The transducer model for contrast detection and discrimination: formal relations, implications, and an empirical test

The transducer function mu for contrast perception describes the nonlinear mapping of stimulus contrast onto an internal response. Under a signal detection theory approach, the transducer model of contrast perception states that the internal response elicited by a stimulus of contrast c is a random variable with mean mu(c). Using this approach, we derive the formal relations between the transducer function, the threshold-versus-contrast (TvC) function, and the psychometric functions for contrast detection and discrimination in 2AFC tasks. We show that the mathematical form of the TvC function is determined only by mu, and that the psychometric functions for detection and discrimination have a common mathematical form with common parameters emanating from, and only from, the transducer function mu and the form of the distribution of the internal responses. We discuss the theoretical and practical implications of these relations, which have bearings on the tenability of certain mathematical forms for the psychometric function and on the suitability of empirical approaches to model validation. We also present the results of a comprehensive test of these relations using two alternative forms of the transducer model: a three-parameter version that renders logistic psychometric functions and a five-parameter version using Foley's variant of the Naka-Rushton equation as transducer function. Our results support the validity of the formal relations implied by the general transducer model, and the two versions that were contrasted account for our data equally well.     

Joint Entropy for Space and Spatial Frequency Domains Estimated from Psychometric Functions of Achromatic Discrimination

We used psychometric functions to estimate the joint entropy for space discrimination and spatial frequency discrimination. Space discrimination was taken as discrimination of spatial extent. Seven subjects were tested. Gábor functions comprising unidimensionalsinusoidal gratings (0.4, 2, and 10 cpd) and bidimensionalGaussian envelopes (1°) were used as reference stimuli. The experiment comprised the comparison between reference and test stimulithat differed in grating''s spatial frequency or envelope''s standard deviation. We tested 21 different envelope''s standard deviations around the reference standard deviation to study spatial extent discrimination and 19 different grating''s spatial frequencies around the reference spatial frequency to study spatial frequency discrimination. Two series of psychometric functions were obtained for 2%, 5%, 10%, and 100% stimulus contrast. The psychometric function data points for spatial extent discrimination or spatial frequency discrimination were fitted with Gaussian functions using the least square method, and the spatial extent and spatial frequency entropies were estimated from the standard deviation of these Gaussian functions. Then, joint entropy was obtained by multiplying the square root of space extent entropy times the spatial frequency entropy. We compared our results to the theoretical minimum for unidimensional Gábor functions, 1/4π or 0.0796. At low and intermediate spatial frequencies and high contrasts, joint entropy reached levels below the theoretical minimum, suggesting non-linear interactions between two or more visual mechanisms. We concluded that non-linear interactions of visual pathways, such as the M and P pathways, could explain joint entropy values below the theoretical minimum at low and intermediate spatial frequencies and high contrasts. These non-linear interactions might be at work at intermediate and high contrasts at all spatial frequencies once there was a substantial decrease in joint entropy for these stimulus conditions when contrast was raised.     

Reinterpreting Behavioral Receptive Fields: Lightness Induction Alters Visually Completed Shape

Background

A classification image (CI) technique has shown that static luminance noise near visually completed contours affects the discrimination of fat and thin Kanizsa shapes. These influential noise regions were proposed to reveal “behavioral receptive fields” of completed contours–the same regions to which early cortical cells respond in neurophysiological studies of contour completion. Here, we hypothesized that 1) influential noise regions correspond to the surfaces that distinguish fat and thin shapes (hereafter, key regions); and 2) key region noise biases a “fat” response to the extent that its contrast polarity (lighter or darker than background) matches the shape''s filled-in surface color.

Results

To test our hypothesis, we had observers discriminate fat and thin noise-embedded rectangles that were defined by either illusory or luminance-defined contours (Experiment 1). Surrounding elements (“inducers”) caused the shapes to appear either lighter or darker than the background–a process sometimes referred to as lightness induction. For both illusory and luminance-defined rectangles, key region noise biased a fat response to the extent that its contrast polarity (light or dark) matched the induced surface color. When lightness induction was minimized, luminance noise had no consistent influence on shape discrimination. This pattern arose when pixels immediately adjacent to the discriminated boundaries were excluded from the analysis (Experiment 2) and also when the noise was restricted to the key regions so that the noise never overlapped with the physically visible edges (Experiment 3). The lightness effects did not occur in the absence of enclosing boundaries (Experiment 4).

