Saccadic eye movements minimize the consequences of motor noise

The durations and trajectories of our saccadic eye movements are remarkably stereotyped. We have no voluntary control over these properties but they are determined by the movement amplitude and, to a smaller extent, also by the movement direction and initial eye orientation. Here we show that the stereotyped durations and trajectories are optimal for minimizing the variability in saccade endpoints that is caused by motor noise. The optimal duration can be understood from the nature of the motor noise, which is a combination of signal-dependent noise favoring long durations, and constant noise, which prefers short durations. The different durations of horizontal vs. vertical and of centripetal vs. centrifugal saccades, and the somewhat surprising properties of saccades in oblique directions are also accurately predicted by the principle of minimizing movement variability. The simple and sensible principle of minimizing the consequences of motor noise thus explains the full stereotypy of saccadic eye movements. This suggests that saccades are so stereotyped because that is the best strategy to minimize movement errors for an open-loop motor system.     

A two dimensional model for saccade generation

A model for the generation of oblique saccades is constructed by extending and modifying the one dimensional local feedback model. It is proposed that the visual system stores target location in inertial coordinates, but that the feedback loop which guides saccades works in retinotopic coordinates. To achieve straight trajectories for centripetal and centrifugal saccades in all meridians, a comparator computes motor error as a vector and uses the vectorial error signal to drive two orthogonally-acting burst generators. The generation of straight saccade trajectories when the extraocular muscles are of unequal strengths requires the introduction of a burst-tonic cell input to motor neurons. The model accounts for the results of two-site stimulation of the superior colliculus and frontal eye fields by allowing simultaneous activation of more than one comparator. The postulated existence of multiple comparators suggests that motor error may be computed topographically.     

How inconsistency between attitude and behavior persists through cultural transmission

Individuals tend to conform their behavior to that of the majority. Consequently, an individual's behavior is not always consistent with his or her attitude, and such inconsistency sometimes causes mental distress. Understanding the mechanism of sustaining inconsistency between attitude and behavior is a challenging problem from the viewpoint of evolutionary theory. We constructed an evolutionary game theory model in which each player has an attitude and behavior toward a single social norm, and the players' attitudes and behaviors are affected by three types of cultural transmission: vertical, oblique, and horizontal. We assumed that strategy is a combination of attitude and behavior and that the process of learning or transmitting the social norm depends on the life stage of each player. Adults play a coordination game in which players whose behaviors match those of the majority obtain a high payoff, which is diminished by any inconsistency between attitude and behavior. The adults' strategies are passed to newborns via vertical transmission, and the frequency of a newborn's replication of strategy is proportional to the corresponding adult's payoff. Newborns imitate behaviors of unrelated adults via oblique transmission. Juveniles change their attitudes or behaviors by observing other juveniles' behaviors or inferring other juveniles' attitudes (horizontal transmission). We conclude that the key factor for sustaining inconsistency between attitude and behavior is the ability of players to infer and imitate others' attitudes, and that oblique transmission promotes inconsistency.     

A correction for axis misalignment in the joint angle curves representing knee movement in gait analysis

This paper derives a simple mathematical model relating changes in the orientations of the two Cartesian coordinate systems involved in recording knee movement and the varus-valgus and the internal-external rotation angles for describing the knee's motion. Rotation matrices are given for changing the orientations of the two Cartesian coordinate systems in such a way that the quadratic variations in the varus-valgus and in the external-internal angles are minimal. These estimated rotation matrices are used to correct for axis misalignment. The correction is calibrated by considering the impact of the new orientation of the thigh Cartesian coordinate system on the hip joint angles. The procedure is applied to kinematic data collected on normal subjects. The uncertainty about the specification of the thigh Cartesian coordinate system is shown to explain some of the between subject variability in the varus-valgus and in the internal-external rotation angles curves.     

Anisotropies in peripheral vernier acuity

Vernier acuity for short horizontal, vertical and oblique target lines was measured in many locations in the periphery of the visual field in normal human observers. In the 10 deg periphery, the average alignment threshold with oblique vernier lines in eight locations for three observers was 2.29 times higher than that with vertical and horizontal target lines. This oblique effect was found everywhere in the visual field. Similar conclusions are drawn for configurations in which the lines were replaced by just their distal endpoints, but here, additionally, performance was distinctly better when the dot pair was collinear with the fixation point, i.e. oriented radially, than when it was oriented tangentially. Both for vernier lines and for dot pairs, in all observers, horizontal configurations showed somewhat better thresholds than vertical ones. These results suggest an inherent pattern of connectivity throughout the visual field favoring processing in the cardinal orientations over the obliques, the radial over the tangential and, to a limited extent, the horizontal over the vertical.     

