The human arm as a redundant manipulator: The control of path and joint angles

The movements studied involved moving the tip of a pointer attached to the hand from a given starting point to a given end point in a horizontal plane. Three joints--the shoulder, elbow and wrist--were free to move. Thus the system represented a redundant manipulator. The coordination of the movements of the three joints was recorded and analyzed. The study concerned how the joints are controlled during a movement. The results are used to evaluate several current hypotheses for motor control. Basically, the incremental changes are calculated so as to move the tip of the manipulator along a straight line in the workspace. The values of the individual joints seem to be determined as follows. Starting from the initial values the incremental changes in the three joint angles represent a compromise between two criteria: 1) the amount of the angular change should be about the same in the three joints, and 2) the angular changes should minimize the total cost of the arm position as determined by cost functions defined for each joint as a function of angle. By itself, this mechanism would produce strongly curved trajectories in joint space which could include additional acceleration and deceleration in a joint. These are reduced by the influence of a third criterion which fits with the mass-spring hypothesis. Thus the path is calculated as a compromise between a straight line in workspace and a straight line in joint space. The latter can produce curved paths in the workspace such as were actually found in the experiments. A model calculation shows that these hypotheses can qualitatively describe the experimental findings.     

Computational model of motor learning and perceptual change

Motor learning in the context of arm reaching movements has been frequently investigated using the paradigm of force-field learning. It has been recently shown that changes to somatosensory perception are likewise associated with motor learning. Changes in perceptual function may be the reason that when the perturbation is removed following motor learning, the hand trajectory does not return to a straight line path even after several dozen trials. To explain the computational mechanisms that produce these characteristics, we propose a motor control and learning scheme using a simplified two-link system in the horizontal plane: We represent learning as the adjustment of desired joint-angular trajectories so as to achieve the reference trajectory of the hand. The convergence of the actual hand movement to the reference trajectory is proved by using a Lyapunov-like lemma, and the result is confirmed using computer simulations. The model assumes that changes in the desired hand trajectory influence the perception of hand position and this in turn affects movement control. Our computer simulations support the idea that perceptual change may come as a result of adjustments to movement planning with motor learning.     

Homing in fiddler crabs (Uca lactea annulipes and Uca vomeris : Ocypodidae)

Fiddler crabs emerge from burrows on intertidal sand- and mudflats to feed during low tide. In the species studied here (Uca lactea annulipes, Uca vomeris) a crab normally wanders no more than about 1 m away from its burrow and, when frightened, dashes back along a straight line to take cover. Feeding crabs tend to move sideways, without changing orientation, along paths radiating from the burrow. When they move along circumferential paths they adjust their orientation so that one side continues to point towards the burrow. The crabs do not need to see the burrow in order to stay aligned with the home vector, and they are not misled by a dummy hole close to their own burrow unless they have come to within about 10 cm of it. The home runs of crabs end within a few centimeters of a burrow that is covered with a sheet of sandpaper and then give way to search runs, centred upon a position slightly short of the burrow location. Feeding crabs can be displaced on sandpapers and their subsequent home runs end at a position where the burrow would be, had there been no displacement. Landmarks close to the burrow do not influence the home runs of displaced crabs. Crabs that are rotated on a sheet of sandpaper, counter-turn to keep their original orientation constant. Fiddler crabs thus employ path integration with external compass information and close range visual guidance for homing. Accepted: 11 May 1998     

Dissociable Perceptual Effects of Visual Adaptation

Neurons in the visual cortex are responsive to the presentation of oriented and curved line segments, which are thought to act as primitives for the visual processing of shapes and objects. Prolonged adaptation to such stimuli gives rise to two related perceptual effects: a slow change in the appearance of the adapting stimulus (perceptual drift), and the distortion of subsequently presented test stimuli (adaptational aftereffects). Here we used a psychophysical nulling technique to dissociate and quantify these two classical observations in order to examine their underlying mechanisms and their relationship to one another. In agreement with previous work, we found that during adaptation horizontal and vertical straight lines serve as attractors for perceived orientation and curvature. However, the rate of perceptual drift for different stimuli was not predictive of the corresponding aftereffect magnitudes, indicating that the two perceptual effects are governed by distinct neural processes. Finally, the rate of perceptual drift for curved line segments did not depend on the spatial scale of the stimulus, suggesting that its mechanisms lie outside strictly retinotopic processing stages. These findings provide new evidence that the visual system relies on statistically salient intrinsic reference stimuli for the processing of visual patterns, and point to perceptual drift as an experimental window for studying the mechanisms of visual perception.     

