1/falpha noise in reaction times: a proposed model based on Piéron's law and information processing

Tenets and Methods of Fractal Analysis (1/f Noise)

This chapter deals with the methodical challenges confronting researchers of the fractal phenomenon known as pink or 1/f noise. This chapter introduces concepts and statistical techniques for identifying fractal patterns in empirical time series. It defines some basic statistical terms, describes two essential characteristics of pink noise (self-similarity and long memory), and outlines four parameters representing the theoretical properties of fractal processes: the Hurst coefficient (H), the scaling exponent (α), the power exponent (β), and the fractional differencing parameter (d) of the ARFIMA (autoregressive fractionally integrated moving average) method. Then, it compares and evaluates different approaches to estimating fractal parameters from observed data and outlines the advantages, disadvantages, and constraints of some popular estimators. The final section of this chapter answers the questions: Which strategy is appropriate for the identification of fractal noise in empirical settings and how can it be applied to the data?

The Fractal Tapestry of Life: III Multifractals Entail the Fractional Calculus

This is the third essay advocating the use the (non-integer) fractional calculus (FC) to capture the dynamics of complex networks in the twilight of the Newtonian era. Herein, the focus is on drawing a distinction between networks described by monfractal time series extensively discussed in the prequels and how they differ in function from multifractal time series, using physiological phenomena as exemplars. In prequel II, the network effect was introduced to explain how the collective dynamics of a complex network can transform a many-body non-linear dynamical system modeled using the integer calculus (IC) into a single-body fractional stochastic rate equation. Note that these essays are about biomedical phenomena that have historically been improperly modeled using the IC and how fractional calculus (FC) models better explain experimental results. This essay presents the biomedical entailment of the FC, but it is not a mathematical discussion in the sense that we are not concerned with the formal infrastucture, which is cited, but we are concerned with what that infrastructure entails. For example, the health of a physiologic network is characterized by the width of the multifractal spectrum associated with its time series, and which becomes narrower with the onset of certain pathologies. Physiologic time series that have explicitly related pathology to a narrowing of multifractal time series include but are not limited to heart rate variability (HRV), stride rate variability (SRV) and breath rate variability (BRV). The efficiency of the transfer of information due to the interaction between two such complex networks is determined by their relative spectral width, with information being transferred from the network with the broader to that with the narrower width. A fractional-order differential equation, whose order is random, is shown to generate a multifractal time series, thereby providing a FC model of the information exchange between complex networks. This equivalence between random fractional derivatives and multifractality has not received the recognition in the bioapplications literature we believe it warrants.

Creative exploration as a scale-invariant search on a meaning landscape

Can knowledge accumulated in systems biology on mechanisms governing cell behavior help us to elucidate cognitive processes, such as human creative search? To address this, we focus on the property of scale invariance, which allows sensory systems to adapt to environmental signals spanning orders of magnitude. For example, bacteria search for nutrients, by responding to relative changes in nutrient concentration rather than absolute levels, via a sensory mechanism termed fold-change detection (FCD). Scale invariance is prevalent in cognition, yet the specific mechanisms are mostly unknown. Here, we screen many possible dynamic equation topologies, to find that an FCD model best describes creative search dynamics. The model further predicts robustness to variations in meaning perception, in agreement with behavioral data. We thus suggest FCD as a specific mechanism for scale invariant search, connecting sensory processes of cells and cognitive processes in human.

The Appropriateness of Contrast Metric for Reaction Times

We analyzed different contrast metrics to scale the stimulus strength for suprathreshold reaction times (RTs) when it is modulated along an achromatic channel (L + M) and both chromatic channels L/M and S/(L + M) considering increments and decrements along these axes. RTs were examined as a function of the Weber luminance contrast; spatial luminance ratio (SRL) and, in terms of threshold units. The results show that when there is only luminance decreasing or increasing, RTs cluster around a single RT/luminance contrast function regardless the stimulus sign and our results indicate that both SRL, Weber luminance contrast or threshold units, equate RT values. While, if the stimulus is modulated along an isoluminant plane, the appropriate contrast is Weber (RMS) or SRL for stimuli modulated along L/M axis and for stimuli modulated along S/L + M, showing an asymmetry between S-cone decrements and increments in L/M cone pathway. Threshold units are not appropriate, showing inconsistencies: The stimulus with chromatic direction equal to 90° appears as the most informative with a maximum gain. Even more so, the shared contrast gain grows as the size of the stimulus decreases.

A variational approach to behavioral and neuroelectrical laws

Variational methods play a fundamental and unifying role in several fields of physics, chemistry, engineering, economics, and biology, as they allow one to derive the behavior of a system as a consequence of an optimality principle. A possible application of these methods to a model of perception is given by considering a psychophysical law as the solution of an Euler-Lagrange equation. A general class of Lagrangians is identified by requiring the measurability of prothetic continua on interval scales. The associated Hamiltonian (the energy of the process) is tentatively connected with neurophysiological aspects. As an example of the suggested approach a particular choice of the Lagrangian, that is a sufficient condition to obtain classical psychophysical laws, while accounting for psychophysical adaptation and the stationarity of neuronal activity, is used to explore a possible relation between a behavioral law and a neuroelectrical ,response based on the Naka-Rushton model.

