Influence of Correspondence Noise and Spatial Scaling on the Upper Limit for Spatial Displacement in Fully-Coherent Random-Dot Kinematogram Stimuli

Correspondence noise is a major factor limiting direction discrimination performance in random-dot kinematograms [1]. In the current study we investigated the influence of correspondence noise on Dmax, which is the upper limit for the spatial displacement of the dots for which coherent motion is still perceived. Human direction discrimination performance was measured, using 2-frame kinematograms having leftward/rightward motion, over a 200-fold range of dot-densities and a four-fold range of dot displacements. From this data Dmax was estimated for the different dot densities tested. A model was proposed to evaluate the correspondence noise in the stimulus. This model summed the outputs of a set of elementary Reichardt-type local detectors that had receptive fields tiling the stimulus and were tuned to the two directions of motion in the stimulus. A key assumption of the model was that the local detectors would have the radius of their catchment areas scaled with the displacement that they were tuned to detect; the scaling factor k linking the radius to the displacement was the only free parameter in the model and a single value of k was used to fit all of the psychophysical data collected. This minimal, correspondence-noise based model was able to account for 91% of the variability in the human performance across all of the conditions tested. The results highlight the importance of correspondence noise in constraining the largest displacement that can be detected.     

Learned changes in the complexity of movement organization during multijoint, standing pulls

 This paper tests the hypothesis that the central nervous system (CNS) learns to organize multijoint movements during a multijoint ‘bouncing pull’ task such that, after practice, motion of the anterior-posterior center of mass (CM_AP) more closely resembles that of a conservative, one degree of freedom (DF), inverted pendulum model. The task requires standing human subjects to produce precise peak pulling forces on a handle while maintaining balance – goals that can be easily accomplished if movement is organized as in the model. Ten freely standing subjects practiced making brief, bouncing pulls in the horizontal direction to target forces (20–80% of maximum) for 5 days. Pulling force, body kinematic and force plate data were recorded. An eight-segment analysis determined sagittal-plane CM motion. We compared the effects of practice on the regression-based fit between actual and model-simulated CM_AP trajectories, and on measures of CM_AP phase plane symmetry and parameter constancy that the model predicts. If the CNS learns to organize movements like the inverted pendulum model, then model fit should improve and all other measures should approach zero after practice. The fit between modeled and actual CM_AP motion did not improve significantly with practice, except for moderate force pulls. Nor did practice increase phase plane symmetry or parameter constancy. Specifically, practice did not decrease the differences between the pre-impact and rebound positions or speeds of the CM_AP, although speed difference increased with pulling force. CM_AP at the end of the movement was anterior to its initial position; the anterior shift increased after practice. Differences between the pre-pull and balance-recovery ankle torque (T _A) impulses were greater on day 5 and correlated with the anterior shift in CM_AP. These results suggest that practice separately influenced the force production and balance recovery phases. A modified model with damping could not explain the observed behaviors. A modified model using the actual time-varying T_A profiles improved fit at lower force levels, but did not explain the increased postural shift after practice. We conclude that the CNS does not learn to organize movements like the conservative, inverted pendulum model, but rather learned a more complex form of organization that capitalized on more time-varying controls and more intersegmental dynamics. We hypothesize that at least one additional DF and at least one time-varying parameter will be needed to explain fully how the CNS learns to organize multijoint, bouncing pulls made while standing. Received: 9 January 1997 / Accepted in revised form: 27 May 1997     

Propagation of photon noise and information transfer in visual motion detection

The extraction of the direction of motion from the time varying retinal images is one of the most basic tasks any visual system is confronted with. However, retinal images are severely corrupted by photon noise, in particular at low light levels, thus limiting the performance of motion detection mechanisms of what sort so ever. Here, we study how photon noise propagates through an array of Reichardt-type motion detectors that are commonly believed to underlie fly motion vision. We provide closed-form analytical expressions of the signal and noise spectra at the output of such a motion detector array. We find that Reichardt detectors reveal favorable noise suppression in the frequency range where most of the signal power resides. Most notably, due to inherent adaptive properties, the transmitted information about stimulus velocity remains nearly constant over a large range of velocity entropies. Action editor: Matthew Wiener     

Relative phase dynamics in perturbed interlimb coordination: stability and stochasticity

