Weber's Law Research Articles

Why and how to apply Weber's Law to coevolution and mimicry.

In mimicry systems, receivers discriminate between the stimuli of models and mimics. Weber's Law of proportional processing states that receiver discrimination is based on proportional, not absolute, differences between stimuli. Weber's Law operates in a variety of taxa and modalities, yet it has largely been ignored in the context of mimicry, despite its potential relevance to whether receivers can discriminate models from mimics. Specifically, Weber's Law implies that for a given difference in stimulus magnitude between a model and mimic, as stimulus magnitudes increase, the mimic will be less discriminable from their model. This implies that mimics should benefit when stimulus magnitudes are high, and that high stimulus magnitudes will reduce selection for mimetic fidelity. Whether models benefit from high stimulus magnitudes depends on whether mimicry is honest or deceptive. We present four testable predictions about evolutionary trajectories of models and mimics based on this logic. We then provide a framework for testing whether receiver discrimination adheres to Weber's Law and illustrate it using coevolutionary examples and case studies from avian brood parasitism. We conclude that, when studying mimicry systems, researchers should consider whether receiver perception conforms to Weber's Law, because it could drive stimulus evolution in counterintuitive directions.

A unifying Bayesian framework accounting for spatiotemporal interferences with a deceleration tendency

Spatial and temporal levels of information processing interfere with each other. The Kappa effect is a well-known spatiotemporal interference in which the estimated time between two lights increases as the distance between them increases, showing a deceleration tendency. A classical model attributes this interference to constant speeds and predicts a linear relation, whereas a slowness model attributes the interference to slow speeds and proposes that the tendency is due to the uncertainty of stimuli locations. This study integrated a unifying Bayesian framework with the classical model and argued that this tendency is the result of the Weber–Fechner law. This hypothesis was tested via two time discrimination tasks that manipulated the uncertainty of stimuli locations and the distance between stimuli. Experiment 1 showed that the estimated time was not modulated by the uncertainty of the stimuli locations. Experiment 2 revealed that the behavioral predictions made by the Bayesian model on logarithmic scales were more accurate than those made by the linear model. Our results suggest that the deceleration tendency in the Kappa effect is the result of the Weber–Fechner law.

Investigation of human flavor perception and discrimination of the fat content in food using DR A-Not A and 3-AFC methods.

This study examined human flavor perception and discrimination of powdered milk samples with various fat contents using two different sensory discrimination methods, DR A-Not A and 3-AFC. DR A-Not A was expected to be more effective. Using skim milk and whole milk powder, five different samples with various fat contents were prepared. An independent samples design was used to compare DR A-Not A and 3-AFC. Each subject performed 24 repeated tests consisting of comparisons of four different test samples from the reference sample. Signal detection d' results showed that sample discrimination was possible using DR A-Not A, but not 3-AFC. Moreover, the just noticeable difference (JND) was calculated using the results of DR A-Not A. The calculated JND was 0.47% (w/v), and the Weber fraction was 0.82. These results confirm that the DR A-Not A method is more effective for studying the human sensitivity to the fat content in food.

Generating artificial sensations with spinal cord stimulation in primates and rodents

For patients who have lost sensory function due to a neurological injury such as spinal cord injury (SCI), stroke, or amputation, spinal cord stimulation (SCS) may provide a mechanism for restoring somatic sensations via an intuitive, non-visual pathway. Inspired by this vision, here we trained rhesus monkeys and rats to detect and discriminate patterns of epidural SCS. Thereafter, we constructed psychometric curves describing the relationship between different SCS parameters and the animal's ability to detect SCS and/or changes in its characteristics. We found that the stimulus detection threshold decreased with higher frequency, longer pulse-width, and increasing duration of SCS. Moreover, we found that monkeys were able to discriminate temporally- and spatially-varying patterns (i.e. variations in frequency and location) of SCS delivered through multiple electrodes. Additionally, sensory discrimination of SCS-induced sensations in rats obeyed Weber's law of just-noticeable differences. These findings suggest that by varying SCS intensity, temporal pattern, and location different sensory experiences can be evoked. As such, we posit that SCS can provide intuitive sensory feedback in neuroprosthetic devices.