Conclusions

Under noisy conditions, lightness induction alters visually completed shape. Moreover, behavioral receptive fields derived in CI studies do not correspond to contours per se but to filled-in surface regions contained by those contours. The relevance of lightness to two-dimensional shape completion supplies a new constraint for models of object perception.     

Intrinsic uncertainty explains second responses

In the simplest form of signal-detection theory (SDT), all stimuli give rise to equal-variance Gaussian probability density functions (PDFs) of sensation, with means proportional to stimulus intensity. As this simple SDT cannot accurately describe psychometric functions for two-alternative forced-choice (2AFC) detection experiments, it is commonly modified in one of two ways: with a non-linear transducer or intrinsic uncertainty. Most results can adequately be explained by either modification, but Swets et al.'s (1961) two-response 4AFC (2R4AFC) detection experiment is an exception. Simple SDT cannot predict the relationship between first- and second-response accuracies and non-linear transduction does not help. A previously unacknowledged facet of intrinsic uncertainty is that the same uncertainty required to fit 2AFC psychometric functions also produces an excellent fit to Swets et al.'s 2R4AFC results, without requiring any additional assumptions. This result is derived within the context of a primer on SDT.     

fMRI Activity in Posterior Parietal Cortex Relates to the Perceptual Use of Binocular Disparity for Both Signal-In-Noise and Feature Difference Tasks

Visually guided action and interaction depends on the brain’s ability to (a) extract and (b) discriminate meaningful targets from complex retinal inputs. Binocular disparity is known to facilitate this process, and it is an open question how activity in different parts of the visual cortex relates to these fundamental visual abilities. Here we examined fMRI responses related to performance on two different tasks (signal-in-noise “coarse” and feature difference “fine” tasks) that have been widely used in previous work, and are believed to differentially target the visual processes of signal extraction and feature discrimination. We used multi-voxel pattern analysis to decode depth positions (near vs. far) from the fMRI activity evoked while participants were engaged in these tasks. To look for similarities between perceptual judgments and brain activity, we constructed ‘fMR-metric’ functions that described decoding performance as a function of signal magnitude. Thereafter we compared fMR-metric and psychometric functions, and report an association between judged depth and fMRI responses in the posterior parietal cortex during performance on both tasks. This highlights common stages of processing during perceptual performance on these tasks.     

A Kramers-Moyal Approach to the Analysis of Third-Order Noise with Applications in Option Valuation

We propose the use of the Kramers-Moyal expansion in the analysis of third-order noise. In particular, we show how the approach can be applied in the theoretical study of option valuation. Despite Pawula’s theorem, which states that a truncated model may exhibit poor statistical properties, we show that for a third-order Kramers-Moyal truncation model of an option’s and its underlier’s price, important properties emerge: (i) the option price can be written in a closed analytical form that involves the Airy function, (ii) the price is a positive function for positive skewness in the distribution, (iii) for negative skewness, the price becomes negative only for price values that are close to zero. Moreover, using third-order noise in option valuation reveals additional properties: (iv) the inconsistencies between two popular option pricing approaches (using a “delta-hedged” portfolio and using an option replicating portfolio) that are otherwise equivalent up to the second moment, (v) the ability to develop a measure R of how accurately an option can be replicated by a mixture of the underlying stocks and cash, (vi) further limitations of second-order models revealed by introducing third-order noise.     

Effects of Virtual Speaker Density and Room Reverberation on Spatiotemporal Thresholds of Audio-Visual Motion Coherence

The present study examined the effects of spatial sound-source density and reverberation on the spatiotemporal window for audio-visual motion coherence. Three different acoustic stimuli were generated in Virtual Auditory Space: two acoustically “dry” stimuli via the measurement of anechoic head-related impulse responses recorded at either 1° or 5° spatial intervals (Experiment 1), and a reverberant stimulus rendered from binaural room impulse responses recorded at 5° intervals in situ in order to capture reverberant acoustics in addition to head-related cues (Experiment 2). A moving visual stimulus with invariant localization cues was generated by sequentially activating LED''s along the same radial path as the virtual auditory motion. Stimuli were presented at 25°/s, 50°/s and 100°/s with a random spatial offset between audition and vision. In a 2AFC task, subjects made a judgment of the leading modality (auditory or visual). No significant differences were observed in the spatial threshold based on the point of subjective equivalence (PSE) or the slope of psychometric functions (β) across all three acoustic conditions. Additionally, both the PSE and β did not significantly differ across velocity, suggesting a fixed spatial window of audio-visual separation. Findings suggest that there was no loss in spatial information accompanying the reduction in spatial cues and reverberation levels tested, and establish a perceptual measure for assessing the veracity of motion generated from discrete locations and in echoic environments.     

