Perception of the tactile texture of raised-dot patterns: a multidimensional analysis

An ALSCAL multidimensional scaling analysis in Euclidean space revealed that three orthogonal perceptual dimensions can account for the judged tactile dissimilarities of raised-dot patterns. Through magnitude estimates of various perceptual attributes, it was determined that the three dimensions consist of blur, roughness, and clarity. The only effect that selective adaptation of the Pacinian (P) channel had was to change the perceptual clarity of the raised dots against their background. Adaptation of the P channel with a 20 dB SL 250 Hz stimulus enhanced clarity. As indicated by magnitude estimates, adaptation of the P channel by the 250 Hz stimulus had no effect on the perceived roughness of the dot pattern but did cause the individual dots of the textured pattern to feel smoother. When the observer was required to estimate magnitude "overall roughness" defined as a combination of dot-pattern roughness and individual-dot roughness, adaptation of the P channel affected perceived roughness by reducing it. Taken as a whole, the results are consistent with the hypothesis that the NP channels and the P channel jointly influence the perception of textured surfaces.     

Roughness perception in tactile channels: Evidence for an opponent process in the sense of touch

Abstract

Magnitude estimates of the tactile roughness of raised-dot surfaces revealed that perceived overall roughness, defined as the combination of the perceived roughness of the dot pattern and the perceived roughness of the individual dots in the pattern, is an inverted U-shaped function of dot spacing, reaching a maximum at approximately 3.0?mm of dot separation. The hypothesis that Pacinian corpuscles are involved in roughness perception has been supported by the finding that selective adaptation of the Pacinian corpuscle (PC) channel with a 250-Hz stimulus at 20-dB SL results in a decrease in the perceived overall roughness of the raised-dot surface at the fingertip. The effect of PC channel adaptation on perceived overall roughness was attributable entirely to a reduction in the perceived roughness of the individual raised dots; PC adaptation had no effect on the perceived roughness of the raised-dot pattern. Selective adaptation of the slowly adapting type I (SA I) channel with a 5-Hz stimulus at 20-dB SL had the opposite effect of PC channel adaptation and resulted in an increase in the perceived roughness of the individual raised dots, and consequently the perceived overall roughness of the raised-dot surface. As was the case with PC channel adaptation, SA I channel adaptation had no effect on the perceived roughness of the pattern. Adaptation with a compound adapting stimulus containing 5- and 250-Hz components at 20-dB SL had no effect on perceived overall roughness, which suggests that the PC and SA I channels operate antagonistically in an opponent-process fashion in the perception of the microstructure of a textured surface. Neither PC adaptation nor SA I adaptation affected perceived pattern roughness, which suggests that pattern roughness is coded by relative rather than by absolute spatial variation in firing rate.     

Perception of the tactile texture of raised-dot patterns: further evidence of an opponent process in the sense of touch

Abstract

Observers judged the tactile dissimilarities of raised-dot surfaces presented in pairs. The role of the SA I channel in determining these tactile dissimilarities was investigated by examining the dissimilarity judgments when this channel was adapted and when it was not. In an earlier study, the role of the PC channel in determining tactile dissimilarity was examined using the same stimulus materials when the PC channel was adapted and when it was not. Three orthogonal perceptual dimensions identified as blur, pattern roughness, and clarity were found using ALSCAL multidimensional analysis to account for the judged dissimilarities. The same three dimensions were found again in the present study. The dimensions of blur and pattern roughness were unaffected by adaptation of either the SA I or the PC channel. The finding of no effect of adaptation of the SA I channel on either of these two dimensions suggests that the roughness of the macrostructure of a textured surface is coded by the relative rather than by the absolute spatial variation in the firing rates of SA I nerve fibers. The dimension of dot clarity was strongly affected by adaptation of both the SA I channel and the PC channel. Adaptation of the PC channel increased dot clarity but adaptation of the SA I channel decreased it. This finding suggests that the perceived roughness of the microstructure of a textured surface is enhanced by the activity of the PC channel but decreased by the activity of the SA I channel.     

