Stevens Power Research Articles

Physics of psychophysics: Large dynamic range in critical square lattices of spiking neurons

Psychophysics try to relate physical input magnitudes to psychological or neural correlates. Microscopic models to account for macroscopic psychophysical laws, in the sense of statistical physics, are an almost unexplored area. Here we examine a sensory epithelium composed of two connected square lattices of stochastic integrate-and-fire cells. With one square lattice we obtain a Stevens's law $\rho \propto h^m$ with Stevens's exponent $m = 0.254$ and a sigmoidal saturation, where $\rho$ is the neuronal network activity and $h$ is the input intensity (external field). We relate Stevens's power law exponent with the field critical exponent as $m = 1/\delta_h = \beta/\sigma$. We also show that this system pertains to the Directed Percolation (DP) universality class (or perhaps the Compact-DP class). With stacked two layers of square lattices, and a fraction of connectivity between the first and second layer, we obtain at the output layer $\rho_ 2 \propto h^{m_2}$, with $m_2 = 0.08 \approx m^2$, which corresponds to a huge dynamic range. This enhancement of the dynamic range only occurs when the layers are close to their critical point.

A Unified Theory of Psychophysical Laws in Auditory Intensity Perception

Psychophysical laws quantitatively relate perceptual magnitude to stimulus intensity. While most people have accepted Stevens’s power function as the psychophysical law, few believe in Fechner’s original idea using just-noticeable-differences (jnd) as a constant perceptual unit to educe psychophysical laws. Here I present a unified theory in hearing, starting with a general form of Zwislocki’s loudness function (1965) to derive a general form of Brentano’s law. I will arrive at a general form of the loudness-jnd relationship that unifies previous loudness-jnd theories. Specifically, the “slope,” “proportional-jnd,” and “equal-loudness, equal-jnd” theories, are three additive terms in the new unified theory. I will also show that the unified theory is consistent with empirical data in both acoustic and electric hearing. Without any free parameters, the unified theory uses loudness balance functions to successfully predict the jnd function in a wide range of hearing situations. The situations include loudness recruitment and its jnd functions in sensorineural hearing loss and simultaneous masking, loudness enhancement and the midlevel hump in forward and backward masking, abnormal loudness and jnd functions in cochlear implant subjects. Predictions of these loudness-jnd functions were thought to be questionable at best in simultaneous masking or not possible at all in forward masking. The unified theory and its successful applications suggest that although the specific form of Fechner’s law needs to be revised, his original idea is valid in the wide range of hearing situations discussed here.

(227) - Individual differences in pain sensitivity: Insights from discriminability of graded noxious heat stimuli

The experience of pain varies for every person in both intensity and unpleasantness. The mechanisms supporting these differences in pain sensitivity are not yet understood, in part due to challenges of dissociating perceptual differences from reporting biases. In this preliminary analysis we sought to assess discriminability of graded noxious stimuli in highly sensitive and insensitive individuals. One hundred and three healthy individuals were asked to rate pain intensity and pain unpleasantness in response to a thermal stimulus paradigm containing 4 sequences of 8 semi-randomized stimuli of 35 and 43 to 49°C for a total of 32 stimuli. In order to identify different pain phenotypes, we employed a data-driven approach using a hierarchical cluster analysis of normalized pain intensity and unpleasantness ratings. A scree plot indicated that participants could be optimally divided into three broad clusters based on their pain ratings. These different phenotypes could be described as insensitive, moderately sensitive, and highly sensitive. A regression analysis was conducted for each cluster to calculate the stimulus response curves for each group according to Steven's Power Law. In all three clusters, pain unpleasantness stimulus response curves were characterized by steeper slopes than pain intensity stimulus response curves. The highly sensitive cluster exhibited a greater y-intercept and shallower slope for both intensity and unpleasantness stimulus response curves in relation to the other two groups. These differences in stimulus response curves could potentially support greater discriminability of small differences in noxious stimulus intensity in the highly sensitive cluster. Repeated measures analysis of variance confirmed that the highly sensitive cluster discriminated noxious stimuli of 1°C differences at lower stimulus intensities than other clusters. As such, these preliminary findings suggest that rating biases are not the primary source of observed individual differences in pain sensitivity. This research was supported by NIH NS085391.