Heart Rate and Systolic Blood Pressure Variability in the Time Domain in Patients with Recent and Long-Standing Diabetes Mellitus

Diabetes Mellitus (DM) affects the cardiovascular response of patients. To study this effect, interbeat intervals (IBI) and beat-to-beat systolic blood pressure (SBP) variability of patients during supine, standing and controlled breathing tests were analyzed in the time domain. Simultaneous noninvasive measurements of IBI and SBP for 30 recently diagnosed and 15 long-standing DM patients were compared with the results for 30 rigorously screened healthy subjects (control). A statistically significant distinction between control and diabetic subjects was provided by the standard deviation and the higher moments of the distributions (skewness, and kurtosis) with respect to the median. To compare IBI and SBP for different populations, we define a parameter, α, that combines the variability of the heart rate and the blood pressure, as the ratio of the radius of the moments for IBI and the same radius for SBP. As diabetes evolves, α decreases, standard deviation of the IBI detrended signal diminishes (heart rate signal becomes more “rigid”), skewness with respect to the median approaches zero (signal fluctuations gain symmetry), and kurtosis increases (fluctuations concentrate around the median). Diabetes produces not only a rigid heart rate, but also increases symmetry and has leptokurtic distributions. SBP time series exhibit the most variable behavior for recently diagnosed DM with platykurtic distributions. Under controlled breathing, SBP has symmetric distributions for DM patients, while control subjects have non-zero skewness. This may be due to a progressive decrease of parasympathetic and sympathetic activity to the heart and blood vessels as diabetes evolves.     

What Do Contrast Threshold Equivalent Noise Studies Actually Measure? Noise vs. Nonlinearity in Different Masking Paradigms

The internal noise present in a linear system can be quantified by the equivalent noise method. By measuring the effect that applying external noise to the system’s input has on its output one can estimate the variance of this internal noise. By applying this simple “linear amplifier” model to the human visual system, one can entirely explain an observer’s detection performance by a combination of the internal noise variance and their efficiency relative to an ideal observer. Studies using this method rely on two crucial factors: firstly that the external noise in their stimuli behaves like the visual system’s internal noise in the dimension of interest, and secondly that the assumptions underlying their model are correct (e.g. linearity). Here we explore the effects of these two factors while applying the equivalent noise method to investigate the contrast sensitivity function (CSF). We compare the results at 0.5 and 6 c/deg from the equivalent noise method against those we would expect based on pedestal masking data collected from the same observers. We find that the loss of sensitivity with increasing spatial frequency results from changes in the saturation constant of the gain control nonlinearity, and that this only masquerades as a change in internal noise under the equivalent noise method. Part of the effect we find can be attributed to the optical transfer function of the eye. The remainder can be explained by either changes in effective input gain, divisive suppression, or a combination of the two. Given these effects the efficiency of our observers approaches the ideal level. We show the importance of considering these factors in equivalent noise studies.     

Principal Semantic Components of Language and the Measurement of Meaning

Metric systems for semantics, or semantic cognitive maps, are allocations of words or other representations in a metric space based on their meaning. Existing methods for semantic mapping, such as Latent Semantic Analysis and Latent Dirichlet Allocation, are based on paradigms involving dissimilarity metrics. They typically do not take into account relations of antonymy and yield a large number of domain-specific semantic dimensions. Here, using a novel self-organization approach, we construct a low-dimensional, context-independent semantic map of natural language that represents simultaneously synonymy and antonymy. Emergent semantics of the map principal components are clearly identifiable: the first three correspond to the meanings of “good/bad” (valence), “calm/excited” (arousal), and “open/closed” (freedom), respectively. The semantic map is sufficiently robust to allow the automated extraction of synonyms and antonyms not originally in the dictionaries used to construct the map and to predict connotation from their coordinates. The map geometric characteristics include a limited number (∼4) of statistically significant dimensions, a bimodal distribution of the first component, increasing kurtosis of subsequent (unimodal) components, and a U-shaped maximum-spread planar projection. Both the semantic content and the main geometric features of the map are consistent between dictionaries (Microsoft Word and Princeton''s WordNet), among Western languages (English, French, German, and Spanish), and with previously established psychometric measures. By defining the semantics of its dimensions, the constructed map provides a foundational metric system for the quantitative analysis of word meaning. Language can be viewed as a cumulative product of human experiences. Therefore, the extracted principal semantic dimensions may be useful to characterize the general semantic dimensions of the content of mental states. This is a fundamental step toward a universal metric system for semantics of human experiences, which is necessary for developing a rigorous science of the mind.     