Factors contributing to the integration of textural qualities: Evidence from virtual surfaces

Two experiments involving indirect touch were carried out to explore the relationships among perceptual dimensions of haptically examined surfaces. Subjects in both experiments used a stylus to evaluate the properties of virtual surfaces created by a force-feedback device; four surface properties (resistance to normal force, coefficient of friction, texture scale, and vibration amplitude) were manipulated in various combinations. In Experiment 1, the extent to which there was a one-to-one relationship between specific stimulus properties and perceptual qualities (“perceptual separability”) was evaluated. A substantial failure of separability was demonstrated, with friction tending to be more separable from the other properties than they were from one another. The pattern of results suggests that the amount of measured separability depends crucially on the way stimulus properties are defined (e.g., force versus displacement). In Experiment 2, surfaces with known perceptual properties were used to study the metric(s) of the relevant perceptual space. By specifying the perceptual, rather than the stimulus, coordinates of the surfaces, it was possible to bypass issues of perceptual separability. For surfaces of equal friction, a Euclidean metric captured the results (r²?=?0.75) more effectively than a city-block metric did; neither metric did well when differences in friction were involved. The fact that—unlike stickiness—hardness, roughness, and perceived vibration intensity are all increasing functions of surface-normal forces may facilitate their integration into a Euclidean space, in both direct (Hollins M, Bensmaïa S, Karlof K, Young F, . Individual differences in perceptual space for tactile textures: Evidence from multidimensional scaling. Percept Psychophys 62:1534–1544.) and indirect touch.     

Temporal coding of pheromone pulses and trains in Manduca sexta

Summary We investigated the ability of pheromone-sensitive olfactory receptors of male Manduca sexta to respond to 20-ms pulses of bombykal, the major component of the conspecific pheromonal blend. Isolated pulses of bombykal elicited a burst of activity which decreased exponentially with a time constant of 160–250 ms. Trains of pulses delivered at increasing frequencies (0.5–10 Hz) elicited temporally modulated responses at up to 3 Hz. Concentration of the stimulus (1, 10, 100 ng per odor source) had a marginal effect on the temporal resolution of the receptors. Within a train, the responses to individual pulses remained constant, except for 10-Hz trains (short-term adaptation). A dose-dependent decline of responsiveness was observed during experiments (long-term adaptation). Although individual neurons may not respond faithfully to each pulse of a train, the population of receptors sampled in this study appears to be capable of encoding the onset of odor pulses at frequencies of up to at least 3 Hz.Abbreviations BAL bombykal or (E,Z)-10,12-hexadecadienal - C15 (E,Z)-11,13-pentadecadienal - HAL (E)-2-hexenal - EAG electroantennogram - P1, P2, P3 single stimulus pulses - PSTH peri-stimulus histogram - SC synchronization coefficient - 0.5, 1, 2, 3, 10 Hz stimulus trains     

A ratio model of perceived speed in the human visual system

The perceived speed of moving images changes over time. Prolonged viewing of a pattern (adaptation) leads to an exponential decrease in its perceived speed. Similarly, responses of neurones tuned to motion reduce exponentially over time. It is tempting to link these phenomena. However, under certain conditions, perceived speed increases after adaptation and the time course of these perceptual effects varies widely. We propose a model that comprises two temporally tuned mechanisms whose sensitivities reduce exponentially over time. Perceived speed is taken as the ratio of these filters' outputs. The model captures increases and decreases in perceived speed following adaptation and describes our data well with just four free parameters. Whilst the model captures perceptual time courses that vary widely, parameter estimates for the time constants of the underlying filters are in good agreement with estimates of the time course of adaptation of direction selective neurones in the mammalian visual system.     