Psychological Space-time Reinforcement Sensitivity Hypothesis & Mental Disorders: From Special to General Relativity Interpretation

The reinforcement sensitivity theory lacks basic sources of any human experience :time, place, and learning contexts that have shaped the reinforcement; therefore I have assumed a missing link in Gray's framework based on special relativity relying on the «what, where, and when of happenning»? as major resources of human conscious experience, which under punishment or reward exceed the sensitivity to pleasant or unpleasant stimuli transcending therefore the Weber law, that's why I called it: Psychological Space-Time Reinforcement Sensitivity “PSTRS” axis. The lasts explains BAS and BIS systems sensitivity to reinforcement across the cognitive space-time continuum of episodic memory, and not only across the two great dimensions of fear/anxiety and defensive distance of the McNaughton & Corr model of 2004. So, based on the disruption of the high-sensitivity information processing system in the brain, the four-dimensional conscious experience is distorted by its underlying sources and context. Thus, one of the timedominating records prevents the individual from overcoming the present., such in depression, obsessive compulsive disorder and post-traumatic stress disorder (psychological sensitivity to the past). These temporal records clearly lose their sequence and associative nature in dissociative symptoms due to the disruption of the most important milestone on which Einstein's physics was based. Consequently, psychological space-time reinforcement sensitivity supposes that psychological disorders can be interpreted according to the laws of special relativity (acceleration / deceleration), but this seems more complicated when it comes to mental disorders where the self is disturbed on its spatio-temporal axis as observed in schizophrenia. Schizophrenia looks like a three-componements disorder characterized by a disruption of the experience of time, place and self, which could be asummed up as a “self space-time disturbance". Notably schizophrenic patients appear losing the ability to gather in a dynamic way these componements, as if the world seemed missig the gestalt characteristic or fragmented. The past felt like an inevitable destiny inhibits the direction towards the future; sometimes disorient the self to the point of feeling lost, as if the psychological time slows down to the point of feeling separated from the « now » the physical time. So are we dealing with an Euclidian space? The article attempts to provide a non-traditional interpretation of mental disorders by including general relativity in psychological studies, based on the neurobiological bases involved in the spatio-temporal processing of the conscious experience in the quantum brain.

Power law model for subjective mental workload and validation through air traffic control human-in-the-loop simulation

We provide evidence for a power law relationship between the subjective one-dimensional Instantaneous Self Assessment workload measure (five-level ISA-WL scale) and the radio communication of air traffic controllers (ATCOs) as an objective task load variable. It corresponds to Stevens’ classical psychophysics relationship between physical stimulus and subjective response, with characteristic power law exponent γ of the order of 1. The theoretical model was validated in a human-in-the loop air traffic control simulation experiment with traffic flow as environmental stimulus that correlates positively with ATCOs frequency and duration of radio calls (task load, RC-TL) and their reported ISA-WL. The theoretical predictions together with nonlinear regression-based model parameter estimates expand previously published results that quantified the formal logistic relationship between the subjective ISA measure and simulated air traffic flow (Fürstenau et al. in Theor Issues Ergon Sci 21(6): 684–708, 2020). The present analysis refers to a psychophysics approach to mental workload suggested by (Gopher and Braune in Hum Factors 26(5): 519–532, 1984) that was recently used by (Bachelder and Godfroy-Cooper in Pilot workload esimation: synthesis of spectral requirements analysis and Weber's law, SCL Tech, San Diego, 2019) for pilot workload estimation, with a corresponding power law exponent in the typical range of Stevens’ exponents. Based on the hypothesis of cognitive resource limitation, we derived the power law by combination of the two logistic models for ISA-WL and communication TL characteristics, respectively. Despite large inter-individual variance, the theoretically predicted logistic and power law parameter values exhibit surprisingly close agreement with the regression-based estimates (for averages across participants). Significant differences between logistic ISA-WL and RC-TL scaling parameters and the corresponding Stevens exponents as ratio of these parameters quantify the TL/WL dissociation with regard to traffic flow. The sensitivity with regard to work conditions of the logistic WL-scaling parameter as well as the power law exponent was revealed by traffic scenarios with a non-nominal event: WL sensitivity increased significantly for traffic flow larger than a critical value. Initial analysis of a simultaneously measured new neurophysiological (EEG) load index (dual frequency head maps, DFHM, (Radüntz in Front Physiol 8: 1–15, 2017)) provided evidence for the power law to be applicable to the DFHM load measure as well.