A Unified Model of Heading and Path Perception in Primate MSTd

Self-motion, steering, and obstacle avoidance during navigation in the real world require humans to travel along curved paths. Many perceptual models have been proposed that focus on heading, which specifies the direction of travel along straight paths, but not on path curvature, which humans accurately perceive and is critical to everyday locomotion. In primates, including humans, dorsal medial superior temporal area (MSTd) has been implicated in heading perception. However, the majority of MSTd neurons respond optimally to spiral patterns, rather than to the radial expansion patterns associated with heading. No existing theory of curved path perception explains the neural mechanisms by which humans accurately assess path and no functional role for spiral-tuned cells has yet been proposed. Here we present a computational model that demonstrates how the continuum of observed cells (radial to circular) in MSTd can simultaneously code curvature and heading across the neural population. Curvature is encoded through the spirality of the most active cell, and heading is encoded through the visuotopic location of the center of the most active cell''s receptive field. Model curvature and heading errors fit those made by humans. Our model challenges the view that the function of MSTd is heading estimation, based on our analysis we claim that it is primarily concerned with trajectory estimation and the simultaneous representation of both curvature and heading. In our model, temporal dynamics afford time-history in the neural representation of optic flow, which may modulate its structure. This has far-reaching implications for the interpretation of studies that assume that optic flow is, and should be, represented as an instantaneous vector field. Our results suggest that spiral motion patterns that emerge in spatio-temporal optic flow are essential for guiding self-motion along complex trajectories, and that cells in MSTd are specifically tuned to extract complex trajectory estimation from flow.     

DNA methylation can enhance or induce DNA curvature.

Oligomers of different palindromic sequences (EcoRI, BamHI, and ClaI linkers) were ligated to form distributions of multimers. These long ligation ladders were methylated using corresponding methylases. The migration of the unmethylated as well as the methylated multimer distributions was analysed in 10% polyacrylamide gels. The migration anomaly of these sequences is interpreted in terms of the curvature of the DNA helix axis. The double-stranded oligomer dCGGAATTCCG is considerably curved in its unmodified form. Its curvature is strongly enhanced when the central dAs are methylated. This result is predicted by a model for DNA curvature. Multimers of the closely related sequence dCGGGATCCCG are straight. When methylated at the central dAs or at the most central dCs, a small curvature of the helix axis is induced. The double-stranded oligomer dCCATCGATGG is straight in its unmodified form as well as when it is methylated. Thus, DNA curvature can be induced or enhanced by methylation. However, DNA methylation at palindromic sequences seems not always to influence the linear path of the DNA helix axis.     

Audiovisual integration: an investigation of the "streaming-bouncing" phenomenon

Temporal aspects of the perceptual integration of audiovisual information were investigated by utilizing the visual "streaming-bouncing" phenomenon. When two identical visual objects move towards each other, coincide, and then move away from each other, the objects can either be seen as streaming past one another or bouncing off each other. Although the streaming percept is dominant, the bouncing percept can be induced by presenting an auditory stimulus during the visual coincidence of the moving objects. Here we show that the bounce-inducing effect of the auditory stimulus is paramount when its onset and offset occur in temporal proximity of the onset and offset of the period of visual coincidence of the moving objects. When the duration of the auditory stimulus exceeded this period, visual bouncing disappears. Implications for a temporal window of audiovisual integration and the design of effective audiovisual warning signals are discussed.     

Strategic Escape Direction: Orientation,Turning, and Escape Trajectories of Zebra‐Tailed Lizards (Callisaurus draconoides)

A prey's body orientation relative to a predator's approach path may affect risk of fleeing straight ahead. Consequently, prey often turn before fleeing. Relationships among orientation, turn, and escape angles and between these angles and predation risk have not been studied in terrestrial vertebrates and have rarely been studied in the field. Escape angles are expected to lead away from predators and be highly variable to avoid being predictable by predators. Using approach speed as a risk factor, we studied these issues in the zebra‐tailed lizard, Callisaurus draconoides. Lizards fled away from human simulated predators, but most did not flee straight away. Escape angles were variable, as expected under the unpredictability hypothesis, and had modes at nearly straight away (i.e., 0°) and nearly perpendicular to the predator's approach path (90°). The straight away mode suggests maximal distancing from the predator; the other mode suggests maintaining ability to monitor the predator or possibly an influence of habitat features such as obstacles and refuges that differ among directions. Turn angles were larger when orientation was more toward the predator, and escape angles were closer to straight away when turn angles were larger. Turning serves to reach a favorable fleeing direction. When orientation angle was more toward the predator, escape angle was unaffected, suggesting that turn angle compensates completely for increased risk of orientation toward the predator. When approached more rapidly, lizards fled more nearly straight away, as expected under greater predation risk. Turn angles were unrelated to approach speed.     

