number sequences. The RNG task is suited for applying non-linear methods needed to uncover the underlying dynamics of random number generation. In the current article we present RandseqR: an R-package that combines the calculation of classic randomization measures and Recurrence Quantification Analysis. RandseqR is an easy to use, flexible and fast way to process random number sequences and readies the RNG task for current scientific and clinical use.

Performance of Children and Adolescents on Random Number Generation as a measure of Executive Functions

This study investigated the age-related differences in the random number generation (RNG) of children aged 7 to 15 years old (n=106) divided into three groups (7-9, 10-12 and 13-15 years of age) as it was compared to computer-generated pseudorandom sequences. The results showed that there was an age effect on four out of seven indices of randomization that are known to tap the Inhibition ability and the Updating ability (i.e., active manipulation of relevant information in working memory). The participants’ (children’s and adolescents’; n=106) responses were significantly different from pseudorandom sequences (n=106) produced by the RgCalc program and no gender differences were observed. The RNG task indices that reflect inhibition ability did not correlate with the participants’ performance on the Stroop color-word task. The development of executive functions in school-aged children and adolescents is discussed.

Cognitive effects of theta frequency bilateral subthalamic nucleus stimulation in Parkinson’s disease: A pilot study

BackgroundThere is significant evidence for cognitive decline following deep brain stimulation (DBS). Current stimulation paradigms utilize gamma frequency stimulation for optimal motor benefits; however, little has been done to optimize stimulation parameters for cognition. Recent evidence implicates subthalamic nucleus (STN) theta oscillations in executive function, and theta oscillations are well-known to relate to episodic memory, suggesting that theta frequency stimulation could potentially improve cognition in Parkinson’s disease (PD). ObjectiveTo evaluate the acute effects of theta frequency bilateral STN stimulation on executive function in PD versus gamma frequency and off, as well as investigate the differential effects on episodic versus nonepisodic verbal fluency. MethodsTwelve patients (all males, mean age 60.8) with bilateral STN DBS for PD underwent a double-blinded, randomized cognitive testing during stimulation at (1) 130–135 Hz (gamma), (2) 10 Hz (theta) and (3) off. Executive functions and processing speed were evaluated using verbal fluency tasks (letter, episodic category, nonepisodic category, and category switching), color-word interference task, and random number generation task. Performance at each stimulation frequency was compared within subjects. ResultsTheta frequency significantly improved episodic category fluency compared to gamma, but not compared to off. There were no significant differences between stimulation frequencies in other tests. ConclusionIn this pilot trial, our results corroborate the role of theta oscillations in episodic retrieval, although it is unclear whether this reflects direct modulation of the medial temporal lobe and whether similar effects can be found with more canonical memory paradigms. Further work is necessary to corroborate our findings and investigate the possibility of interleaving theta and gamma frequency stimulation for concomitant motor and cognitive effects.

The Morra Game as a Naturalistic Test Bed for Investigating Automatic and Voluntary Processes in Random Sequence Generation.

Morra is a 3,000-years-old hand game of prediction and numbers. The two players reveal their hand simultaneously, presenting a number of fingers between 1 and 5, while calling out a number between 2 and 10. Any player who successfully guesses the summation of fingers revealed by both players scores a point. While the game is extremely fast-paced, making it very difficult for players to achieve a conscious control of their game strategies, expert players regularly outperform non-experts, possibly with strategies residing out of conscious control. In this study, we used Morra as a naturalistic setting to investigate the necessity of attentive control in generation of sequence of items and the ability to proceduralize random number generation, which are both a crucial defensive strategy in Morra and a well-known empirical procedure to test the central executive capacity within the working memory model. We recorded the sequence of numbers generated by expert players in a Morra tournament in Sardinia (Italy) and by undergraduate students enrolled in a course-based research experience (CRE) course at Lawrence Technological University in the United States. Number sequences generated by non-expert and expert players both while playing Morra and in a random number generation task (RNGT) were compared in terms of randomness scores. Results indicate that expert players of Morra largely outperformed non-experts in the randomness scores only within Morra games, whereas in RNGT the two groups were very similar. Importantly, survey data acquired after the games indicate that expert players have very poor conscious recall of their number generation strategies used during the Morra game. Our results indicate that the ability of generating random sequences can be proceduralized and do not necessarily require attentive control. Results are discussed in the framework of the dual processing theory and its automatic-parallel-fast vs. controlled-sequential-slow polarities.