Modeling personalized cognition of customers in online shopping

Online reviews play an important role in online shopping. Previous studies on Multi-Criteria Decision Making (MCDM) based on customer reviews focused too much on sentiment words in text reviews but ignored the personalized semantics of linguistic terms. In addition, only considering the qualitative information of products/services is not enough to simulate the purchase behaviors of customers given that the customers are also concerned with quantitative parameters. To bridge these research gaps, this study models the personalized cognition of customers on both quantitative and qualitative information, and proposes an MCDM framework for online shopping. Firstly, we determine the personalized semantics of linguistic terms through the emotional consistency between star ratings and text reviews. Afterwards, we investigate the “psychological intensity” based on Weber-Fechner's law to determine the utilities of quantitative parameters. A utility-based translation method is then developed to express both quantitative parameters and text reviews as probabilistic linguistic term sets. The unified information is further aggregated to represent the performance of products/services. The applicability of the proposed method is illustrated by a case study of television selection from Amazon.com. The results demonstrate that the personalized cognition has an influence on the judgments of products/services.

An optimal subsidy scheduling strategy for electric vehicles in multi-energy systems

With the increasing demand for multi-purpose energy, multi-energy systems (MES) have become the trend of urban development. To coordinate disorder charging among electric vehicles(EVs) in MES, this paper presents an optimal subsidy scheduling strategy for EVs. The strategy can decrease the fluctuation of the load of grids. Firstly, we use Monte Carlo approach based on historical data to simulate users’ charging behaviors. Orderly charging model is established according to simulation results. Then, multi-beneficial model is established based on time of use(TOU) tariff. The multi-beneficial model can be optimized by using Particle Swarm Optimization(PSO). Next, Weber-Fechner law is applied to further enhance users’ satisfaction. Moreover, dynamic non-cooperative game simulation is used to adjust both the users and the grids’ behaviors. By using the method of traverse and PSO, data including the optimal subsidy time and quantity can be obtained. In the end, the results of case study show that multi-beneficial benefit increases by 23.19%, the users benefit increases by 1.33% and the grid benefit increases by 21.86%. This can prove that the strategy is beneficial both to the users and the grid.

Agent-based automated persuasion with adaptive concessions tuned by emotions

Human-to-agent automated negotiation has many potentials in a variety of applications. How to design an agent with equivalent persuasion capabilities with its human rivals is the key to the success of such systems but the research on this problem is still at its early stage. With the aim of improving agents’ persuasion ability, this paper proposes to construct emotional agents and emotion-dependent persuasion actions in automated negotiation with multiple issues. First, a multi-issue evaluation function adjusted by the rival’s reputation is constructed to determine whether emotional persuasion is needed. Then, by applying the Weber-Fechner Law, this paper proposes a method to measure an agent’s emotion generated by evaluating the rival’s proposal. Persuasion is categorized into four types and an emotion-based method is proposed for an agent to select a persuasion type. The selected persuasion type is further related to updating concessions, so that an agent can make concessions adaptive to both the rival’s proposal and the focal agent’s emotional state. Moreover, a series of numerical experiments on bilateral negotiation between agents are conducted to illustrate the proposed model and validate its effectiveness in improving negotiation efficiency. Theoretical and practical implications as well as limitations are discussed in the end.