A ratio code for vibrotactile pitch

Subjective impressions of pitch for 80 different sinusoidal vibrotactile stimuli delivered to the index finger were measured by free magnitude estimation in four subjects. In three of the subjects, pitch at a given frequency decreased as stimulus amplitude increased. The data of these subjects were well described by a model of pitch based on the relative levels of activation of the three major tactile channels. The main element in this model was a ratio of P channel activity to the sum of the activity levels of the P, NPI, and NPIII channels. Activity levels of the channels were estimated on the basis of the psychophysical literature, including a study of vibrotactile loudness using the same subjects and stimuli as those employed here. A fourth subject, whose pattern of loudness judgments had previously been shown to differ from those of the other subjects, did not conform to this pitch model: her data revealed significant increases in pitch with increases in amplitude, and appear to reflect an inability to combine signals across vibrotactile channels. Pitch changes resulting from vibrotactile adaptation were directionally consistent with our ratio model: pitch was slightly increased by adaptation to a 25 Hz stimulus, and slightly decreased by 200 Hz adaptation.     

Factors contributing to the integration of textural qualities: evidence from virtual surfaces

Two experiments involving indirect touch were carried out to explore the relationships among perceptual dimensions of haptically examined surfaces. Subjects in both experiments used a stylus to evaluate the properties of virtual surfaces created by a force-feedback device; four surface properties (resistance to normal force, coefficient of friction, texture scale, and vibration amplitude) were manipulated in various combinations. In Experiment 1, the extent to which there was a one-to-one relationship between specific stimulus properties and perceptual qualities ("perceptual separability") was evaluated. A substantial failure of separability was demonstrated, with friction tending to be more separable from the other properties than they were from one another. The pattern of results suggests that the amount of measured separability depends crucially on the way stimulus properties are defined (e.g., force versus displacement). In Experiment 2, surfaces with known perceptual properties were used to study the metric(s) of the relevant perceptual space. By specifying the perceptual, rather than the stimulus, coordinates of the surfaces, it was possible to bypass issues of perceptual separability. For surfaces of equal friction, a Euclidean metric captured the results (r(2) = 0.75) more effectively than a city-block metric did; neither metric did well when differences in friction were involved. The fact that-unlike stickiness-hardness, roughness, and perceived vibration intensity are all increasing functions of surface-normal forces may facilitate their integration into a Euclidean space, in both direct and indirect touch.     

Visual contributions to human self-motion perception during horizontal body rotation

It is still an enigma how human subjects combine visual and vestibular inputs for their self-motion perception. Visual cues have the benefit of high spatial resolution but entail the danger of self motion illusions. We performed psychophysical experiments (verbal estimates as well as pointer indications of perceived self-motion in space) in normal subjects (Ns) and patients with loss of vestibular function (Ps). Subjects were presented with horizontal sinusoidal rotations of an optokinetic pattern (OKP) alone (visual stimulus; 0.025-3.2 Hz; displacement amplitude, 8 degrees) or in combinations with rotations of a Bárány chair (vestibular stimulus; 0.025-0.4 Hz; +/- 8 degrees). We found that specific instructions to the subjects created different perceptual states in which their self-motion perception essentially reflected three processing steps during pure visual stimulation: i) When Ns were primed by a procedure based on induced motion and then they estimated perceived self-rotation upon pure optokinetic stimulation (circular vection, CV), the CV has a gain close to unity up to frequencies of almost 0.8 Hz, followed by a sharp decrease at higher frequencies (i.e., characteristics resembling those of the optokinetic reflex, OKR, and of smooth pursuit, SP). ii) When Ns were instructed to "stare through" the optokinetic pattern, CV was absent at high frequency, but increasingly developed as frequency was decreased below 0.1 Hz. iii) When Ns "looked at" the optokinetic pattern (accurately tracked it with their eyes) CV was usually absent, even at low frequency. CV in Ps showed similar dynamics as in Ns in condition i), independently of the instruction. During vestibular stimulation, self-motion perception in Ns fell from a maximum at 0.4 Hz to zero at 0.025 Hz. When vestibular stimulation was combined with visual stimulation while Ns "stared through" OKP, perception at low frequencies became modulated in magnitude. When Ns "looked" at OKP, this modulation was reduced, apart from the synergistic stimulus combination (OKP stationary) where magnitude was similar as during "staring". The obtained gain and phase curves of the perception were incompatible with linear systems prediction. We therefore describe the present findings by a non-linear dynamic model in which the visual input is processed in three steps: i) It shows dynamics similar to those of OKR and SP; ii) it is shaped to complement the vestibular dynamics and is fused with a vestibular signal by linear summation; and iii) it can be suppressed by a visual-vestibular conflict mechanism when the visual scene is moving in space. Finally, an important element of the model is a velocity threshold of about 1.2 degrees/s which is instrumental in maintaining perceptual stability and in explaining the observed dynamics of perception. We conclude from the experimental and theoretical evidence that self-motion perception normally is related to the visual scene as a reference, while the vestibular input is used to check the kinematic state of the scene; if the scene appears to move, the visual signal becomes suppressed and perception is based on the vestibular cue.     