Dopaminergic medication improves cognitive control under low cognitive demand in Parkinson's disease.

Dopamine agonists are the main pharmacological intervention for the motor symptoms of Parkinson's disease (PD). However, dopaminergic medication has been associated with disinhibitory psychopathology in some patients. The aim of this study was to test the effect of dopaminergic medication on inhibitory control in patients with PD using the paced Random Number Generation task (RNG), which requires inhibition of prepotent counting in series to produce a random sequence of numbers. Twenty-three PD patients performed RNG on and off dopaminergic medication. Cognitive load was manipulated by performing RNG at faster (1Hz) and slower (0.5 Hz) rates. For RNG, two scores (CS1 and CS2) were derived, which are considered indices of more automatic and more controlled counting, respectively. There were no main effects of medication on RNG performance. There was a significant main effect of cognitive load on CS1, with higher CS1 scores at the faster rate (p = <.01). A significant interaction effect between medication and rate (cognitive load; p = .03) followed by post hoc testing, revealed that CS2 scores were higher, on medication, at the slower but not the faster rate. Patients with PD displayed increased use of more controlled processing strategies on medication at the slowest rate of RNG. Therefore, while dopaminergic medication has been associated with disinhibitory psychopathology, our results suggest that dopamine therapy may enhance some forms of inhibitory cognitive control in PD, but only if there is sufficient time to engage controlled processing strategies. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Multi-core fiber integrated multi-port beam splitters for quantum information processing

Multi-port beam splitters are cornerstone devices for high-dimensional quantum information tasks, which can outperform the two-dimensional ones. Nonetheless, the fabrication of such devices has proven to be challenging with progress only recently achieved with the advent of integrated photonics. Here, we report on the production of high-quality N × N (with N = 4 , 7 ) multi-port beam splitters based on a new scheme for manipulating multi-core optical fibers. By exploring their compatibility with optical fiber components, we create four-dimensional quantum systems and implement the measurement-device-independent random number generation task with a programmable four-arm interferometer operating at a 2 MHz repetition rate. Due to the high visibilities observed, we surpass the one-bit limit of binary protocols and attain 1.23 bits of certified private randomness per experimental round. Our result demonstrates that fast switching, low loss, and high optical quality for high-dimensional quantum information can be simultaneously achieved with multi-core fiber technology.

Effects of an 8-week training cessation period on cognition and functional capacity in older adults.

Multiple types of exercise interventions have been described as effective methods for improving cognition and mobility in older adults. In addition to combined strength and aerobic training, gross motor activities have shown benefits. However, adherence to exercise is a challenge, which may bring about periods of training cessation. Importantly, short-term training cessation may lead to a loss of fitness adaptations. The effects of training cessation on cognition and functional capacity are not well known, especially within the context of dual-tasking in older adults. We examined the effects of an 8-week training cessation period on cognition (executive functioning (EF) in single (ST) and dual-task (DT)) and functional capacity (10m Walk and 6Minute Walk Test) of healthy older adults, after one of three training interventions: combined lower body strength and aerobic, combined upper body strength and aerobic, or gross motor activities. Forty older adults (70.5±5.5years, 67.5% F) participated in training sessions, 3×/week for 8weeks prior to training cessation. Pre (T0), post (T1) and follow-up (post-cessation, T2) measures of EF (performance in inhibition and updating/working memory indices of the Random Number Generation task) in ST and DT (treadmill walking at 0.67m·s-1, 1.11m·s-1, and 1.56m·s-1), and functional capacity were assessed. Changes in ST and DT as well as functional capacity tests were analyzed using two-way ANOVAs (time∗group) with repeated measures for the time factor (T0, T1 and T2). Improvements in inhibition indices were observed in ST for all time comparisons (T0-T1, T1-T2 and T0-T2). Inhibition in DT improved from T0-T2 and from T1-T2. Working memory declined from T0-T2 and from T1-T2. Functional capacity performance was maintained from T1-T2 (small improvement from T0-T1 and from T0-T2). Performances in inhibition were maintained or improved after cessation of training. We found no interaction between training groups, whatever the condition, indicating similar training cessation effects regardless of the intervention. Multiple types of exercise interventions may lead to positive benefit to inhibition and functional capacity in older adults, and it may also be possible to retain these benefits after a short cessation period.