Moving muscle points provide accurate curved muscle paths in a model of the cervical spine

Muscle paths in musculoskeletal models have been modeled using several different methods; however, deformation of soft tissue with changes in posture is rarely accounted for, and often only the neutral posture is used to define a muscle path. The objective of this study was to model curved muscle paths in the cervical spine that take into consideration soft tissue deformation with changes in neck posture. Two subject-specific models were created from magnetic resonance images (MRI) in 5 different sagittal plane neck postures. Curved paths of flexor and extensor muscles were modeled using piecewise linear lines-of-action in two ways; (1) using fixed via points determined from muscle paths in the neutral posture and (2) using moving muscle points that moved relative to the bones determined from muscle paths in all 5 postures. Accuracy of each curved modeled muscle path was evaluated by an error metric, the distance from the anatomic (centroid) muscle path determined from the MRI. Error metric was compared among three modeled muscle path types (straight, fixed via and moving muscle point) using a repeated measures one-way ANOVA (α=0.05). Moving muscle point paths had 21% lower error metric than fixed via point paths over all 15 pairs of neck muscles examined over 5 postures (3.86 mm vs. 4.88 mm). This study highlights the importance of defining muscle paths in multiple postures in order to properly define the changing curvature of a muscle path due to soft tissue deformation with posture.     

Modulation of the reaction rate of regulating protein induces large morphological and motional change of amoebic cell

Morphologies of moving amoebae are categorized into two types. One is the "neutrophil" type in which the long axis of cell roughly coincides with its moving direction. This type of cell extends a leading edge at the front and retracts a narrow tail at the rear, whose shape has been often drawn as a typical amoeba in textbooks. The other one is the "keratocyte" type with widespread lamellipodia along the front side arc. Short axis of cell in this type roughly coincides with its moving direction. In order to understand what kind of molecular feature causes conversion between two types of morphologies, and how two typical morphologies are maintained, a mathematical model of amoebic cells is developed. This model describes movement of cell and intracellular reactions of activator, inhibitor and actin filaments in a unified way. It is found that the producing rate of activator is a key factor of conversion between two types. This model also explains the observed data that the keratocyte type cells tend to rapidly move along a straight line. The neutrophil type cells move along a straight line when the moving velocity is small, but they show fluctuated motions deviating from a line when they move as fast as the keratocyte type cells. Efficient energy consumption in the neutrophil type cells is predicted.     

Multiple Manifold Clustering Using Curvature Constrained Path

The problem of multiple surface clustering is a challenging task, particularly when the surfaces intersect. Available methods such as Isomap fail to capture the true shape of the surface near by the intersection and result in incorrect clustering. The Isomap algorithm uses shortest path between points. The main draw back of the shortest path algorithm is due to the lack of curvature constrained where causes to have a path between points on different surfaces. In this paper we tackle this problem by imposing a curvature constraint to the shortest path algorithm used in Isomap. The algorithm chooses several landmark nodes at random and then checks whether there is a curvature constrained path between each landmark node and every other node in the neighborhood graph. We build a binary feature vector for each point where each entry represents the connectivity of that point to a particular landmark. Then the binary feature vectors could be used as a input of conventional clustering algorithm such as hierarchical clustering. We apply our method to simulated and some real datasets and show, it performs comparably to the best methods such as K-manifold and spectral multi-manifold clustering.     