Tests of Models for Saccade–Vergence Interaction using Novel Stimulus Conditions

During natural activities, two types of eye movements - saccades and vergence - are used in concert to point the fovea of each eye at features of interest. Some electrophysiological studies support the concept of independent neurobiological substrates for saccades and vergence, namely saccadic and vergence burst neurons. Discerning the interaction of these two components is complicated by the near-synchronous occurrence of saccadic and vergence components. However, by positioning the far target below the near target, it is possible to induce responses in which the peak velocity of the vertical saccadic component precedes the peak velocity of the horizontal vergence component by approximately 75 ms. When saccade-vergence responses are temporally dissociated in this way, the vergence velocity waveform changes, becoming less skewed. We excluded the possibility that such change in skewing was due to visual feedback by showing that similar behavior occurred in darkness. We then tested a saccade-related vergence burst neuron (SVBN) model proposed by Zee et al. in J Neurophysiol 68:1624-1641 (1992), in which omnipause neurons remove inhibition from both saccadic and vergence burst neurons. The technique of parameter estimation was used to calculate optimal values for responses from human subjects in which saccadic and convergence components of response were either nearly synchronized or temporally dissociated. Although the SVBN model could account for convergence waveforms when saccadic and vergence components were nearly synchronized, it could not when the components were temporally dissociated. We modified the model so that the saccadic pulse changed the parameter values of the convergence burst units if both components were synchronized. The modified model accounted for velocity waveforms of both synchronous and dissociated convergence movements. We conclude that both the saccadic pulse and omnipause neuron inhibition influence the generation of vergence movements when they are made synchronously with saccades.     

Contrast sensitivity functions to stimuli defined in Cartesian, polar and hyperbolic coordinates

Recent electrophysiological studies indicate that cells in the LGN, V1, V2, and V4 areas in monkeys are specifically sensitive to Cartesian, polar and hyperbolic stimuli. We have characterized the contrast sensitivity functions (CSF) to stimuli defined in these coordinates with the two-alternatives forced-choice paradigm. CSFs to Cartesian, concentric, and hyperbolic stimuli have had similar shapes, with peak sensitivity at approximately 3 c/deg. However, the Cartesian CSF peak sensitivity has been at least 0.1 log units higher than that to stimuli in any other coordinate system. The concentric-Bessel CSF has a low-pass shape, peaking at 1.5 c/deg or below. The radial CSF has a bell shape with maximum sensitivity at 8 c/360 degrees. Only the concentric-Bessel CSF could be explained in terms of the components of maximum amplitude of the Fourier transform. Neural models, which in previous studies predicted the responses to Cartesian and polar Glass patterns, failed to account for the full CSFs data.     

Asymmetry of the latent periods of saccades in human depending on visual space complicity

Saccadic latencies of visually-guided saccades of 10 right-handed subjects with right-leading eyes were studied. Stimulation paradigm was spatially bidimentional, and stimuli were shown along horizontal and vertical meridians. Three traditional single step GAP - NO DELAY - OVERLAP temporal paradigms were used. In the first experiment, each paradigm was applied separately (simple visual space). In the second experiment, all the three paradigms were varied pseudo-random order and equiprobably, which complicated the time parameters of visual stimulation (complicated visual space). Asymmetry of visually-guided saccades along the vertical and horizontal meridians was revealed. The character of this asymmetry varied between subjects. MANOVA showed that the factor of visual space complicity (simple or complicated visual space) affected the latent period of saccades to a greater extent than the factor of stimulus lateralization (stimulus presentation in the left/right or upper/lower visual hemifields).     

Parametric-equation representation of biconcave erythrocytes

The representation of the shape of a biconcave erythrocyte by a set of three parametric equations was achieved by using the expressions that transform the curvilinear coordinates from the disc-cyclide coordinate system [denoted J2R; Moon and Spencer (1988), Field Theory Handbook, Springer-Verlag, Berlin] to Cartesian coordinates. The equations are products of elliptic functions, so the challenge was to relate the three major ’shape-defining’ measurements of the human erythrocyte in Cartesian coordinates to three parameters in the new curvilinear coordinates, to give a realistic representation of the shape of the membrane-surface. The relationships between the coefficients of the Cartesian degree-4 surface that describes the discocyte and the coordinate transformation equations were derived with the aid of Mathematica; and the membrane-surface of the cell was drawn using the ParametricPlot3D function in this ‘package’. By having the erythrocyte shape expressed in its new form it is readily amenable to further transformations that might be used to model those changes in shape that are seen when the cells are immersed in media of various osmolalities, or when they change metabolic ’states’. On the other hand, the relationship between the coefficients of the Cartesian expression for the disc-cyclide surface is relevant to image analysis of erythrocytes, as determined by physical methods that rely on Cartesian imaging ’slices’. These methods include confocal microscopy and various nuclear magnetic resonance microimaging procedures.     