Energy model for contrast detection: spatiotemporal characteristics of threshold vision

A model for contrast detection of spatiotemporal stimuli is proposed which consists of a spatiotemporal linear filter, an energy device and a threshold device. Assuming the existence of independent intrinsic noise, the probability of stimulus detection was approximated by a Weibull function of the response energy. With this assumption, the stimulus energy is a constant at fixed detection probability. This energy model for contrast detection satisfactorily accounted for the elliptical threshold contours of line pairs at stimulus separations within the range 2–30 min and at stimulus onset asynchronies within the range 20–140 ms. The threshold contour at a large stimulus onset asynchrony (300 ms) was in the form of a rounded square. This finding was explained by assuming that the probability of seeing the line pair was determined by the joint probability that at least one stimulus had been detected. With the energy model, the temporal and spatial autocorrelation functions of the response to a flashed line were evaluated. The autocorrelation functions thus determined were used to predict the temporal contrast sensitivity function to a flickering line stimulus and the spatial contrast sensitivity function to flashed gratings, which were in agreement with the experimental data. The data obtained were fitted adequately by an impulse response approximated by a spatiotemporal Gabor-like function. Received: 08 December 1997 / Accepted in revised form: 26 January 1999     

Parturition Signaling by Visual Cues in Female Marmosets (Callithrix jacchus)

New World monkeys have polymorphic color vision, in which all males and some females are dichromats, while most females are trichromats. There is little consensus about which selective pressures fashioned primate color vision, although detection of food, mates and predators has been hypothesized. Behavioral evidence shows that males from different species of Neotropical primates seem to perceive the timing of female conception and gestation, although, no signals fulfilling this function have been identified. Therefore, we used visual models to test the hypothesis that female marmosets show chromatic and/or achromatic cues that may indicate the time of parturition for male and female conspecifics. By recording the reflectance spectra of female marmosets’ (Callithrix jacchus) sexual skin, and running chromatic and achromatic discrimination models, we found that both variables fluctuate during the weeks that precede and succeed parturition, forming “U” and inverted “U” patterns for chromatic and achromatic contrast, respectively. We suggest that variation in skin chroma and luminance might be used by female helpers and dominant females to identify the timing of birth, while achromatic variations may be used as clues by potential fathers to identify pregnancy stage in females and prepare for paternal burdens as well as to detect oestrus in the early post-partum period.     

An Automated,Adaptive Framework for Optimizing Preprocessing Pipelines in Task-Based Functional MRI

BOLD fMRI is sensitive to blood-oxygenation changes correlated with brain function; however, it is limited by relatively weak signal and significant noise confounds. Many preprocessing algorithms have been developed to control noise and improve signal detection in fMRI. Although the chosen set of preprocessing and analysis steps (the “pipeline”) significantly affects signal detection, pipelines are rarely quantitatively validated in the neuroimaging literature, due to complex preprocessing interactions. This paper outlines and validates an adaptive resampling framework for evaluating and optimizing preprocessing choices by optimizing data-driven metrics of task prediction and spatial reproducibility. Compared to standard “fixed” preprocessing pipelines, this optimization approach significantly improves independent validation measures of within-subject test-retest, and between-subject activation overlap, and behavioural prediction accuracy. We demonstrate that preprocessing choices function as implicit model regularizers, and that improvements due to pipeline optimization generalize across a range of simple to complex experimental tasks and analysis models. Results are shown for brief scanning sessions (<3 minutes each), demonstrating that with pipeline optimization, it is possible to obtain reliable results and brain-behaviour correlations in relatively small datasets.     