Approximate multiplication in young children prior to multiplication instruction

Prior work indicates that children have an untrained ability to approximately calculate using their approximate number system (ANS). For example, children can mentally double or halve a large array of discrete objects. Here, we asked whether children can perform a true multiplication operation, flexibly attending to both the multiplier and multiplicand, prior to formal multiplication instruction. We presented 5- to 8-year-olds with nonsymbolic multiplicands (dot arrays) or symbolic multiplicands (Arabic numerals) ranging from 2 to 12 and with nonsymbolic multipliers ranging from 2 to 8. Children compared each imagined product with a visible comparison quantity. Children performed with above-chance accuracy on both nonsymbolic and symbolic approximate multiplication, and their performance was dependent on the ratio between the imagined product and the comparison target. Children who could not solve any single-digit symbolic multiplication equations (e.g., 2 × 3) on a basic math test were nevertheless successful on both our approximate multiplication tasks, indicating that children have an intuitive sense of multiplication that emerges independent of formal instruction about symbolic multiplication. Nonsymbolic multiplication performance mediated the relation between children’s Weber fraction and symbolic math abilities, suggesting a pathway by which the ANS contributes to children’s emerging symbolic math competence. These findings may inform future educational interventions that allow children to use their basic arithmetic intuition as a scaffold to facilitate symbolic math learning.

Formalin-induced pain prolongs sub- to supra-second time estimation in rats.

BackgroundTemporal estimation can be influenced by pain, which is a complex psychological and physiological phenomenon. However, the time range in which perception is most sensitive to pain remains unclear.MethodsIn the present study, we explored the effects of acute inflammatory pain on time perception in the sub- to supra-second (0.6–2.4-s) and supra-second (2–8-s) ranges in rats. Plantar formalin injection was used to induce acute inflammatory pain, and a temporal bisection task was used to measure time perception. Task test sessions were held for five consecutive days (one per day): the day before injection (baseline), immediately after injection, and the three post-injection days. The point of subjective equality (PSE, which reflects the subjective duration) and Weber fraction (which reflects temporal sensitivity) were calculated and analysed.ResultsIn the 0.6–2.4-s range, the PSE was significantly lower, indicating prolonged subjective duration, in the formalin group relative to the saline group (p = 0.049) immediately after injection. Formalin-induced pain also tended to lengthened time perception in the 0.6–2.4-s range on post-injection days 2 (p = 0.06) and 3 (p = 0.054). In the 2–8-s range, formalin injection did not affect the PSE or Weber fraction.ConclusionsThe enhanced effect of pain on temporal perception in the sub- to supra-second range is observed in this study and this effect is attenuated with the prolongation of estimated time, even in rats.

Statistical Mechanical Foundation of Weber–Fechner Laws

Even though the phenomenological relations between perception and stimulus have been firmly established, a theoretical argument for Weber's and Fechner's law in terms of relevant models or from statistical physics is largely missing. We present such a discussion in terms of response theory for nonequilibrium systems, where the induced displacement or current, which stands for the perceived stimulus, crucially depends on the change in time-symmetric reactivities. Stationary nonequilibria may indeed generate extra currents by changing the dynamical activity. The argument finishes by understanding how the extra dynamical activity logarithmically encodes the actual stimulus.

Logarithms Are Hot Stuff: A New Rating Scale for Chili Peppers

ABSTRACT The typical trigonometry, precalculus, or calculus student might not agree that logarithms are hot stuff, but we drew motivation from chili peppers to help students get a better taste for logarithms. The Scoville scale, which ranges from 0 to 16,000,000, has been the sole quantitative metric to measure the pungency (spiciness) of peppers since its creation in 1912. With justification from the Weber–Fechner Law (perception is the logarithm of stimulus), students were challenged to create a more palatable rating scale for chili peppers. The first author devised a simple but effective 0–10 rating scale for peppers, calling this new rating system the “Ferven scale.” While the Weber–Fechner Law has been applied to the senses of touch, sight, and hearing, this paper presents the first known application of this law to the sense of taste.

