What is white?

To shed light on the perceptual basis of the color white, we measured settings of unique white in a dark surround. We find that settings reliably show more variability in an oblique (blue-yellow) direction in color space than along the cardinal axes of the cone-opponent mechanisms. This is against the idea that white perception arises at the null point of the cone-opponent mechanisms, but one alternative possibility is that it occurs through calibration to the visual environment. We found that the locus of maximum variability in settings lies close to the locus of natural daylights, suggesting that variability may result from uncertainty about the color of the illuminant. We tested this by manipulating uncertainty. First, we altered the extent to which the task was absolute (requiring knowledge of the illumination) or relative. We found no clear effect of this factor on the reduction in sensitivity in the blue-yellow direction. Second, we provided a white surround as a cue to the illumination or left the surround dark. Sensitivity was selectively worse in the blue-yellow direction when the surround was black than when it was white. Our results can be functionally related to the statistics of natural images, where a greater blue-yellow dispersion is characteristic of both reflectances (where anisotropy is weak) and illuminants (where it is very pronounced). Mechanistically, the results could suggest a neural signal responsive to deviations from the blue-yellow locus or an adaptively matched range of contrast response functions for signals that encode different directions in color space.

Passive hinge forces in the feeding apparatus of Aplysia aid retraction during biting but not during swallowing.

Swallowing and biting responses in the marine mollusk Aplysia are both mediated by a cyclical alternation of protraction and retraction movements of the grasping structure, the radula and underlying odontophore, within the feeding apparatus of the animal, the buccal mass. In vivo observations demonstrate that Aplysia biting is associated with strong protractions and rapid initial retractions, whereas Aplysia swallowing is associated with weaker protractions and slower initial retractions. During biting, the musculature joining the radula/odontophore to the buccal mass (termed the "hinge") is stretched more than in swallowing. To test the hypothesis that stretch of the hinge might contribute to rapid retractions observed in biting, we analyzed the hinge's passive properties. During biting, the hinge is stretched sufficiently to assist retraction. In contrast, during swallowing, the hinge is not stretched sufficiently for its passive forces to assist retraction, because the odontophore's anterior movement is smaller than during biting. A quantitative model demonstrated that steady-state passive forces were sufficient to generate the retraction movements observed during biting. Experimental measures of the relative magnitude of the hinge's active and passive forces at the protraction displacements of biting suggest that passive forces are at least a third of the total force.

Pre-exposure to contrast selectively compresses the achromatic half-axes of color space.

The gamut of perceived colors can be represented in a space with bright-dark, red-green and blue-yellow axes. Pre-exposure to a field that changes periodically over time in luminance or along one of the color axes reduces vividness of colors along the entire axis [Webster and Mollon (1991) Nature, 349, 235-238]. But is it possible to reduce vividness or perceived contrast selectively for half-axes in color space? We assessed such selective compression of the bright-dark axis using a task where subjects matched tests in a pre-adapted region to ones in an un-adapted region. Tests were bright or dark pinstripes on a gray background, and pre-exposure was to multiple drifting pinstripes. Matches made after pre-exposure indicate a combination of symmetric and asymmetric compression, with more compression when adapting and test stimulus were similar in contrast polarity.

Analysis of a distributed model of leg coordination. I. Individual coordination mechanisms.

Using tools from discrete dynamical systems theory, we begin a systematic analysis of a distributed model of leg coordination with both biological and robotic applications. In this paper, we clarify the role of individual coordination mechanisms by studying a system of two leg oscillators coupled in one direction by each of the three major mechanisms that have been described for the stick insect Carausius morosus. For each mechanism, we derive analytical return maps, and analyze the behavior of these return maps under iteration in order to determine the asymptotic phase relationship between the two legs. We also derive asymptotic relative phase densities for each mechanism and compare these densities to those obtained from numerical simulations of the model. Our analysis demonstrates that, although each of these mechanisms can individually compress a range of initial conditions into a narrow band of relative phase, this asymptotic relative phase relationship is, in general, only neutrally stable. We also show that the nonlinear dependence of relative phase on walking speed along the body in the full hexapod model can be explained by our analysis. Finally, we provide detailed parameter charts of the range of behavior that each mechanism can produce as coupling strength and walking speed are varied.