Segregation of odor identity and intensity during odor discrimination in Drosophila mushroom body

Molecular and cellular studies have begun to unravel a neurobiological basis of olfactory processing, which appears conserved among vertebrate and invertebrate species. Studies have shown clearly that experience-dependent coding of odor identity occurs in “associative” olfactory centers (the piriform cortex in mammals and the mushroom body [MB] in insects). What remains unclear, however, is whether associative centers also mediate innate (spontaneous) odor discrimination and how ongoing experience modifies odor discrimination. Here we show in naïve flies that G_αq-mediated signaling in MB modulates spontaneous discrimination of odor identity but not odor intensity (concentration). In contrast, experience-dependent modification (conditioning) of both odor identity and intensity occurs in MB exclusively via G_αs-mediated signaling. Our data suggest that spontaneous responses to odor identity and odor intensity discrimination are segregated at the MB level, and neural activity from MB further modulates olfactory processing by experience-independent G_αq-dependent encoding of odor identity and by experience-induced G_αs-dependent encoding of odor intensity and identity.     

Longitudinal Treatment Outcomes of Microsurgical Treatment of Neurosensory Deficit after Lower Third Molar Surgery: A Prospective Case Series

Objective

To prospectively evaluate the longitudinal subjective and objective outcomes of the microsurgical treatment of lingual nerve (LN) and inferior alveolar nerve (IAN) injury after third molar surgery.

Materials and Methods

A 1-year longitudinal observational study was conducted on patients who received LN or IAN repair after third molar surgery-induced nerve injury. Subjective assessments (“numbness”, “hyperaesthesia”, “pain”, “taste disturbance”, “speech” and “social life impact”) and objective assessments (light touch threshold, two-point discrimination, pain threshold, and taste discrimination) were recorded.

Results

12 patients (10 females) with 10 LN and 2 IAN repairs were recruited. The subjective outcomes at post-operative 12 months for LN and IAN repair were improved. “Pain” and “hyperaesthesia” were most drastically improved. Light touch threshold improved from 44.7g to 1.2g for LN repair and 2g to 0.5g for IAN repair.

Conclusion

Microsurgical treatment of moderate to severe LN injury after lower third molar surgery offered significant subjective and objective sensory improvements. 100% FSR was achieved at post-operative 6 months.     

A Visual Dual-Aptamer Logic Gate for Sensitive Discrimination of Prion Diseases-Associated Isoform with Reusable Magnetic Microparticles and Fluorescence Quantum Dots

Molecular logic gates, which have attracted increasing research interest and are crucial for the development of molecular-scale computers, simplify the results of measurements and detections, leaving the diagnosis of disease either “yes” or “no”. Prion diseases are a group of fatal neurodegenerative disorders that happen in human and animals. The main problem with a diagnosis of prion diseases is how to sensitively and selectively discriminate and detection of the minute amount of PrP^Res in biological samples. Our previous work had demonstrated that dual-aptamer strategy could achieve highly sensitive and selective discrimination and detection of prion protein (cellular prion protein, PrP^C, and the diseases associated isoform, PrP^Res) in serum and brain. Inspired by the advantages of molecular logic gate, we further conceived a new concept for dual-aptamer logic gate that responds to two chemical input signals (PrP^C or PrP^Res and Gdn-HCl) and generates a change in fluorescence intensity as the output signal. It was found that PrP^Res performs the “OR” logic operation while PrP^C performs “XOR” logic operation when they get through the gate consisted of aptamer modified reusable magnetic microparticles (MMPs-Apt1) and quantum dots (QDs-Apt2). The dual-aptamer logic gate simplifies the discrimination results of PrP^Res, leaving the detection of PrP^Res either “yes” or “no”. The development of OR logic gate based on dual-aptamer strategy and two chemical input signals (PrP^Res and Gdn-HCl) is an important step toward the design of prion diseases diagnosis and therapy systems.     

Temporal Characteristics of Gustatory Responses in Rat Parabrachial Neurons Vary by Stimulus and Chemosensitive Neuron Type