Stevens’s law for time: A direct comparison of prospective and retrospective judgments

Participants are aware that they have to perform a temporal task in a prospective timing condition but not in a retrospective timing condition. In the present study, a direct comparison of temporal estimates under each paradigm is proposed via a strategy where each participant is restricted to only 1 response. Participants were assigned to either a prospective or retrospective testing condition and asked to reproduce and then estimate verbally 1 of 6 intervals lasting .5 to 16 s. The analyses based on Stevens's power law were restricted to intervals lasting 2 to 16 s. With a verbal estimate method, the results indicate that the exponent is higher in retrospective than in prospective conditions (1.20 vs. 1.10 for females and 1.31 vs. 1.02 for males, respectively). For the interval reproduction task, the exponent based on Eisler's (1975) model was slightly higher for males (1.13) than for females (1.08) in prospective timing, but slightly higher for females (1.10) than for males (1.04) in retrospective timing. The results based on inferential statistics and the 6 intervals reveal that, with the verbal estimate method, females make significantly larger relative verbal estimates than males and, at 16 s, intervals were judged as longer in the retrospective than in the prospective condition; with the reproduction method, the perceived duration is about the same in each paradigm and there is no significant sex effect. Overall, the data do not confirm that temporal intervals are perceived as longer in the prospective than in the retrospective conditions.

Improvement of Estimation of Objective Scores of Answer Statements Posted at Q&A Sites

To eliminate mismatches between the intentions of questioners and respondents of Question and Answer (Q&A) sites, the authors have clarified the characteristics of the question and answer statements. It has been shown that the impression of the statements could be captured by nine factors, and the factor scores could be estimated from the feature values of the statements. Here, the objective scores of answer statements are provided. So far the authors have tried to estimate the objective scores of answer statements through multiple regression analysis. They are estimated from the factor scores estimated by using multiple regression formulas already obtained. As a result, with the consideration of natural logarithm, objective scores of the statements on love counseling & human relationships could be estimated good. The estimation accuracy of the statements on Yahoo! Auction and PC, however, is required to be improved. Therefore, this paper tries to improve the estimation accuracy of objective scores of Yahoo! Auction and PC. Here, the authors adopt Steven's power law as well as Fechner's law as new explanatory variables. In considering multicollinearity, the authors selected as many explanatory variables as possible. As a result, objective scores of the statements of PC are estimated fairly good.

Effect of Enzymatic Protein Deamidation on Protein Solubility and Flavor Binding Properties of Soymilk

The effect of enzymatic deamidation by protein-glutaminase (PG) on protein solubility and flavor binding potential of soymilk was studied. Treatment of soymilk with PG for 2 h (temperature of 44 °C and enzyme:substrate ratio (E/S) of 40 U/g protein) resulted in high degree of protein deamidation (66.4% DD) and relatively low degree of protein hydrolysis (4.25% DH). Deamidated (DSM) and control soymilks (CSM) did not differ with respect to aroma, but differed in taste characteristics by sensory evaluation. Protein solubility in DSM was enhanced at weakly acidic conditions (pH 5.0), but did not differ from non-deamidated soymilk at pH values of 3.0 and 7.0. Odor detection thresholds for the flavor compounds vanillin and maltol were approximately 5 and 3 fold lower, respectively, in DSM than in CSM. Dose-response curves (Fechner's law plots and n exponents from Stevens's power law) further demonstrated that DSM had a lower flavor binding potential than CSM. PG deamidation has the potential to reduce flavor binding problems encountered in high protein-containing foods and beverages. The findings of this study can help lead to the development of technology to produce protein-containing foods with improved functional properties, especially protein solubility, and potentially decreased flavor fade problems associated with flavor-protein interactions, especially with carbonyl containing flavor compounds.

Multimodal urgency coding: auditory, visual, and tactile parameters and their impact on perceived urgency

Through a series of investigations involving different levels of contextual fidelity we developed scales of perceived urgency for several dimensions of the auditory, visual, and tactile modalities. Psychophysical ratings of perceived urgency, annoyance, and acceptability as well as behavioral responses to signals in each modality were obtained and analyzed using Steven's Power Law to allow comparison across modalities. Obtained results and their implications for use as in-vehicle alerts and warnings are discussed.

