Physics of psychophysics: Stevens and Weber-Fechner laws are transfer functions of excitable media

Copelli, Mauro; Roque, Antônio C.; Oliveira, Ricardo Ferraz de; Kinouchi, Osame

doi:10.1103/physreve.65.060901

Cited by 77 publications

(117 citation statements)

References 10 publications

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“…5). This is supported by the experimental evidence that gap junctions are present in the sensory periphery (which was in fact what motivated the model [7]). Recent experiments in the mammalian retina [6] show that knocking out the gene responsible for connexin-36 (which accounts for the neuron-neuron gap junction channels) leads to a dramatic decrease in the dynamical range of ganglion cell responses.…”

Section: Resultssupporting

confidence: 64%

“…However, we have also examined more biologically realistic models previously, leading to results similar to those of the GHCA [7,22]. The robustness of the results presented in this contribution with respect to different excitable models, lattice connectivity and stimulus statistics is the subject of ongoing research.…”

Section: Discussionmentioning

confidence: 99%

“…The one-dimensional case, which may be thought of as an approximation for networks where neurons are coupled to two neighbors in average, has been previously addressed in Ref. [7].…”

Section: Introductionmentioning

confidence: 99%

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Intensity coding in two-dimensional excitable neural networks

Copelli

Kinouchi

2005

Physica A: Statistical Mechanics and its Applications

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In the light of recent experimental findings that gap junctions are essential for low level intensity detection in the sensory periphery, the Greenberg-Hastings cellular automaton is employed to model the response of a two-dimensional sensory network to external stimuli. We show that excitable elements (sensory neurons) that have a small dynamical range are shown to give rise to a collective large dynamical range. Therefore the network transfer (gain) function (which is Hill or Stevens law-like) is an emergent property generated from a pool of small dynamical range cells, providing a basis for a "neural psychophysics". The growth of the dynamical range with the system size is approximately logarithmic, suggesting a functional role for electrical coupling. For a fixed number of neurons, the dynamical range displays a maximum as a function of the refractory period, which suggests experimental tests for the model. A biological application to ephaptic interactions in olfactory nerve fascicles is proposed.

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Section: Resultssupporting

confidence: 64%

Section: Discussionmentioning

confidence: 99%

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Intensity coding in two-dimensional excitable neural networks

Copelli

Kinouchi

2005

Physica A: Statistical Mechanics and its Applications

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“…They are presented to the IDM only after being processed by sensory neurons and possibly a series of other predecision processes, most likely in a nonlinear fashion (Copelli, Roque, Oliveira, & Kinouchi, 2002;Yang & Wu, 1997). In what follows, we do not consider these sensory and preprocessing stages and focus solely on what happens after the input strengths have been computed.…”

Section: Two-stimulus Comparison: Weber's Lawmentioning

confidence: 99%

“…It is also found in more advanced tasks such as, for example, line length and number estimation (Cantlon, Platt, & Brannon, 2009; see also Smith & Ratcliff, 2009). Weber's law could emerge at different stages of processing: Automatic data compression at early sensory stages has been suggested as a possible explanation (Copelli et al, 2002), but also the discrimination/decision process itself has been put forward (Deco et al, 2007). In light of this last possibility, we check if it is possible to have Weber-like behavior in the IDM.…”

Section: Two-stimulus Comparison: Weber's Lawmentioning

confidence: 99%

The Ising Decision Maker: A binary stochastic network for choice response time.

Verdonck

Tuerlinckx

2014

Psychological Review

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The Ising Decision Maker (IDM) is a new formal model for speeded two-choice decision making derived from the stochastic Hopfield network or dynamic Ising model. On a microscopic level, it consists of 2 pools of binary stochastic neurons with pairwise interactions. Inside each pool, neurons excite each other, whereas between pools, neurons inhibit each other. The perceptual input is represented by an external excitatory field. Using methods from statistical mechanics, the high-dimensional network of neurons (microscopic level) is reduced to a two-dimensional stochastic process, describing the evolution of the mean neural activity per pool (macroscopic level). The IDM can be seen as an abstract, analytically tractable multiple attractor network model of information accumulation. In this article, the properties of the IDM are studied, the relations to existing models are discussed, and it is shown that the most important basic aspects of two-choice response time data can be reproduced. In addition, the IDM is shown to predict a variety of observed psychophysical relations such as Piéron's law, the van der Molen-Keuss effect, and Weber's law. Using Bayesian methods, the model is fitted to both simulated and real data, and its performance is compared to the Ratcliff diffusion model. The speeded two-choice response time (RT) task is a wellestablished paradigm in experimental psychology for investigating the principles underlying simple decision making. In the psychological literature, several successful models have been proposed based on the idea of the accumulation of noisy evidence over time (Link & Heath, 1975;Ratcliff, 1978;Stone, 1960;Usher & McClelland, 2001;Vickers, 1970). An important class of accumulator models, of which the drift diffusion model is the prime example, relies on a single or a few linear stochastic differential equations (SDEs). Decades of careful research resulted in excellent fits between the best accumulator models and behavioral data from speeded twochoice RT tasks. Initially, these models were conceived as abstract representations of the decision process. In the last decade however, there has been an increasing trend of investigating their neurophysiological underpinnings (

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Criticality at Work: How Do Critical Networks Respond to Stimuli?

Copelli¹

2014

Criticality in Neural Systems

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IntroductionMost models of critical neuronal networks have in common the theoretical ingredient of separation of time scales, according to which the interval between neuronal avalanches is much longer than their duration. This framework has proven useful for several reasons, among which are the possibilities of learning from an extensive literature on models of self-organized criticality and of comparing results with data obtained from some experimental setups. The brain of a freely behaving animal, however, is often found to operate away from this regime, thereby raising doubts about the relevance of criticality for brain function. In this chapter, two questions aimed at this direction are reviewed. From a theoretical perspective, how could criticality be harnessed by neuronal networks for processing incoming stimuli? From an experimental perspective, how could we know that the brain during natural behavior is critical?In 2003, the idea that the brain (as a dynamical system) sits at (or fluctuates around) a critical point received compelling experimental support from Dietmar Plenz's lab: cortical slices show spontaneous activity in ''bursts'' with the very peculiar feature of not having a characteristic size. As described in the now-classic paper by Beggs and Plenz [1], the probability distributions of size (s) and duration (d) of these neuronal avalanches were experimentally measured and shown to be compatible with power laws, respectively, P(s) ∼ s −3∕2 and P(d) ∼ d −2 . In the following, I will briefly review how this experimental result is connected with the theoretical idea of a critical brain (a much more expanded review can be found e.g., in Ref.[2]). Phase Transition in a Simple ModelIn order to do that, let us consider a very simple model of activity (e.g., spike) propagation in a network of connected neurons. We will make the drastic simplification that a neuron can be modeled by a finite set of states: if s i (t) = 0, neuron i is in a Criticality in Neural Systems, First Edition. Edited by Dietmar Plenz and Ernst Niebur.

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Physics of psychophysics: Stevens and Weber-Fechner laws are transfer functions of excitable media

Cited by 77 publications

References 10 publications

Intensity coding in two-dimensional excitable neural networks

Intensity coding in two-dimensional excitable neural networks

The Ising Decision Maker: A binary stochastic network for choice response time.

Criticality at Work: How Do Critical Networks Respond to Stimuli?

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