It has been demonstrated that temporal features of spike trains can increase the amount of information available for gustatory processing. However, the nature of these temporal characteristics and their relationship to different taste qualities and neuron types are not well-defined. The present study analyzed the time course of taste responses from parabrachial (PBN) neurons elicited by multiple applications of “sweet” (sucrose), “salty” (NaCl), “sour” (citric acid), and “bitter” (quinine and cycloheximide) stimuli in an acute preparation. Time course varied significantly by taste stimulus and best-stimulus classification. Across neurons, the ensemble code for the three electrolytes was similar initially but quinine diverged from NaCl and acid during the second 500ms of stimulation and all four qualities became distinct just after 1s. This temporal evolution was reflected in significantly broader tuning during the initial response. Metric space analyses of quality discrimination by individual neurons showed that increases in information (H) afforded by temporal factors was usually explained by differences in rate envelope, which had a greater impact during the initial 2s (22.5% increase in H) compared to the later response (9.5%). Moreover, timing had a differential impact according to cell type, with between-quality discrimination in neurons activated maximally by NaCl or citric acid most affected. Timing was also found to dramatically improve within-quality discrimination (80% increase in H) in neurons that responded optimally to bitter stimuli (B-best). Spikes from B-best neurons were also more likely to occur in bursts. These findings suggest that among PBN taste neurons, time-dependent increases in mutual information can arise from stimulus- and neuron-specific differences in response envelope during the initial dynamic period. A stable rate code predominates in later epochs.     

Repeated Evolution of Inactive Pseudonucleases in a Fungal Branch of the Dis3/RNase II Family of Nucleases

The RNase II family of 3′–5′ exoribonucleases is present in all domains of life, and eukaryotic family members Dis3 and Dis3L2 play essential roles in RNA degradation. Ascomycete yeasts contain both Dis3 and inactive RNase II-like “pseudonucleases.” The latter function as RNA-binding proteins that affect cell growth, cytokinesis, and fungal pathogenicity. However, the evolutionary origins of these pseudonucleases are unknown: What sequence of events led to their novel function, and when did these events occur? Here, we show how RNase II pseudonuclease homologs, including Saccharomyces cerevisiae Ssd1, are descended from active Dis3L2 enzymes. During fungal evolution, active site mutations in Dis3L2 homologs have arisen at least four times, in some cases following gene duplication. In contrast, N-terminal cold-shock domains and regulatory features are conserved across diverse dikarya and mucoromycota, suggesting that the nonnuclease function requires these regions. In the basidiomycete pathogenic yeast Cryptococcus neoformans, the single Ssd1/Dis3L2 homolog is required for cytokinesis from polyploid “titan” growth stages. This phenotype of C. neoformans Ssd1/Dis3L2 deletion is consistent with those of inactive fungal pseudonucleases, yet the protein retains an active site sequence signature. We propose that a nuclease-independent function for Dis3L2 arose in an ancestral hyphae-forming fungus. This second function has been conserved across hundreds of millions of years, whereas the RNase activity was lost repeatedly in independent lineages.     

麻城黄山松天然林直径分布

为研究黄山松天然次生林直径分布特征,以麻城市黄山松天然次生林为研究对象,采用标准样地调查,计算林分直径的偏度、峰度,林分直径分布的Shannon-Weiner和Simpson指数,运用负指数分布、normal分布、lognormal分布、logistic分布和Weibull分布等5种概率密度函数对黄山松天然次生林林分直...     

Do Cost Functions for Tracking Error Generalize across Tasks with Different Noise Levels?

Control of human-machine interfaces are well modeled by computational control models, which take into account the behavioral decisions people make in estimating task dynamics and state for a given control law. This control law is optimized according to a cost function, which for the sake of mathematical tractability is typically represented as a series of quadratic terms. Recent studies have found that people actually use cost functions for reaching tasks that are slightly different than a quadratic function, but it is unclear which of several cost functions best explain human behavior and if these cost functions generalize across tasks of similar nature but different scale. In this study, we used an inverse-decision-theory technique to reconstruct the cost function from empirical data collected on 24 able-bodied subjects controlling a myoelectric interface. Compared with previous studies, this experimental paradigm involved a different control source (myoelectric control, which has inherently large multiplicative noise), a different control interface (control signal was mapped to cursor velocity), and a different task (the tracking position dynamically moved on the screen throughout each trial). Several cost functions, including a linear-quadratic; an inverted Gaussian, and a power function, accurately described the behavior of subjects throughout this experiment better than a quadratic cost function or other explored candidate cost functions (p<0.05). Importantly, despite the differences in the experimental paradigm and a substantially larger scale of error, we found only one candidate cost function whose parameter was consistent with the previous studies: a power function (cost ∝ error^α) with a parameter value of α = 1.69 (1.53–1.78 interquartile range). This result suggests that a power-function is a representative function of user’s error cost over a range of noise amplitudes for pointing and tracking tasks.