 Various stability features of bimanual rhythmic coordination, including phase transitions, have been modeled successfully by means of a one-dimensional equation of motion for relative phase obeying a gradient dynamics, the Haken-Kelso-Bunz model. The present study aimed at assessing pattern stability for stationary performance and estimating the model parameters (a, b, and Q) for the stochastic extension of this model. Estimates of a and b allowed for reconstruction of the potential defining the gradient dynamics. Two coordination patterns between the forearms (in-phase, anti-phase) were performed at seven different frequencies. Model parameters were estimated on the basis of an exponential decay parameter describing the relaxation behavior of continuous relative phase following a mechanical perturbation. Variability of relative phase and relaxation time provided measures of pattern stability. Although the predicted inverse relation between pattern stability and movement frequency was observed for the lower tempo conditions, it was absent for the higher tempos, reflecting the influence of task constraints. No statistically significant differences in stability were observed between the two coordination modes, indicating the influence of intention. The reconstructed potential reflected the observed stability features, underscoring the adequacy of the parameter estimations. The relaxation process could not be captured adequately by means of a simple exponential decay function but required an additional oscillatory term. In accordance with previous assumptions, noise strength Q did not vary as a function of movement frequency. However, systematic differences in Q were observed between the two coordination modes. The advantages and (potential) pitfalls of using stationary performance of single patterns to examine the stability features of a bistable potential were discussed. Received: 12 July 1999 / Accepted in revised form: 14 April 2000     

Analysis and implementation of a neural extended Kalman filter for target tracking

Having a better motion model in the state estimator is one way to improve target tracking performance. Since the motion model of the target is not known a priori, either robust modeling techniques or adaptive modeling techniques are required. The neural extended Kalman filter is a technique that learns unmodeled dynamics while performing state estimation in the feedback loop of a control system. This coupled system performs the standard estimation of the states of the plant while estimating a function to approximate the difference between the given state-coupling function model and the behavior of the true plant dynamics. At each sample step, this new model is added to the existing model to improve the state estimate. The neural extended Kalman filter has also been investigated as a target tracking estimation routine. Implementation issues for this adaptive modeling technique, including neural network training parameters, were investigated and an analysis was made of the quality of performance that the technique can have for tracking maneuvering targets.     

Threshold fatigue and information transfer

Neurons in vivo must process sensory information in the presence of significant noise. It is thus plausible to assume that neural systems have developed mechanisms to reduce this noise. Theoretical studies have shown that threshold fatigue (i.e. cumulative increases in the threshold during repetitive firing) could lead to noise reduction at certain frequencies bands and thus improved signal transmission as well as noise increases and decreased signal transmission at other frequencies: a phenomenon called noise shaping. There is, however, no experimental evidence that threshold fatigue actually occurs and, if so, that it will actually lead to noise shaping. We analyzed action potential threshold variability in intracellular recordings in vivo from pyramidal neurons in weakly electric fish and found experimental evidence for threshold fatigue: an increase in instantaneous firing rate was on average accompanied by an increase in action potential threshold. We show that, with a minor modification, the standard Hodgkin–Huxley model can reproduce this phenomenon. We next compared the performance of models with and without threshold fatigue. Our results show that threshold fatigue will lead to a more regular spike train as well as robustness to intrinsic noise via noise shaping. We finally show that the increased/reduced noise levels due to threshold fatigue correspond to decreased/increased information transmission at different frequencies. Action Editor: David Golomb     

POLLEN CAPTURE AND WIND-INDUCED MOVEMENT OF COMPACT AND DIFFUSE GRASS PANICLES: IMPLICATIONS FOR POLLINATION EFFICIENCY

The motion induced by wind of Setaria geniculate (Lam.) Beauv. and Agrostis hiemalis (Walt.) B.S.P. panicles is shown to have harmonic characteristics that can influence pollination. During each cycle of its motion, the panicle of S. geniculata repeats a sequence of reorientations to the direction of ambient airflow. This repetition is correlated with a reiteration of airflow patterns through which airborne pollen grains must pass to reach floral surfaces. The panicle decelerates as it moves toward either of the two extreme positions of its oscillatory motion. The decelerations introduce a bias in the time the panicle spends in each of its orientations. This bias generates “preferred orientations” to the direction of ambient airflow which in turn results in biasing the aerodynamics of pollen capture. Similar phenomena are reported for the panicle of A. hiemalis, although a more complex pattern of oscillatory motion is observed. The reciprocity between the mechanics of oscillatory motion and the aerodynamics of pollen capture is shown to have deterministic properties which may surface above the “noise” produced by other, stochastic features influencing wind pollination.     