Grasping preparation enhances orientation change detection

Preparing a goal directed movement often requires detailed analysis of our environment. When picking up an object, its orientation, size and relative distance are relevant parameters when preparing a successful grasp. It would therefore be beneficial if the motor system is able to influence early perception such that information processing needs for action control are met at the earliest possible stage. However, only a few studies reported (indirect) evidence for action-induced visual perception improvements. We therefore aimed to provide direct evidence for a feature-specific perceptual modulation during the planning phase of a grasping action. Human subjects were instructed to either grasp or point to a bar while simultaneously performing an orientation discrimination task. The bar could slightly change its orientation during grasping preparation. By analyzing discrimination response probabilities, we found increased perceptual sensitivity to orientation changes when subjects were instructed to grasp the bar, rather than point to it. As a control experiment, the same experiment was repeated using bar luminance changes, a feature that is not relevant for either grasping or pointing. Here, no differences in visual sensitivity between grasping and pointing were found. The present results constitute first direct evidence for increased perceptual sensitivity to a visual feature that is relevant for a certain skeletomotor act during the movement preparation phase. We speculate that such action-induced perception improvements are controlled by neuronal feedback mechanisms from cortical motor planning areas to early visual cortex, similar to what was recently established for spatial perception improvements shortly before eye movements.     

Paradoxical Interaction between Ocular Activity,Perception, and Decision Confidence at the Threshold of Vision

In humans and some other species perceptual decision-making is complemented by the ability to make confidence judgements about the certainty of sensory evidence. While both forms of decision process have been studied empirically, the precise relationship between them remains poorly understood. We performed an experiment that combined a perceptual decision-making task (identifying the category of a faint visual stimulus) with a confidence-judgement task (wagering on the accuracy of each perceptual decision). The visual stimulation paradigm required steady fixation, so we used eye-tracking to control for stray eye movements. Our data analyses revealed an unexpected and counterintuitive interaction between the steadiness of fixation (prior to and during stimulation), perceptual decision making, and post-decision wagering: greater variability in gaze direction during fixation was associated with significantly increased visual-perceptual sensitivity, but significantly decreased reliability of confidence judgements. The latter effect could not be explained by a simple change in overall confidence (i.e. a criterion artifact), but rather was tied to a change in the degree to which high wagers predicted correct decisions (i.e. the sensitivity of the confidence judgement). We found no evidence of a differential change in pupil diameter that could account for the effect and thus our results are consistent with fixational eye movements being the relevant covariate. However, we note that small changes in pupil diameter can sometimes cause artefactual fluctuations in measured gaze direction and this possibility could not be fully ruled out. In either case, our results suggest that perceptual decisions and confidence judgements can be processed independently and point toward a new avenue of research into the relationship between them.     

How Moving Backgrounds Influence Interception

Reaching movements towards an object are continuously guided by visual information about the target and the arm. Such guidance increases precision and allows one to adjust the movement if the target unexpectedly moves. On-going arm movements are also influenced by motion in the surrounding. Fast responses to motion in the surrounding could help cope with moving obstacles and with the consequences of changes in one’s eye orientation and vantage point. To further evaluate how motion in the surrounding influences interceptive movements we asked subjects to tap a moving target when it reached a second, static target. We varied the direction and location of motion in the surrounding, as well as details of the stimuli that are known to influence eye movements. Subjects were most sensitive to motion in the background when such motion was near the targets. Whether or not the eyes were moving, and the direction of the background motion in relation to the direction in which the eyes were moving, had very little influence on the response to the background motion. We conclude that the responses to background motion are driven by motion near the target rather than by a global analysis of the optic flow and its relation with other information about self-motion.     

Discrimination Contours for Moving Sounds Reveal Duration and Distance Cues Dominate Auditory Speed Perception

Evidence that the auditory system contains specialised motion detectors is mixed. Many psychophysical studies confound speed cues with distance and duration cues and present sound sources that do not appear to move in external space. Here we use the ‘discrimination contours’ technique to probe the probabilistic combination of speed, distance and duration for stimuli moving in a horizontal arc around the listener in virtual auditory space. The technique produces a set of motion discrimination thresholds that define a contour in the distance-duration plane for different combination of the three cues, based on a 3-interval oddity task. The orientation of the contour (typically elliptical in shape) reveals which cue or combination of cues dominates. If the auditory system contains specialised motion detectors, stimuli moving over different distances and durations but defining the same speed should be more difficult to discriminate. The resulting discrimination contours should therefore be oriented obliquely along iso-speed lines within the distance-duration plane. However, we found that over a wide range of speeds, distances and durations, the ellipses aligned with distance-duration axes and were stretched vertically, suggesting that listeners were most sensitive to duration. A second experiment showed that listeners were able to make speed judgements when distance and duration cues were degraded by noise, but that performance was worse. Our results therefore suggest that speed is not a primary cue to motion in the auditory system, but that listeners are able to use speed to make discrimination judgements when distance and duration cues are unreliable.     

