Power-Law Distribution of Natural Visibility Graphs from Reaction Times Series

Mira‐Iglesias, Ainara; Navarro‐Pardo, Esperanza; Conejero, J. Alberto

doi:10.3390/sym11040563

Cited by 8 publications

(11 citation statements)

References 64 publications

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“…The ADHD and autism spectrum disorder (ASD) among children aged 7-10 years is studied [22] to gain insights into the attentional fluctuations, related to increased reaction time variability. The use of the ex-Gaussian function to fit reaction time data has been used extensively in the literature [11][12][13][14][15][16][17][18][19][20][21][22][23][24]. On reviewing the previous works, we could not come across any clear and direct correlation between the ex-Gaussian parameters and cognitive disorders.…”

Section: Introductionmentioning

confidence: 92%

“…The ex-Gaussian parameters derived from representing RT data are usually interpreted in connection with cognitive disorders as certain correlations are claimed to exist [14][15][16][17][18][19][20]. For instance, the most commonly diagnosed cognitive disorder in childhood affecting the RT is Attention Deficit and Hyperactivity Disorder (ADHD).…”

Section: Introductionmentioning

confidence: 99%

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Human Reaction Times: Linking Individual and Collective Behaviour Through Physics Modeling

et al. 2021

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An individual’s reaction time data to visual stimuli have usually been represented in Experimental Psychology by means of an ex-Gaussian function. In most previous works, researchers have mainly aimed at finding a meaning for the parameters of the ex-Gaussian function which are known to correlate with cognitive disorders. Based on the recent evidence of correlations between the reaction time series to visual stimuli produced by different individuals within a group, we go beyond and propose a Physics-inspired model to represent the reaction time data of a coetaneous group of individuals. In doing so, a Maxwell–Boltzmann-like distribution appeared, the same distribution as for the velocities of the molecules in an Ideal Gas model. We describe step by step the methodology we use to go from the individual reaction times to the distribution of the individuals response within the coetaneous group. In practical terms, by means of this model we also provide a simple entropy-based methodology for the classification of the individuals within the collective they belong to with no need for an external reference which can be applicable in diverse areas of social sciences.

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Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Human Reaction Times: Linking Individual and Collective Behaviour Through Physics Modeling

et al. 2021

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“…RT distributions are asymmetric functions [4,5], which cannot be fully described by the mean and standard deviations [6]. The ex-Gaussian parameters obtained from fitting reaction time distributions to visual stimuli are interpretable in relation to cognitive disorders as certain correlations are evidenced to exist [7][8][9][10][11][12][13]. This is the case of Attention Deficit and Hyperactivity Disorder (ADHD), the most usual diagnosed cognitive disorder in school-aged children.…”

Section: Introductionmentioning

confidence: 99%

“…Coefficient of determinationas a function of the dispersion of the SD of the Gaussian components (k = 3, 5). The points in the plot have been connected by means of RKHS interpolations[9,10].…”

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confidence: 99%

Monte Carlo Simulation of a Modified Chi Distribution with Unequal Variances in the Generating Gaussians. A Discrete Methodology to Study Collective Response Times

et al. 2020

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The Chi distribution is a continuous probability distribution of a random variable obtained from the positive square root of the sum of k squared variables, each coming from a standard Normal distribution (mean = 0 and variance = 1). The variable k indicates the degrees of freedom. The usual expression for the Chi distribution can be generalised to include a parameter which is the variance (which can take any value) of the generating Gaussians. For instance, for k = 3, we have the case of the Maxwell-Boltzmann (MB) distribution of the particle velocities in the Ideal Gas model of Physics. In this work, we analyse the case of unequal variances in the generating Gaussians whose distribution we will still represent approximately in terms of a Chi distribution. We perform a Monte Carlo simulation to generate a random variable which is obtained from the positive square root of the sum of k squared variables, but this time coming from non-standard Normal distributions, where the variances can take any positive value. Then, we determine the boundaries of what to expect when we start from a set of unequal variances in the generating Gaussians. In the second part of the article, we present a discrete model to calculate the parameter of the Chi distribution in an approximate way for this case (unequal variances). We also comment on the application of this simple discrete model to calculate the parameter of the MB distribution (Chi of k = 3) when it is used to represent the reaction times to visual stimuli of a collective of individuals in the framework of a Physics inspired model we have published in a previous work.

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“…For more details, we refer to [CSN09]. In the next chapters, we will use Clauset's et al algorithm to demonstrate that the degree distributions of certain NVGs follow a power-law distribution based on scale-free networks, as we did in our published work [MINPC19].…”

Section: Applications Of the Visibility Graphs Approachmentioning

confidence: 99%

Applications of Visibility Graphs for the representation of Time Series

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Power-Law Distribution of Natural Visibility Graphs from Reaction Times Series

Cited by 8 publications

References 64 publications

Human Reaction Times: Linking Individual and Collective Behaviour Through Physics Modeling

Human Reaction Times: Linking Individual and Collective Behaviour Through Physics Modeling

Monte Carlo Simulation of a Modified Chi Distribution with Unequal Variances in the Generating Gaussians. A Discrete Methodology to Study Collective Response Times

Applications of Visibility Graphs for the representation of Time Series

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