1/f Noise in human color vision: the role of S-cone signals

We examine the functional role of S-cone signals on reaction time (RT) variability in human color vision. Stimuli were selected along red-green and blue-yellow cardinal directions and at random directions in the isoluminant plane of the color space. Trial-to-trial RT variability was not statistically independent but correlated across experimental conditions and exhibited 1/f noise spectra with an exponent close to unity in most of the cases. Regarding contrast coding, 1/f noise for random chromatic stimuli at isoluminance was similar to that for achromatic stimuli, thus suggesting that S-cone signals reduce variability of higher order color mechanisms. If we regard spatial coding, the effect of S-cone density in the retina on RT variability was investigated. The magnitude of 1/f noise at 16 min of arc (S-cone free zone) was higher than at 90 min of arc in the blue-yellow channel, and it was similar for the red-green channel. The results suggest that S-cone signals are beneficial and they modulate 1/f noise spectra at postreceptoral stages. The implications related to random multiplicative processes as a possible source of 1/f noise and the optimal information processing in color vision are discussed.

Causality, criticality, and reading words: distinct sources of fractal scaling in behavioral sequences

The finding of fractal scaling (FS) in behavioral sequences has raised a debate on whether FS is a pervasive property of the cognitive system or is the result of specific processes. Inferences about the origins of properties in time sequences are causal. That is, as opposed to correlational inferences reflecting instantaneous symmetrical relations, causal inferences concern asymmetric relations lagged in time. Here, I integrate Granger-causality with inferences about FS. Four simulations illustrate that causal analyses can isolate distinct FS sources, whereas correlational techniques cannot. I then analyze three simultaneous sequences of responses from a database of word-naming trials. I find that two, or perhaps three, distinct sources account for the presence of FS in these sequences, but FS is not a general property of the system. This suggests that FS arises due to the properties of a limited number of identifiable psychological and/or neural processes. Finally, I reanalyze a previously published dataset of acoustic frequency spectra using the new tools. The causality/criticality combination introduced here offers a new important perspective in the study of cognition.

S-cone excitation ratios for reaction times to blue-yellow suprathreshold changes at isoluminance

We examined different contrast metrics to scale visual latencies for suprathreshold stimuli modulated along tritan confusion lines. S-cone increments ('blue') and decrements ('yellow') were isolated along two different tritan confusion lines, each one having a different luminance value. Reaction times (RT) were evaluated as a function of the Weber contrast and the S-cone excitation ratio between the test stimulus and the background. RTs were described using a model that generalizes Piéron's law and incorporates the notion of threshold units and power law scaling. Our results show that RTs for S-cone increments and decrements equate better when using the S-cone excitation ratio. However, a single function did not describe all RT data. S-cone RTs are better described by separate functions. We conclude that S-cone increments and decrements do not scale in the same manner. Both Weber contrast and the S-cone excitation ratio are plausible metrics at isoluminance. The implications for the S-cone pathways are discussed.

Effects of multiplicative power law neural noise in visual information processing

The human visual system is intrinsically noisy. The benefits of internal noise as part of visual code are controversial. Here the information-theoretic properties of multiplicative (i.e. signal-dependent) neural noise are investigated. A quasi-linear communication channel model is presented. The model shows that multiplicative power law neural noise promotes the minimum information transfer after efficient coding. It is demonstrated that Weber's law and the human contrast sensitivity function arise on the basis of minimum transfer of information and power law neural noise. The implications of minimum information transfer in self-organized neural networks and weakly coupled neurons are discussed.

Fractal complexity in spontaneous EEG metastable-state transitions: new vistas on integrated neural dynamics

Resting-state EEG signals undergo rapid transition processes (RTPs) that glue otherwise stationary epochs. We study the fractal properties of RTPs in space and time, supporting the hypothesis that the brain works at a critical state. We discuss how the global intermittent dynamics of collective excitations is linked to mentation, namely non-constrained non-task-oriented mental activity.

Beyond the death of linear response: 1/f optimal information transport

Nonergodic renewal processes have recently been shown by several authors to be insensitive to periodic perturbations, thereby apparently sanctioning the death of linear response, a building block of nonequilibrium statistical physics. We show that it is possible to go beyond the "death of linear response" and establish a permanent correlation between an external stimulus and the response of a complex network generating nonergodic renewal processes, by taking as stimulus a similar nonergodic process. The ideal condition of 1/f noise corresponds to a singularity that is expected to be relevant in several experimental conditions.

Complex intermittency blurred by noise: theory and application to neural dynamics

We propose a model for the passage between metastable states of mind dynamics. As changing points we use the rapid transition processes simultaneously detectable in EEG signals related to different cortical areas. Our model consists of a non-Poissonian intermittent process, which signals that the brain is in a condition of complexity, upon which a Poisson process is superimposed. We provide an analytical solution for the waiting-time distribution for the model, which is well obeyed by physiological data. Although the role of the Poisson process remains unexplained, the model is able to reproduce many behaviors reported in literature, although they seem contradictory.

The Living Matter Way to exchange information

It is hypothesized that the special way information is exchanged between living networks, the Living Matter Way (LMW), is determined by the Principle of Complexity Matching, which asserts that the relative complexity of two complex networks determines the transfer of information between them. The LMW explains the neurophysiology of habituation and why classical music persists in your head long after the music stops.

Spontaneous brain activity as a source of ideal 1/f noise

We study the electroencephalogram (EEG) of 30 closed-eye awake subjects with a technique of analysis recently proposed to detect punctual events signaling rapid transitions between different metastable states. After single-EEG-channel event detection, we study global properties of events simultaneously occurring among two or more electrodes termed coincidences. We convert the coincidences into a diffusion process with three distinct rules that can yield the same mu only in the case where the coincidences are driven by a renewal process. We establish that the time interval between two consecutive renewal events driving the coincidences has a waiting-time distribution with inverse power-law index mu approximately 2 corresponding to ideal 1/f noise. We argue that this discovery, shared by all subjects of our study, supports the conviction that 1/f noise is an optimal communication channel for complex networks as in art or language and may therefore be the channel through which the brain influences complex processes and is influenced by them.