Saccadic Compression of Rectangle and Kanizsa Figures: Now You See It,Now You Don't

Background

Observers misperceive the location of points within a scene as compressed towards the goal of a saccade. However, recent studies suggest that saccadic compression does not occur for discrete elements such as dots when they are perceived as unified objects like a rectangle.

Methodology/Principal Findings

We investigated the magnitude of horizontal vs. vertical compression for Kanizsa figure (a collection of discrete elements unified into single perceptual objects by illusory contours) and control rectangle figures. Participants were presented with Kanizsa and control figures and had to decide whether the horizontal or vertical length of stimulus was longer using the two-alternative force choice method. Our findings show that large but not small Kanizsa figures are perceived as compressed, that such compression is large in the horizontal dimension and small or nil in the vertical dimension. In contrast to recent findings, we found no saccadic compression for control rectangles.

Conclusions

Our data suggest that compression of Kanizsa figure has been overestimated in previous research due to methodological artifacts, and highlight the importance of studying perceptual phenomena by multiple methods.     

Pudendal and median nerve sensory perception threshold: A comparison between normative studies

Background: For the evaluation of sensory innervation, normative data are necessary as a comparison.

Aims: To compare our current perception thresholds (CPTs) with normative data from other research.

Methods: Healthy volunteers were assessed for 2000, 250, and 5?Hz CPTs of the median and pudendal nerve and data were compared with other studies.

Results: Normative data in the studied group n?=?41 (male: 21; female: 20) for the median nerve, 2?kHz, 250?Hz, and 5?Hz were respectively: 241.85?±?67.72 (140–444); 106.27?±?39.12 (45–229); 82.05?±?43.40 (13–271). Pudendal nerve CPTs 250?Hz were: 126.44?±?69.46 (6–333). For men 2?kHz: 349.95?±?125.76 (100–588); 5?Hz: 132.67?±?51.81 (59–249) and women 2?kHz: 226.20?±?119.65 (64–528); 5?Hz: 92.45?±?44.66 (35–215). For the median nerve no statistical differences for gender were shown. For the pudendal nerve, only 250?Hz showed no difference for gender (t-test: 0.516). Comparison of our data with CPTs of other normative data showed no agreement for the pudendal nerve. For the median nerve only 2?kHz showed agreement in three studies and for 5?Hz with one study.

Conclusion: Comparing normative data of multiple studies shows a variety of results and poor agreement. Therefore, referring to normative data of other studies should be handled with caution.     