A neural network model of speech acquisition and motor equivalent speech production

This article describes a neural network model that addresses the acquisition of speaking skills by infants and subsequent motor equivalent production of speech sounds. The model learns two mappings during a babbling phase. A phonetic-to-orosensory mapping specifies a vocal tract target for each speech sound; these targets take the form of convex regions in orosensory coordinates defining the shape of the vocal tract. The babbling process wherein these convex region targets are formed explains how an infant can learn phoneme-specific and language-specific limits on acceptable variability of articulator movements. The model also learns an orosensory-to-articulatory mapping wherein cells coding desired movement directions in orosensory space learn articulator movements that achieve these orosensory movement directions. The resulting mapping provides a natural explanation for the formation of coordinative structures. This mapping also makes efficient use of redundancy in the articulator system, thereby providing the model with motor equivalent capabilities. Simulations verify the model's ability to compensate for constraints or perturbations applied to the articulators automatically and without new learning and to explain contextual variability seen in human speech production.Supported in part by AFOSR F49620-92-J-0499     

Finding motion parameters from spherical motion fields (or the advantages of having eyes in the back of your head)

A theory is developed for determining the motion of an observer given the motion field over a full 360 degree image sphere. The method is based on the fact that for an observer translating without rotation, the projected circular motion field about any equator can be divided into disjoint semicircles of clockwise and counterclockwise flow, and on the observation that the effects of rotation decouple around the three equators defining the three principal axes of rotation. Since the effect of rotation is geometrical, the three rotational parameters can be determined independently by searching, in each case, for a rotational value for which the derotated equatorial motion field can be partitioned into 180 degree arcs of clockwise and counterclockwise flow. The direction of translation is also obtained from this analysis. This search is two dimensional in the motion parameters, and can be performed relatively efficiently. Because information is correlated over large distances, the method can be considered a pattern recognition rather than a numerical algorithm. The algorithm is shown to be robust and relatively insensitive to noise and to missing data. Both theoretical and empirical studies of the error sensitivity are presented. The theoretical analysis shows that for white noise of bounded magnitude M, the expected errors is at worst linearly proportional to M. Empirical tests demonstrate negligible error for perturbations of up to 20% in the input, and errors of less than 20% for perturbations of up to 200%.     

A Bayesian model of stereopsis depth and motion direction discrimination

 The extraction of stereoscopic depth from retinal disparity, and motion direction from two-frame kinematograms, requires the solution of a correspondence problem. In previous psychophysical work [Read and Eagle (2000) Vision Res 40: 3345–3358], we compared the performance of the human stereopsis and motion systems with correlated and anti-correlated stimuli. We found that, although the two systems performed similarly for narrow-band stimuli, broad-band anti-correlated kinematograms produced a strong perception of reversed motion, whereas the stereograms appeared merely rivalrous. I now model these psychophysical data with a computational model of the correspondence problem based on the known properties of visual cortical cells. Noisy retinal images are filtered through a set of Fourier channels tuned to different spatial frequencies and orientations. Within each channel, a Bayesian analysis incorporating a prior preference for small disparities is used to assess the probability of each possible match. Finally, information from the different channels is combined to arrive at a judgement of stimulus disparity. Each model system – stereopsis and motion – has two free parameters: the amount of noise they are subject to, and the strength of their preference for small disparities. By adjusting these parameters independently for each system, qualitative matches are produced to psychophysical data, for both correlated and anti-correlated stimuli, across a range of spatial frequency and orientation bandwidths. The motion model is found to require much higher noise levels and a weaker preference for small disparities. This makes the motion model more tolerant of poor-quality reverse-direction false matches encountered with anti-correlated stimuli, matching the strong perception of reversed motion that humans experience with these stimuli. In contrast, the lower noise level and tighter prior preference used with the stereopsis model means that it performs close to chance with anti-correlated stimuli, in accordance with human psychophysics. Thus, the key features of the experimental data can be reproduced assuming that the motion system experiences more effective noise than the stereoscopy system and imposes a less stringent preference for small disparities. Received: 2 March 2001 / Accepted in revised form: 5 July 2001     

Pattern-recognition by an artificial network derived from biologic neuronal systems

A novel artificial neural network, derived from neurobiological observations, is described and examples of its performance are presented. This DYnamically STable Associative Learning (DYSTAL) network associatively learns both correlations and anticorrelations, and can be configured to classify or restore patterns with only a change in the number of output units. DYSTAL exhibits some particularly desirable properties: computational effort scales linearly with the number of connections, i.e., it is0(N) in complexity; performance of the network is stable with respect to network parameters over wide ranges of their values and over the size of the input field; storage of a very large number of patterns is possible; patterns need not be orthogonal; network connections are not restricted to multi-layer feed-forward or any other specific structure; and, for a known set of deterministic input patterns, the network weights can be computed, a priori, in closed form. The network has been associatively trained to perform the XOR function as well as other classification tasks. The network has also been trained to restore patterns obscured by binary or analog noise. Neither global nor local feedback connections are required during learning; hence the network is particularly suitable for hardware (VLSI) implementation.     