PREDICTION OF HUMAN PSYCHOPHYSICAL PERCEPTION OF FABRIC CRISPNESS AND COOLNESS HAND FROM RAPIDLY MEASURABLE LOW-STRESS MECHANICAL AND THERMAL PARAMETERS

ABSTRACT This work investigated the possibility of predicting the human psychophysical perception of crispness and coolness hand of men's suit fabrics made from animal fibers (wool, mohair, cashmere and alpaca) from rapidly measurable low-stress mechanical and thermal parameters. Thanks to Fabric Assurance by Simple Testing (FAST) and Alambeta instruments, in about 1 h for sample, it was possible to simply obtain eight parameters that together described low-stress compressional, bending, shearing, and tensile deformations and thermal behavior. Sensory hand evaluation was performed by a panel of eight experts. After assessing the inter-expert concordance, the sensory-instrumental relationship was explored using multiple linear regression and comparing three mathematical models: a linear function, the Weber–Fechner law and the Stevens's power law, with the last two being well-established psychophysical models to translate instrumentally measured fabric properties into corresponding hand parameters. PRACTICAL APPLICATIONS The textile and clothing industry is increasingly interested in the development of tools to describe and grade the sensory quality of its products. Especially finishing companies, largely small and medium-sized, require objective methods for online controlling fabric handle and just-in-time setting their finishing machines and processes. Even if some industrial and commercial sectors have switched to trained sensory panels, this solution is difficult to apply in the textile finishing sector, that is more and more interested in instrumental methods for evaluating the effectiveness of finishing processes, checking the efficiency of machine operations and troubleshooting. This demand is undermined by the limited availability of skilled technicians able to use complex and costly fabric objective measurement systems, such as the Kawabata's Evaluation System for Fabrics one (KES-F), that, in addition, does not allow quick responses. This work proposed the reliable, simple and rapid measurement of hand-related properties, both mechanical and thermal, with FAST and Alambeta instruments, to be translated in a powerful prediction model for the human psychophysical perception of crispness and coolness hand of both winter and summer men's suit fabrics made from animal fibers (wool, mohair, cashmere and alpaca).

Benchmarking consumer perceptions of retail constructs for apparel merchandisers using magnitude estimation

PurposeThe purpose of this paper is to establish a measurement process for consumer perceptions and judgments of strategic importance to apparel retailers like hedonic and utilitarian shopping behavior, as well as internal process benchmarks such as apparel brands' names, store signage, and textile preferences. The paper aims to provide a simple, flexible and easy to use measurement technique that can be applied to small samples of respondents in order to capture their overall perceptions and judgments of key interest to management.Design/methodology/approachMagnitude estimation, along with a repeated measures design, was tested and evaluated based on the validation process put forth by Steven's power law. Data were collected from three focus groups whose respondents were selected based on their store loyalty and prior purchase of women's petit apparel in a discount outlet store. Their responses were benchmarked with those of other competitive discount retailers and with selected internal process measures.FindingsAll applications of the measurement technique were validated. Loyal shoppers for apparel purchased in a value store were found to have a preference to a competitive set of value stores but perceived all other discount stores as higher in store shopping experience. Findings were presented to articulate the resolution and clarity of the magnitude‐determined ratio scales versus those of typical interval scales and multi‐attribute measures.Research limitations/implicationsThe comparisons provided here are for illustrative purposes only and are based on a selected group of one company's loyal customers during a defined shopping season.Originality/valueConsumer perceptions of key interest to retail management are shown to be measured and benchmarked in a practical setting using this technique.

Hyperbolic discounting may be reduced to electrical coupling in dopaminergic neural circuits

Loss of self-control in drug addicts (e.g. cocaine and amphetamine dependent patients) has been associated with hyperbolic discounting of delayed rewards (i.e., inconsistency in intertemporal choice). Neurobiophysical mechanisms underlying hyperbolic discounting are still unknown in spite of recent extensive work in neuroeconomics. Understanding of neuronal mechanisms of hyperbolic discounting is important for establishing neuropharmacological treatment of addiction. At the cognitive level, previous studies have indicated that psychophysics of time-estimation (i.e., Weber-Fechner law and Steven's power law of time-perception) may explain inconsistency in intertemporal choice. Regarding neuronal substrates of time-estimation, drugs of abuse dramatically change time-estimation, indicating that dopaminergic activities may mediate time-estimation. With respect to neuronal changes induced by drugs of abuse, recent studies have revealed that gap junction proteins (e.g., connexin 36) in dopamine neurons are increased by an self-administration of dopaminergic drugs such as cocaine and amphetamine. However, it has been yet to be examined how the enhanced electrical coupling due to substance administration induces addiction. Furthermore, a recent biophysical modelling study has demonstrated that the effect of the psychophysical laws are potentiated by non-synaptic electrical coupling between neurons via gap junctions. Based on these current findings, we hypothesized that hyperbolic discounting may be reduced to biophysical characteristics of dopamine neural circuits, that is, electrical coupling between time-encoding dopaminergic neurons via gap junctions. The present hypothesis states that drugs of abuse may induce addiction by exacerbating subject's impulsivity (a discount rate) and inconsistency (hyperbolicity) in intertemporal choice partly due to enhanced expression of gap junction proteins in dopaminergic neurons. Possible psychopharmacological treatments of impulsivity in drug addicts implied by our present hypothesis, e.g., administration of a gap junction blocker, are discussed.