Deep reinforcement learning framework for dynamic pricing demand response of regenerative electric heating

Applications of electric heating, which can improve carbon emission reduction and renewable energy utilization, have brought new challenges to the safe operation of energy systems around the world. Regenerative electric heating with load aggregators and demand response is an effective means to mitigate the wind curtailment and grid operational risks caused by electric heating. However, there is still a lack of models related to demand response, which results in participants not being able to obtain maximum benefits through dynamic subsidy prices. This study uses the Weber–Fechner law and a clustering algorithm to construct quantitative response characteristics models. The deep Q network was used to build a dynamic subsidy price generation framework for load aggregators. Through simulation analysis based on the evolutionary game model of a project in a rural area in Tianjin, China, the following conclusions were drawn: compared with the benchmark model, regenerative electric heating users can save up to 8.7% of costs, power grid companies can save 56.6% of their investment, and wind power plants can increase wind power consumption by 17.6%. The framework proposed in this study considers user behavior quantification of demand response participants and the differences among users. Therefore, the framework can provide a more reasonable, applicable, and intelligent system for regenerative electric heating.

Behavioural thresholds of blue tit colour vision and the effect of background chromatic complexity

Vision is a vital attribute to foraging, navigation, mate selection and social signalling in animals, which often have a very different colour perception in comparison to humans. For understanding how animal colour perception works, vision models provide the smallest colour difference that animals of a given species are assumed to detect. To determine the just-noticeable-difference, or JND, vision models use Weber fractions that set discrimination thresholds of a stimulus compared to its background. However, although vision models are widely used, they rely on assumptions of Weber fractions since the exact fractions are unknown for most species. Here, we test; i) which Weber fractions in long-, middle- and shortwave (i.e. L, M, S) colour channels best describe the blue tit (Cyanistes caeruleus) colour discrimination, ii) how changes in hue of saturated colours and iii) chromatic background noise impair search behaviour in blue tits. We show that the behaviourally verified Weber fractions on achromatic backgrounds were L: 0.05, M: 0.03 and S: 0.03, indicating a high colour sensitivity. In contrast, on saturated chromatic backgrounds, the correct Weber fractions were considerably higher for L: 0.20, M: 0.17 and S: 0.15, indicating a less detailed colour perception. Chromatic complexity of backgrounds affected the longwave channel, while middle- and shortwave channels were mostly unaffected. We caution that using a vision model whereby colour discrimination is determined in achromatic viewing conditions, as they often are, can lead to misleading interpretations of biological interactions in natural – colourful – environments.

Novel features for art movement classification of portrait paintings

The increasing availability of extensive digitized fine art collections opens up new research directions. In particular, correctly identifying the artistic style or art movement of paintings is crucial for large artistic database indexing, painter authentication, and mobile recognition of painters. Even though the implementation of CNN on artwork classification improved the performance dramatically compared to tradition classifier, the feature extraction methods are still valuable to help establishing better image representation for both common classifiers and neural networks. The main goal of this article is to present three novel features and a mature model structure for artistic movement recognition of portrait paintings. The proposed features include two unique color features and one texture feature: (a) Modified Color Distance (MCD), (b) ColorRatio Feature and (c) Weber's law Based Texture Feature. We demonstrate the superiority of our proposed method over the state-of-the-art approaches, and how successful our features are to support features from various neural networks. Another contribution of our work is a new portrait database that consists of 927 paintings from 6 different art movements. Extensive computer evaluations on this database show that we achieved an average accuracy of 98% for classifying two categories and 82.6% for classifying all 6 categories. Besides, our novel features improved the performance of pre-trained CNN significantly.

Estimation of Torso Vibrotactile Thresholds Using Eccentric Rotating Mass Motors.