Variation in Avian Vocalizations during the Non‐Breeding Season in Response to Traffic Noise

Low‐frequency traffic noise that leads to acoustic masking of vocalizations may cause birds to alter the frequencies or other components of their vocalizations in order to be heard by conspecifics and others. Altering parts of a vocalization may result in poorer vocal performance or the message contained in the vocalization being received incorrectly. During the winters of 2011–2012 and 2012–2013, we recorded and measured the ‘chick‐a‐dee’ call of Black‐capped Chickadees (Poecile atricapillus) and the ‘po‐ta‐to‐chip’ call of American Goldfinches (Spinus tristis) to determine whether components of the calls produced in areas of high traffic noise and low traffic noise differed in any way. We found that both chickadee and goldfinch calls had higher minimum frequencies in areas with high traffic‐noise than in low traffic‐noise areas. The maximum frequencies showed no differences in either species' calls. This suggests that chickadees and goldfinches alter the part of their calls that are acoustically masked by traffic noise in effort to better transmit the vocalization. These differences suggest that increasing anthropogenic noise may influence avian communication and that noise management should be included in conservation planning.     

Electrical noise from lipid bilayer membranes in the presence of hydrophobic ions

Summary In the presence of the hydrophobic ion dipicrylamine, lipid bilayer membranes exhibit a characteristic type of noise spectrum which is different from other forms of noise described so far. The spectral density of current noise measured at zero voltage increases in proportion to the square of frequency at low frequencies and becomes constant at high frequencies. The observed form of the noise spectrum can be interpreted on the basis of a transport model for hydrophobic ions in which it is assumed that the ions are adsorbed in potential-energy minima at either membrane surface and are able to cross the central energy barrier by thermal activation. Accordingly, current-noise results from random fluctuations in the number of ions jumping over the barrier from right to left and from left to right. On the basis of this model the rate constantk _i for the translocation of the hydrophobic ion across the barrier, as well as the mean surface concentrationN _t of adsorbed ions may be caluculated from the observed spectral intensity of current noise. The values ofk _i obtained in this way closely agree with the results of previous relaxation experiments. A similar, although less quantitative, agreement is also found for the surface concentrationN _t .     

Image motion environments: background noise for movement-based animal signals

Understanding the evolution of animal signals has to include consideration of the structure of signal and noise, and the sensory mechanisms that detect the signals. Considerable progress has been made in understanding sounds and colour signals, however, the degree to which movement-based signals are constrained by the particular patterns of environmental image motion is poorly understood. Here we have quantified the image motion generated by wind-blown plants at 12 sites in the coastal habitat of the Australian lizard Amphibolurus muricatus. Sampling across different plant communities and meteorological conditions revealed distinct image motion environments. At all locations, image motion became more directional and apparent speed increased as wind speeds increased. The magnitude of these changes and the spatial distribution of image motion, however, varied between locations probably as a function of plant structure and the topographic location. In addition, we show that the background motion noise depends strongly on the particular depth-structure of the environment and argue that such microhabitat differences suggest specific strategies to preserve signal efficacy. Movement-based signals and motion processing mechanisms, therefore, may reveal the same type of habitat specific structural variation that we see for signals from other modalities.     

A study of bacterial flagellar bundling

Certain bacteria, such as Escherichia coli (E. coli) and Salmonella typhimurium (S. typhimurium), use multiple flagella often concentrated at one end of their bodies to induce locomotion. Each flagellum is formed in a left-handed helix and has a motor at the base that rotates the flagellum in a corkscrew motion.We present a computational model of the flagellar motion and their hydrodynamic interaction. The model is based on the equations of Stokes flow to describe the fluid motion. The elasticity of the flagella is modeled with a network of elastic springs while the motor is represented by a torque at the base of each flagellum. The fluid velocity due to the forces is described by regularized Stokeslets and the velocity due to the torques by the associated regularized rotlets. Their expressions are derived. The model is used to analyze the swimming motion of a single flagellum and of a group of three flagella in close proximity to one another. When all flagellar motors rotate counterclockwise, the hydrodynamic interaction can lead to bundling. We present an analysis of the flow surrounding the flagella. When at least one of the motors changes its direction of rotation, the same initial conditions lead to a tumbling behavior characterized by the separation of the flagella, changes in their orientation, and no net swimming motion. The analysis of the flow provides some intuition for these processes.     