Animal navigation: general properties of directed walks

The ability to locomote is a defining characteristic of all animals. Yet, all but the most trivial forms of navigation are poorly understood. Here we report and discuss the analytical results of an in-depth study of a simple navigation problem. In principle, there are two strategies for navigating a straight course. One is to use an external directional reference and to continually reorient with reference to it. The other is to monitor body rotations from internal sensory information only. We showed previously that, at least for simple representations of locomotion, the first strategy will enable an animal or mobile agent to move arbitrarily far away from its starting point, but the second strategy will not do so, even after an infinite number of steps. This paper extends and generalizes the earlier results by demonstrating that these findings are true even when a very general model of locomotion is used. In this general model, error components within individual steps are not independent, and directional errors may be biased. In the absence of a compass, the expected path of a directed walk in general approximates a logarithmic spiral. Some examples are given to illustrate potential applications of the quantitative results derived here. Motivated by the analytical results developed in this work, a nomenclature for directed walks is proposed and discussed. Issues related to path integration in mammals and robots, and measuring the curvature of a noisy path are also addressed using directed walk theory.     

Neuronal activity and its links with the perception of multi-stable figures

In order to isolate the neuronal activity that relates to the making of perceptual decisions, we have made use of a perceptually ambiguous motion stimulus. This stimulus lies on the boundary between two perceptual categories that correspond to clockwise and counter-clockwise rotation of a three-dimensional figure. It consists of a two-dimensional pattern of moving dots that are capable of generating these two, distinct, three-dimensional percepts. We have studied the responses of neurons in cortical area V5/MT whilst macaque monkeys report judgements about the perceptual configuration of this stimulus. We extract a quantitative statistic called 'choice probability' that expresses the covariation of neuronal activity and perceptual choice. An analysis of choice probabilities shows that the pool of neurons involved in the perceptual decisions is a tightly constrained subset of the population of sensory neurons relevant to the perceptual task.     

Aggregation as an antipredator strategy in the rock-paper-scissors model

We study a nonhierarchical tritrophic system, whose predator-prey interactions are described by the rock-paper-scissors game rules. In our stochastic simulations, individuals may move strategically towards the direction with more conspecifics to form clumps instead of moving aimlessly on the lattice. Considering that the conditioning to move gregariously depends on the organism's physical and cognitive abilities, we introduce a maximum distance an individual can perceive the environment and a minimum conditioning level to perform the gregarious movement. We investigate the pattern formation and compute the average size of the single-species spatial domains emerging from the grouping behaviour. The results reveal that the defence tactic reduces the predation risk significantly, being more profitable if individuals perceive further distances, thus creating bigger groups. Our outcomes show that the species with more conditioned organisms dominate the cyclic spatial game, controlling most of the territory. On the other hand, the species with fewer individuals ready to perform aggregation strategy gives its predator the chance to fill the more significant fraction of the grid. The spatial interactions assumed in our numerical experiments constitute a data set that may help biologists and data scientists understand how local interactions influence ecosystem dynamics.     

Walking Paths to and from a Goal Differ: On the Role of Bearing Angle in the Formation of Human Locomotion Paths

The path that humans take while walking to a goal is the result of a cognitive process modulated by the perception of the environment and physiological constraints. The path shape and timing implicitly embeds aspects of the architecture behind this process. Here, locomotion paths were investigated during a simple task of walking to and from a goal, by looking at the evolution of the position of the human on a horizontal (x,y) plane. We found that the path while walking to a goal was not the same as that while returning from it. Forward-return paths were systematically separated by 0.5-1.9m, or about 5% of the goal distance. We show that this path separation occurs as a consequence of anticipating the desired body orientation at the goal while keeping the target in view. The magnitude of this separation was strongly influenced by the bearing angle (difference between body orientation and angle to goal) and the final orientation imposed at the goal. This phenomenon highlights the impact of a trade-off between a directional perceptual apparatus—eyes in the head on the shoulders—and and physiological limitations, in the formation of human locomotion paths. Our results give an insight into the influence of environmental and perceptual variables on human locomotion and provide a basis for further mathematical study of these mechanisms.