Low numbers from a low head? Effects of observed head orientation on numerical cognition.

The present research shows effects of observed vertical head orientation of another person on numerical cognition in the observer. Participants saw portrait-like photographs of persons from a frontal view with gaze being directed at the camera and the head being tilted up or down (vs. not tilted). The photograph appeared immediately before each trial in different numerical cognition tasks. In Experiment 1, participants produced smaller numbers in a random number generation task after having viewed persons with a down-tilted head orientation relative to up-tilted and non-tilted head orientations. In Experiment 2, numerical estimates in an anchoring-like trivia question task were smaller following presentations of persons with a down-tilted head orientation relative to a non-tilted head orientation. In Experiment 3, a response key that was associated with larger numbers in a numerical magnitude task was pressed less frequently in a randomly intermixed free choice task when the photograph showed a person with a down-tilted relative to an up-tilted head orientation. These findings consistently show that social displays can influence numerical cognition across a variety of task settings.

Gravity modulates behaviour control strategy.

Human behaviour is a trade-off between exploitation of familiar resources and exploration of new ones. In a challenging environment-such as outer space-making the correct decision is vital. On Earth, gravity is always there, and is an important reference for behaviour. Thus, altered gravitational signals may affect behaviour control strategies. Here, we investigated whether changing the body's orientation to the gravitational vector would modulate the balance between routine and novel behaviour. Participants completed a random number generation task while upright or supine. We found decreased randomness when participants were supine. In particular, the degree of equiprobability of pairs of consecutive responses was reduced in the supine orientation. Online gravitational signals may shape the balance between exploitation and exploration, in favour of more stereotyped and routine responses.

Vertical spatial representation of numbers across two cultures

There is strong evidence that numbers are spatially represented. However, much of the research has been concerned with investigating number representation within the horizontal rather than the vertical dimension. It has been suggested that the organisation of the writing system, by rows or by columns, plays a pivotal role in shaping the mental number representation. We investigated the vertical number representation in British and Japanese participants, who were asked to randomly generate numbers after turning their heads up or down. Previous works showed that this method facilitated the access to the corresponding portions of the horizontal mental number representation. We found that neither group seemed to be affected by the up/ down head turns. These results are discussed in terms of cultural crossover, differences in the horizontal vs. vertical spatial and numerical representation, and sensitivity of the random number generation task.

Sharing a mental number line across individuals? The role of body position and empathy in joint numerical cognition.

A growing body of research shows that the human brain acts differently when performing a task together with another person than when performing the same task alone. In this study, we investigated the influence of a co-actor on numerical cognition using a joint random number generation (RNG) task. We found that participants generated relatively smaller numbers when they were located to the left (vs. right) of a co-actor (Experiment 1), as if the two individuals shared a mental number line and predominantly selected numbers corresponding to their relative body position. Moreover, the mere presence of another person on the left or right side or the processing of numbers from loudspeaker on the left or right side had no influence on the magnitude of generated numbers (Experiment 2), suggesting that a bias in RNG only emerged during interpersonal interactions. Interestingly, the effect of relative body position on RNG was driven by participants with high trait empathic concern towards others, pointing towards a mediating role of feelings of sympathy for joint compatibility effects. Finally, the spatial bias emerged only after the co-actors swapped their spatial position, suggesting that joint spatial representations are constructed only after the spatial reference frame became salient. In contrast to previous studies, our findings cannot be explained by action co-representation because the consecutive production of numbers does not involve conflict at the motor response level. Our results therefore suggest that spatial reference coding, rather than motor mirroring, can determine joint compatibility effects. Our results demonstrate how physical properties of interpersonal situations, such as the relative body position, shape seemingly abstract cognition.