Natural static magnetic field-induced apoptosis in liver cancer cell

Purpose: To observe the apoptotic effects of NSMF on human hepatoma cells and to investigate the mechanisms. Materials and methods: Human hepatoma cell line Bel-7402 and Hep G-2 were treated by 0.2?T rotary NSMF (30?min/d) with 250?Hz, 400?Hz and 500?Hz for 3?d and 6?d, respectively. Apoptosis was analyzed with flow cytometry. Cell proliferation was measured with XTT assay. Expression of Bcl-2, caspase3/8/9 was analyzed with ELISA. Results: After 6?d treatment, significant apoptosis was induced by 400?Hz in Bel-7402 cells. Slight cell apoptosis was observed at 250?Hz, while Hep G-2 cells exhibited slight apoptosis at 250?Hz and 400?Hz. After 3?d treatment, no apoptosis exhibited in both cell types. Compared with control group, expression of Bcl-2 and Caspase 8 in treated Bel-7402 cells were significantly reduced (p?p?Conclusions: NSMF upregulates caspase 9 and downregulates Bel-2 expression, which results in higher level of active caspase 3 to trigger apoptosis in cells. Different cell types require different NSMF factors like rotary frequency and treatment time to induce apoptosis.     

Hybridization,polyploidy and clonality influence geographic patterns of diversity and salt tolerance in the model halophyte seashore paspalum (Paspalum vaginatum)

In plant species, variation in levels of clonality, ploidy and interspecific hybridization can interact to influence geographic patterns of genetic diversity. These factors commonly vary in plants that specialize on saline habitats (halophytes) and may play a role in how they adapt to salinity variation across their range. One such halophyte is the turfgrass and emerging genomic model system seashore paspalum (Paspalum vaginatum Swartz). To investigate how clonal propagation, ploidy variation, and interspecific hybridization vary across ecotypes and local salinity levels in wild P. vaginatum, we employed genotyping‐by‐sequencing, cpDNA sequencing and flow cytometry in 218 accessions representing > 170 wild collections from throughout the coastal southern United States plus USDA germplasm. We found that the two morphologically distinct ecotypes of P. vaginatum differ in their adaptive strategies. The fine‐textured ecotype is diploid and appears to reproduce in the wild both sexually and by clonal propagation; in contrast, the coarse‐textured ecotype consists largely of clonally‐propagating triploid and diploid genotypes. The coarse‐textured ecotype appears to be derived from hybridization between fine‐textured P. vaginatum and an unidentified Paspalum species. These clonally propagating hybrid genotypes are more broadly distributed than clonal fine‐textured genotypes and may represent a transition to a more generalist adaptive strategy. Additionally, the triploid genotypes vary in whether they carry one or two copies of the P. vaginatum subgenome, indicating multiple evolutionary origins. This variation in subgenome composition shows associations with local ocean salinity levels across the sampled populations and may play a role in local adaptation.     

Dependence of Subjective Traverse Length on Velocity of Moving Tactile Stimuli

Two series of experiments were performed to assess the effects of stimulus velocity on human subjects' perception of the distance traversed by a moving tactile stimulus. In all experiments, constant-velocity stimuli were applied to the dorsal surface of the left forearm; velocities ranging between 1.0 and 256 cm/sec were used. In some experiments the stimuli moved from distal to proximal over the skin, and in others they moved from proximal to distal. The length of skin contacted by the moving stimulus was defined by a plate having an aperture of 4.0 × 0.5 cm.

In the first series of experiments, subjects were required to compare the distance traversed by a test stimulus delivered 2 sec after a standard stimulus, and also to report the on-locus and the off-locus of the brushing stimulus. In the second series of experiments, the subjects rated the perceived distance on the skin using a free-magnitude-estimation procedure. The data from both series of experiments defined the same relationship between stimulus velocity and perceived stimulus distance. More specifically, although the length of skin contacted by the stimulus was the same at all velocities, subjects' estimates of stimulus distance decreased with increasing stimulus velocity. In addition, the function relating estimates of stimulus distance to velocity was flat for velocities between 5 and 20 cm/sec, but possessed an appreciable negative slope at lower and higher velocities.

It is interesting that the plateau of the relationship between perceived stimulus distance and velocity occurred within the range of velocities that human subjects employ to scan textured surfaces; it also corresponded precisely with the range of stimulus velocities at which the directional sensitivity of somatosensory cortical neurons and human subjects is optimal.     