The characterization of vibrotactile perception is crucial to accurately configure haptic devices and create appropriate stimuli for improving user performance in human-machine interaction systems. This article presents a study aiming to determine the absolute and differential vibrotactile thresholds in different areas of the torso to develop reliable haptic patterns to be displayed using a haptic vest. In the 'absolute threshold' experiment, we measure the minimum detectable vibration using a forced-choice task. Furthermore, in the 'differential threshold' experiment, we measure the minimum frequency change needed for users to discriminate two successive vibrotactile stimuli using a vibration matching task. The first experiment does not show differences between absolute thresholds, opening up the possibility of setting a unique minimal vibration for creating haptic patterns. Similarly, the second experiment does not show differences between differential thresholds. Moreover, as these thresholds follow Weber's law, it is viable to estimate any upper or lower differential threshold for any reference stimulus using a K-value. These results are a first step for creating vibrotactile patterns over the torso with the employed eccentric rotating mass motors. Moreover, the whole study provides a method to obtain these psychophysical values since the usage of different motors can change these results.

Application Research on Objective Evaluation of Vehicle Interior Odor Based On Weber-Fechner Law

In this paper, four typical compounds of odorants were selected as the research objects. The mathematical model hypothesis is established which based on the Weber-Fechner law, and then the relationship between the concentration of odor substances and the odor grade is verified to judge whether this law is applicable to the objective evaluation of vehicle interior odor. The results show that: the concentration of single odor substance and odor grade, the concentration of two kinds of odor substances and odor grade are in accordance with this law. It is proved that the relationship between odor substance concentration and odor grade conforms to the law to a certain extent, which provides an important theoretical basis for objective evaluation of vehicle interior odor and control vehicle environment to create an environmental and healthy vehicle.

Variation in the “coefficient of variation”: Rethinking the violation of the scalar property in time-duration judgments

The coefficient of variation (CV), also known as relative standard deviation, has been used to measure the constancy of the Weber fraction, a key signature of efficient neural coding in time perception. It has long been debated whether or not duration judgments follow Weber's law, with arguments based on examinations of the CV. However, what has been largely ignored in this debate is that the observed CVs may be modulated by temporal context and decision uncertainty, thus questioning conclusions based on this measure. Here, we used a temporal reproduction paradigm to examine the variation of the CV with two types of temporal context: full-range mixed vs. sub-range blocked intervals, separately for intervals presented in the visual and auditory modalities. We found a strong contextual modulation of both interval-duration reproductions and the observed CVs. We then applied a two-stage Bayesian model to predict those variations. Without assuming a violation of the constancy of the Weber fraction, our model successfully predicted the central-tendency effect and the variation in the CV. Our findings and modeling results indicate that both the accuracy and precision of our timing behavior are highly dependent on the temporal context and decision uncertainty. And, critically, they advise caution with using variations of the CV to reject the constancy of the Weber fraction of duration estimation.

DEEP CONVOLUTIONAL NEURAL STRATEGY FOR DETECTION AND PREDICTION OF MELANOMA SKIN CANCER

The research work has focused on detection and prediction of melanoma which is done by subjecting to features extraction, where the features of an image consisting of melanoma regions are detected by analysis and this analysis is done by considering the features like color and texture-based features learning strategy. These features are extracted by combining color and texture-based features extraction with deep convolutional features representation learning strategy. The colors of images are extracted by representing the colors of different channels into red, green and blue channel information. The combination of texture features extraction with color-based features extraction in addition to Alex net features extraction learning has made the system more robust and efficient toward the segmentation and classification of images. Further, the erected method involves convoluting the features of extracted information with color and texture-based method which has led our system to full convolution neural networks with images features extraction. The melanoma is detected and segmented with watershed segmentation, these segmented features are subjected to the proposed features extraction method, where the features are extracted by combining the methods of texture with color-based information. These colors are made available to the proposed method by analyzing the regions of melanoma images. The erected method does the task of features extraction by Weber law descriptors in combination with red, green, blue channels information extracted from features representation learning. The proposed method has yielded an accuracy of 94.12% of segmentation accuracy and a classification accuracy of 94.32% with respect to various other classification techniques.