1∕fαnoise in reaction times: A proposed model based on Piéron’s law and information processing

Abstract

Piéron's law relates human reaction times to the intensity of a sensory stimulus by a power function. The neural processes responsible for this nonlinear behavior are not understood. A simple neural model based on the Brownian motion of spikes and information theory is presented. The model shows that Piéron's law is a transformation function in time. The shape of Piéron's law is invariant and scales into the intensity-response function of single neurons in a fractal-like process. The model also shows that Piéron's law gives rise to 1/falpha noise together with a high-frequency thermal noise limit. It is proposed that the biophysical origin of reaction time variability is related to a form of noise-induced synchronization in weakly coupled neurons. The implications in visual-motor transduction are discussed.

Macroscopic thermodynamics of reaction times

“…In a -preliminaryinvestigation of this issue, I did not observe evidence for Tsallis' entropic index q significantly deviating from one in these data. Alternatively, following the work of Norwich (1993), it has recently been proposed that 1/f α noise might arise in RT sequences without the need for generalizing entropy (Medina, 2009). The data I report are not specially informative on the effects of 1/f α noise on temporal entropy estimates, I thus leave the matter open for further research.…”

A theory of power laws in human reaction times: insights from an information-processing approach

“…), t n represents the asymptotic component of the mean RT reached at very high stimulus strength and d and p are two parameters (Luce, 1986). The sub-index n denotes the time step or order and it indicates a causal process: t n + 1 grows from the previous stage t n by an additive factor that depends on the stimulus strength S (Medina, 2009). The previous stage t n contains those processes at the threshold at an earlier time and t n + 1 in Equation (1) describes those processes at suprathreshold conditions at a later time (Norwich et al, 1989; Medina, 2009).…”

“…Maximum production of entropy and then, a reduction of uncertainty in ΔH as a function of time are concepts introduced from statistical physics, the latter as expressed by Boltzmann (Norwich, 1993). Based on an analytical model of the H -function (Norwich, 1993), the gain of information ΔH is connected with the formation of an internal threshold in Equation (1) (Norwich et al, 1989; Medina, 2009):…”

“…Third property, the reciprocal of Piéron's law is invariant under rescaling (Chater and Brown, 1999; Medina, 2009). Taking the reciprocal of the mean RT, R = 1/ t n + 1 .…”

“…Therefore, the reciprocal of the Equation (4) defines an affine transformation over multiple time scales that can be mapped into the Naka-Rushton equation at the cellular level (Naka and Rushton, 1966) and the Michaelis-Menten equation in enzyme reactions at the sub-cellular level (Michaelis and Menten, 1913; Pins and Bonnet, 1996). This suggests that some general properties of RT patterns governed by Piéron's law could be mirrored in part into the dynamics of the Naka-Rushton equation and/or the Michealis kinetics (Medina, 2009, 2012). The Naka-Rushton equation represents a canonical form of non-linear gain control in neural responses before saturation (Albrecht and Hamilton, 1982; Billock and Tsou, 2011; Carandini and Heeger, 2012).…”