Influence of light,water motion,and stocking density on the growth and pigment content of Halymenia durvillei (Rhodophyceae) under laboratory conditions

The tropical red seaweed Halymenia durvillei Bory de Saint Vincent is a potential source of the high-value pigments, r-phycoerythrin (RPE) and r-phycocyanin (RPC). The unique properties of these pigments find many applications—from food to cosmetics, pharmaceuticals, and biomedical research. This study aimed to improve the land-based culture technology of H. durvillei by determining the appropriate combination of light, water motion, and stocking density that would result in high growth performance and high RPE and RPC content. Combinations of two light levels (full light, 100% and reduced light, 67%), two water motion levels (low and moderate), and three stocking densities (50, 100, and 200 g) were studied using 64.5-L glass tanks with flow-through seawater and aeration systems at the outdoor land-based seaweed nursery in Bolinao, Pangasinan, Philippines. After 6 weeks of culture, growth performance (growth rate and productivity) of H. durvillei and phycobiliprotein content were best under a combination of full light (100%), moderate water motion, and 50-g stocking density. The generally low light regime during the experimental period, which coincided with the cold, dry season characterized by shorter days and overcast skies, may have influenced H. durvillei to maximize the use of available resources such as light and possible increased nutrient availability from water motion to promote growth and phycobiliprotein synthesis. Treatments with low stocking densities generally showed satisfactory growth and phycobiliprotein content. This study provides groundwork for future research into mechanisms by which these and other factors affect the growth and physiology of H. durvillei in culture.

     

A unified probabilistic model of the perception of three-dimensional structure from optic flow

Human observers can perceive the three- dimensional (3-D) structure of their environment using various cues, an important one of which is optic flow. The motion of any point’s projection on the retina depends both on the point’s movement in space and on its distance from the eye. Therefore, retinal motion can be used to extract the 3-D structure of the environment and the shape of objects, in a process known as structure-from-motion (SFM). However, because many combinations of 3-D structure and motion can lead to the same optic flow, SFM is an ill-posed inverse problem. The rigidity hypothesis is a constraint supposed to formally solve the SFM problem and to account for human performance. Recently, however, a number of psychophysical results, with both moving and stationary human observers, have shown that the rigidity hypothesis alone cannot account for human performance in SFM tasks, but no model is known to account for the new results. Here, we construct a Bayesian model of SFM based mainly on one new hypothesis, that of stationarity, coupled with the rigidity hypothesis. The predictions of the model, calculated using a new and powerful methodology called Bayesian programming, account for a wide variety of experimental findings.     

Parametric analysis of dynamic postural responses

A detailed theoretical understanding of postural control mechanisms must be preceded by careful quantification of both the deterministic and stochastic aspects of postural behavior of normal and abnormal subjects under various dynamic conditions. Toward this end, concise parametric transfer function plus noise models were derived for both shoulder and waist position data obtained by applying a linear anteriorposterior bandlimited pseudorandom disturbance to the base of support of human subjects. Model orders as well as model parameters were determined empirically. One advantage of this modeling procedure is the conciseness of the postural models, permitting easy statistical analysis of the data obtained under different dynamic conditions from many subjects. Model features, including pole and zero locations, from 6 normal subjects each tested on 5 consecutive days under 3 input amplitudes and eyes open and closed conditions are presented. The resulting transfer function models consist of only 1 or 2 poles near the integration position on the Z plane unit circle and 0 to 2 zeros. Locations of the poles indicate that the eyes closed responses are more oscillatory, less damped, and with higher gains than the eyes open responses. These transfer functions are similar to nonparametric ones of other authors. The noise model orders are also small. Their spectra are those of low pass systems. Also, the quantity and frequency range of the postural noise is positively related to the amplitude of platform motion as well as related to the presence or absence of vision. Present address: Kresge Hearing Research Institute, University of Michigan Medical School, 1301 E. Ann St., Ann Arbor, MI 48109, USA     

Model selection and parameter estimation for ion channel recordings with an application to the K + outward-rectifier in barley leaf

We present a statistical method, and its accompanying algorithms, for the selection of a mathematical model of the gating mechanism of an ion channel and for the estimation of the parameters of this model. The method assumes a hidden Markov model that incorporates filtering, colored noise and state-dependent white excess noise for the recorded data. The model selection and parameter estimation are performed via a Bayesian approach using Markov chain Monte Carlo. The method is illustrated by its application to single-channel recordings of the K⁺ outward-rectifier in barley leaf.Acknowledgement The authors thank Sake Vogelzang, Bert van Duijn and Bert de Boer for their helpful advice and useful comments and suggestions.