Designing acoustic and non-acoustic parameters of synthesized speech warnings to control perceived urgency

To refine synthesized speech warning systems with urgency mapping, various kinds of acoustic and non-acoustic parameters were explored, and the relationship between the parameters and the subjectively perceived urgency was investigated through a series of experiments. The results showed that the speech rate, average fundamental frequency ( F0), warning message, message format, gender of voice, and interval between warning messages strongly influence the subjectively perceived urgency of synthesized voice warnings. For the three quantitative parameters: speech rate, average F0, and interval between warning messages, the results showed that it is possible to use psychophysical techniques (Stevens's power law) to quantify the effects of acoustic changes on perceived urgency.

Relationships between Odorant Concentration and Aroma Intensity

Aroma intensity of 5 concentrations (0.5, 2.5, 12.5, 62.5, and 312.5 ppm) of dimethyl trisulfide, methional [3-(methylthio) propionaldehyde], linalool (3,7-dimethyl-1, 6-octadien-3-ol), and vanillin (4-hydroxy-3-methoxybenzaldehyde) were evaluated by using sensory panels (n= 15) and gas chromatography olfactometry (GCO, n= 3) coupled with the Osme technique. The exponent (n) from Steven's Power Law was calculated as the slope of the logarithmic scale of perceived intensity versus compound concentration. Both sensory analysis and GCO data demonstrated that all odorants of interest followed Steven's Power Law (R2= 0.92 to 0.99). The relationship between concentration and aroma intensity was more completely explained by Steven's Law than by dilution methods. Results also revealed that GCO-Osme is a time-saving method that provides valuable information about odorants in foods. This method may also be used with other GCO techniques such as combined hedonic aroma response measurement (CHARM) and aroma extraction dilution analysis (AEDA) to more completely explain the contribution of compounds to the flavor of food products.

The Quantitative Model for Optimal Threshold and Gamma of Display Using Brightness Function

We investigated physical conditions for optimum display systems on various TV viewing conditions, and found that visual brightness function could be derived from relationships between Steven's power law and Bartleson-Breneman's brightness function, and that the optimum physical contrast ratio and compensated gamma for display system with adaptation luminance level could be obtained from the proposed brightness function.

Training to yoga respiration selectively increases respiratory sensation in healthy man

Because yoga practitioners think they are benefiting from their breath training we hypothesized that yoga respiration training (YRT) could modify the respiratory sensation. Yoga respiration (YR) ("ujjai") consisted of very slow, deep breaths (2-3 min(-1)) with sustained breath-hold after each inspiration and expiration. At inclusion in the study and after a 2-month YRT program, we determined in healthy subjects their eupneic ventilatory pattern and their capacity to discriminate external inspiratory resistive loads (respiratory sensation), digital tactile mechanical pressures (somesthetic sensation) and sound-pressure stimulations (auditory sensation). Data were compared to a gender-, age-, and weight-matched control group of healthy subjects who did not undergo the YRT program but were explored at the same epochs. After the 2-month YRT program, the respiratory sensation increased. Thus, both the exponent of the Steven's power law (Psi=kPhin) and the slope of the linear-linear plot between Psi and mouth pressure (Pm) were significantly higher, and the intercept with ordinate axis of the Psi versus Pm relationship was lower. After YRT, the peak Pm developed against inspiratory loads was significantly lower, reducing the load-induced activation of respiratory afferents. YRT induced long-lasting modifications of the ventilatory pattern with a significant lengthening of expiratory duration and a modest tidal volume increase. No significant changes in somesthetic and auditory sensations were noted. In the control group, the respiratory sensation was not modified during a 15-min period of yoga respiration, despite the peak Pm changes in response to added loads were then significantly reduced. These data suggest that training to yoga respiration selectively increases the respiratory sensation, perhaps through its persistent conditioning of the breathing pattern.