Predicting human perceptual decisions by decoding neuronal information profiles

Perception relies on the response of populations of neurons in sensory cortex. How the response profile of a neuronal population gives rise to perception and perceptual discrimination has been conceptualized in various ways. Here we suggest that neuronal population responses represent information about our environment explicitly as Fisher information (FI), which is a local measure of the variance estimate of the sensory input. We show how this sensory information can be read out and combined to infer from the available information profile which stimulus value is perceived during a fine discrimination task. In particular, we propose that the perceived stimulus corresponds to the stimulus value that leads to the same information for each of the alternative directions, and compare the model prediction to standard models considered in the literature (population vector, maximum likelihood, maximum-a-posteriori Bayesian inference). The models are applied to human performance in a motion discrimination task that induces perceptual misjudgements of a target direction of motion by task irrelevant motion in the spatial surround of the target stimulus (motion repulsion). By using the neurophysiological insight that surround motion suppresses neuronal responses to the target motion in the center, all models predicted the pattern of perceptual misjudgements. The variation of discrimination thresholds (error on the perceived value) was also explained through the changes of the total FI content with varying surround motion directions. The proposed FI decoding scheme incorporates recent neurophysiological evidence from macaque visual cortex showing that perceptual decisions do not rely on the most active neurons, but rather on the most informative neuronal responses. We statistically compare the prediction capability of the FI decoding approach and the standard decoding models. Notably, all models reproduced the variation of the perceived stimulus values for different surrounds, but with different neuronal tuning characteristics underlying perception. Compared to the FI approach the prediction power of the standard models was based on neurons with far wider tuning width and stronger surround suppression. Our study demonstrates that perceptual misjudgements can be based on neuronal populations encoding explicitly the available sensory information, and provides testable neurophysiological predictions on neuronal tuning characteristics underlying human perceptual decisions.     

Temporal gap detection in tactile channels

The ability of observers to detect temporal gaps in bursts of sinusoids or bursts of band-limited noise was measured to assess the temporal acuity of Pacinian (P) and non-Pacinian (NP) tactile information processing channels. The P channel was isolated by delivering high frequency sinusoids or high frequency noise through a large 1.5-cm² contactor to the thenar eminence. The NP channels were isolated from the P channel by delivering these stimuli as well as stimuli with lower frequencies through a small 0.01-cm² contactor to the same site. Gap detection thresholds were higher for gaps in noise than for gaps in sinusoids but did not differ among conditions designed to isolate P and NP channels. The finding that temporal acuity does not differ among channels supports the hypothesis that, after termination of a stimulus, the P and NP channels exhibit the same amount of neural persistence. Also consistent with this hypothesis are the earlier findings that the enhancement of the sensation magnitude of a stimulus by a prior stimulus (Verrillo and Gescheider, Percept Psychophys 18: 128–136, 1975) and the duration of sensation after the termination of a stimulus (Gescheider et al., J Acoust Soc Am 91: 1690–1696, 1992) are independent of stimulus frequency. One important implication of this hypothesis, if true, is that the presence of temporal summation in the P channel and its absence in the NP channels, results, not from the lack of neural persistence in the NP channels, but instead, in marked contrast to the P channel, from the lack of a mechanism for integrating persistent neural activity over time.     

Spatial summation in the tactile sensory system: Probability summation and neural integration

Psychophysical thresholds for the detection of a 300-Hz burst of vibration applied to the thenar eminence were measured for stimuli applied to the skin through 1.5?cm² and through 0.05?cm² contactors. Thresholds were approximately 13?dB lower when the area of the contactor was 1.5?cm² than when it was 0.05?cm². The difference between the thresholds measured with the large and small contactors was significantly reduced when only the lowest thresholds obtained in the testing sessions were considered. This result supports the hypothesis that one component of spatial summation in the P channel is probability summation. In addition, threshold measurements within a session were less variable when measured with the 1.5?cm² contactor. We conclude that spatial summation in the P channel is a joint function of two processes that occur as the areal extent of the stimulus increases: probability summation in which the probability of exceeding the psychophysical detection threshold increases as the number of receptors of varying sensitivities increases, and neural integration in which neural activity originating from separate receptors is combined within the central nervous system rendering the channel more sensitive to the stimulus.     