Evolution and analysis of model CPGs for walking: I. Dynamical modules.

Can one develop an abstract description of the dynamics of pattern generators that provides quantitative insight into their operation? We explored this question by examining the dynamics of a model central pattern generator that was created using an evolutionary algorithm. We propose an abstract description based on the concept of a dynamical module, a set of neurons that simultaneously make their transitions from one quasistable state to another while the synaptic inputs that they receive from other neurons remain essentially constant, thus temporarily reducing the dimensionality of the circuit dynamics. Using the mathematical tools of dynamical systems theory, we describe a method for identifying dynamical modules and demonstrate that this concept can be used to quantitatively characterize constraints on neural architecture, account for phase durations, and predict the effects of parameter changes. Moreover, this abstract description reveals coordinated parameter changes that leave the overall circuit dynamics essentially unchanged. In a companion article we employ this abstract description to examine the relationship between general principles and individual variability in large populations of evolved model pattern generators.

Evolution and analysis of model CPGs for walking: II. General principles and individual variability.

Are there general principles for pattern generation? We examined this question by analyzing the operation of large populations of evolved model central pattern generators (CPGs) for walking. Three populations of model CPGs were evolved, containing three, four, or five neurons. We identified six general principles. First, locomotion performance increased with the number of interneurons. Second, the top 10 three-, four-, and five-neuron CPGs could be decomposed into dynamical modules, an abstract description developed in a companion article. Third, these dynamical modules were multistable: they could be switched between multiple stable output configurations. Fourth, the rhythmic pattern generated by a CPG could be understood as a closed chain of successive destabilizations of one dynamical module by another. A combinatorial analysis enumerated the possible dynamical modular structures. Fifth, one-dimensional modules were frequently observed and, in some cases, could be assigned specific functional roles. Finally, dynamic dynamical modules, in which the modular structure itself changed over one cycle, were frequently observed. The existence of these general principles despite significant variability in both patterns of connectivity and neural parameters was explained by degeneracy in the maps from neural parameters to neural dynamics to behavior to fitness. An analysis of the biomechanical properties of the model body was essential for relating neural activity to behavior. Our studies of evolved model circuits suggest that, in the absence of other constraints, there is no compelling reason to expect neural circuits to be functionally decomposable as the number of interneurons increase. Analyzing idealized model pattern generators may be an effective methodology for gaining insights into the operation of biological pattern generators.

Biorobotic approaches to the study of motor systems.

Biorobotics is a promising new area of research at the interface between biology and robotics. Robots can either be used as physical models of biological systems or be directly inspired by biological studies. A great deal of progress has recently been made in biorobotic studies of locomotion, orientation, and vertebrate arm control.

The brain has a body: adaptive behavior emerges from interactions of nervous system, body and environment.

Studies of mechanisms of adaptive behavior generally focus on neurons and circuits. But adaptive behavior also depends on interactions among the nervous system, body and environment: sensory preprocessing and motor post-processing filter inputs to and outputs from the nervous system; co-evolution and co-development of nervous system and periphery create matching and complementarity between them; body structure creates constraints and opportunities for neural control; and continuous feedback between nervous system, body and environment are essential for normal behavior. This broader view of adaptive behavior has been a major underpinning of ecological psychology and has influenced behavior-based robotics. Computational neuroethology, which jointly models neural control and periphery of animals, is a promising methodology for understanding adaptive behavior.

Simulation of adaptive behavior.

Behaviors as diverse as swimming, withdrawal, escape, locomotion and feeding have been simulated using neuroethological and neurophysiological data obtained from a variety of animals. These simulations are providing new insights into the neural circuitry that generates adaptive behavior, as well as new ideas for the design of artificial autonomous devices.