Objective measurement of the start-motion quality of a forklift truck

An objective index is developed for the estimation of ride quality during a forklift truck start. After consultation with test drivers, start-motion quality is defined and three governing parameters selected: engagement shock in the driving direction, vertical vibration, and pitch vibration. Subjective evaluation of the starting motion and objective measurements of vehicle vibration were performed on five forklift trucks with various load capacities. The vibration measured at the driver's seat was changed into a perceptual amount by using the frequency weighting curves and the fourth power dose method suggested in ISO 2631-1 (Mechanical Vibration and Shock-evaluation of Human Exposure to Whole-body Vibration—Part 1: General Requirements. International Organization for Standardization). Regression between the perceptual vibrations, expressed as a vibration dose value, and the subjective rating scores yielded an index equation in the form of Steven's psychophysical power law: ψ=1.912 φ −0.601, where ψ is the sensation magnitude of start-motion quality and φ is the stimulus magnitude of the vibration dose value.

Pitch strength and Stevens's power law.

Recent studies have suggested that the saliency or the strength of pitch of complex sounds can be accounted for on the basis of the temporal properties in the stimulus waveform as measured by the height of the first peak in the waveform autocorrelation function. We used a scaling procedure to measure the pitch strength from 15 listeners for four different pitches of complex sounds in which the height of the first peak in the autocorrelation function systematically varied. Pitch strength judgments were evaluated in terms of a modification of Stevens's power law in which temporal information was used from both the waveform fine structure and the envelope. Best fits of this modified power law to the judged pitch strengths indicate that the exponent in Stevens's power law is greater than 1. The results suggest that pitch strength is primarily determined by the waveform fine structure, but the stimulus envelope can also contribute to the pitch strength.

Odour from municipal solid waste (MSW) landfills: A study on the analysis of perception

The objective of this work was to develop a relationship between odour intensity and odour concentration by using data collected from various sensitive areas of the municipal solid waste (MSW) landfill site. A number of well-known psychophysical models (e.g., Weber–Fechner law, Steven's power law, Beidler's and Laffort's models) have been discussed that can successfully relate the perceived intensity with the odour concentration. Respective parameters for each of the models were estimated by the nonlinear Levenburg–Marquardt parameter estimation method. The overall performance of the model was tested statistically against sets of data from the olfactometry analysis. The model based on the Weber–Fechner law was ranked 1 in case of five out of nine samples and it has been found more representative of the less intense odour samples. The model based on Laffort's equation has represented the intensity–concentration relationship better with extremely low uncertainties on both parameters k 1 and k 2 for comparatively more intense odour samples.

One Hundred Years of Laws in Psychology

Mainstream psychology in the 20th century has been conceived as a nomothetic science, but few psychological "laws" have been proposed. A PsycLit search of journal abstracts from 1900 to 1999 yielded a total of 3,093 "law" citations, or 22 per 10,000 entries, with two psychophysical laws (Weber's law and Stevens's power law) and two learning laws (Herrnstein's matching law and Thorndike's law of effect) as the most frequently cited. The number of law citations has been decreasing throughout the century, to 10 per 10,000 entries in the last decade, with few references to laws of recent origin. This could be the result of increasing doubts about the lawfulness of psychological processes coupled with a general preference for less ambitious terms (such as effects, principles, models, or functions).

Using Psychophysics to Design Speech Warnings

An experiment is reported which applies psychophysical scaling techniques to the design of speech warnings. Participants used magnitude estimation to rate the perceived urgency of computer generated warning signal words (Deadly, Danger, Warning, Caution, Note) that varied systematically in speed. Stevens (1957) Power Law was used to model the relationship between changes in the acoustic parameter and changes in the perceived urgency of a particular signal word. The value for warning designers of the power function exponent, which quantifies and predicts the effect of acoustic changes on perceived urgency, is discussed.

A Union Function for Neural and Psychological Response

The union function proposed in this article is a generalization of the stimulus-effect model formerly established by the author. The union function has a better fit with experimental data in various sensory channels than does G. T. Fechner's (1877) logarithmic law or S. S. Stevens's (1957) power function law; it also has the generality to suggest rules or regularities relevant to local and global psychophysics. The goodness of fit with experimental data is demonstrated with numerical examples.