Plant gene responses to frequency-specific sound signals

We identified a set of sound-responsive genes in plants using a sound-treated subtractive library and demonstrated sound regulation through mRNA expression analyses. Under both light and dark conditions, sound up-regulated expression of rbcS and ald. These are also light-responsive genes and these results suggest that sound could represent an alternative to light as a gene regulator. Ald mRNA expression increased significantly with treatment at 125 and 250 Hz, whereas levels decreased significantly with treatment at 50 Hz, indicating a frequency-specific response. To investigate whether the ald promoter responds to sound, we generated transgenic rice plants harboring a chimeric gene comprising a fusion of the ald promoter and GUS reporter. In three independent transgenic lines treated with 50 or 250 Hz for 4 h, GUS mRNA expression was up-regulated at 250 Hz, but down-regulated at 50 Hz. Thus, the sound-responsive mRNA expression pattern observed for the ald promoter correlated closely with that of ald, suggesting that the 1,506 bp ald promoter is sound-responsive. Therefore, we propose that in transgenic plants, specific frequencies of sound treatment could be used to regulate the expression of any gene fused to the ald promoter.     

Evidence Accumulation in the Magnitude System

Perceptual interferences in the estimation of quantities (time, space and numbers) have been interpreted as evidence for a common magnitude system. However, if duration estimation has appears sensitive to spatial and numerical interferences, space and number estimation tend to be resilient to temporal manipulations. These observations question the relative contribution of each quantity in the elaboration of a representation in a common mental metric. Here, we elaborated a task in which perceptual evidence accumulated over time for all tested quantities (space, time and number) in order to match the natural requirement for building a duration percept. For this, we used a bisection task. Experimental trials consisted of dynamic dots of different sizes appearing progressively on the screen. Participants were asked to judge the duration, the cumulative surface or the number of dots in the display while the two non-target dimensions varied independently. In a prospective experiment, participants were informed before the trial which dimension was the target; in a retrospective experiment, participants had to attend to all dimensions and were informed only after a given trial which dimension was the target. Surprisingly, we found that duration was resilient to spatial and numerical interferences whereas space and number estimation were affected by time. Specifically, and counter-intuitively, results revealed that longer durations lead to smaller number and space estimates whether participants knew before (prospectively) or after (retrospectively) a given trial which quantity they had to estimate. Altogether, our results support a magnitude system in which perceptual evidence for time, space and numbers integrate following Bayesian cue-combination rules.     

Perceptual organization as nested control

It is argued here that perceptual organization is the structuring of environmental stimuli into nested structures of control. This view is derived from our proposal that the perceptual system forces any stimulus set to have the algebraic structure G of a machine, and that G is given a specific factorization sequence, G=G ₁ ·G ₂ · ... ·G _n , induced by dynamical systems criteria which the organism imposes on the environment.An investigation into these factorization sequences reveals that any such sequence is split into two subsequences, one structuring the way in which the stimulus set can change under external action, and the other describing the way in which the set is perceived as internally generated. An examination of the nested control structure of the latter yields a theory of grouping. The external and internal sequences are shown to be strongly related to each other in that the symmetry axes of the internal sequence are eigenspaces of the most stable subgroup factors of the external sequence. It is claimed that cartesian reference frames are subsequences of the full sequences. Using these principles, a unified theory is offered of several apparently quite separate perceptual areas; e.g. Marr-Nishihara shape perception, gestalt grouping, the orientation-and-form problem, and motion perception.The final claim is that planning hierarchies have the same dynamically-structured algebraic sequences and therefore that the study of perceptual organization should, in a very deep sense, be formally equivalent to the study of planning.