Social learning among Congo Basin hunter-gatherers

This paper explores childhood social learning among Aka and Bofi hunter-gatherers in Central Africa. Existing literature suggests that hunter-gatherer social learning is primarily vertical (parent-to-child) and that teaching is rare. We use behavioural observations, open-ended and semi-structured interviews, and informal and anecdotal observations to examine the modes (e.g. vertical versus horizontal/oblique) and processes (e.g. teaching versus observation and imitation) of cultural transmission. Cultural and demographic contexts of social learning associated with the modes and processes of cultural transmission are described. Hunter-gatherer social learning occurred early, was relatively rapid, primarily vertical under age 5 and oblique and horizontal between the ages of 6 and 12. Pedagogy and other forms of teaching existed as early as 12 months of age, but were relatively infrequent by comparison to other processes of social learning such as observation and imitation.     

A computational model of visual anisotropy

Visual anisotropy has been demonstrated in multiple tasks where performance differs between vertical, horizontal, and oblique orientations of the stimuli. We explain some principles of visual anisotropy by anisotropic smoothing, which is based on a variation on Koenderink's approach in [1]. We tested the theory by presenting gaussian elongated luminance profiles and measuring the perceived orientations by means of an adjustment task. Our framework is based on the smoothing of the image with elliptical gaussian kernels and it correctly predicted an illusory orientation bias towards the vertical axis. We discuss the scope of the theory in the context of other anisotropies in perception.     

Eye Movements in Ephedrone-Induced Parkinsonism

Patients with ephedrone parkinsonism (EP) show a complex, rapidly progressive, irreversible, and levodopa non-responsive parkinsonian and dystonic syndrome due to manganese intoxication. Eye movements may help to differentiate parkinsonian syndromes providing insights into which brain networks are affected in the underlying disease, but they have never been systematically studied in EP. Horizontal and vertical eye movements were recorded in 28 EP and compared to 21 Parkinson''s disease (PD) patients, and 27 age- and gender-matched healthy subjects using standardized oculomotor tasks with infrared videooculography. EP patients showed slow and hypometric horizontal saccades, an increased occurrence of square wave jerks, long latencies of vertical antisaccades, a high error rate in the horizontal antisaccade task, and made more errors than controls when pro- and antisaccades were mixed. Based on oculomotor performance, a direct differentiation between EP and PD was possible only by the velocity of horizontal saccades. All remaining metrics were similar between both patient groups. EP patients present extensive oculomotor disturbances probably due to manganese-induced damage to the basal ganglia, reflecting their role in oculomotor system.     

The evolutionary language game: an orthogonal approach

Evolutionary game dynamics have been proposed as a mathematical framework for the cultural evolution of language and more specifically the evolution of vocabulary. This article discusses a model that is mutually exclusive in its underlying principals with some previously suggested models. The model describes how individuals in a population culturally acquire a vocabulary by actively participating in the acquisition process instead of passively observing and communicate through peer-to-peer interactions instead of vertical parent-offspring relations. Concretely, a notion of social/cultural learning called the naming game is first abstracted using learning theory. This abstraction defines the required cultural transmission mechanism for an evolutionary process. Second, the derived transmission system is expressed in terms of the well-known selection-mutation model defined in the context of evolutionary dynamics. In this way, the analogy between social learning and evolution at the level of meaning-word associations is made explicit. Although only horizontal and oblique transmission structures will be considered, extensions to vertical structures over different genetic generations can easily be incorporated. We provide a number of simplified experiments to clarify our reasoning.     

Bilateral Symmetry Detection on the Basis of Scale Invariant Feature Transform

The automatic detection of bilateral symmetry is a challenging task in computer vision and pattern recognition. This paper presents an approach for the detection of bilateral symmetry in digital single object images. Our method relies on the extraction of Scale Invariant Feature Transform (SIFT) based feature points, which serves as the basis for the ascertainment of the centroid of the object; the latter being the origin under the Cartesian coordinate system to be converted to the polar coordinate system in order to facilitate the selection symmetric coordinate pairs. This is followed by comparing the gradient magnitude and orientation of the corresponding points to evaluate the amount of symmetry exhibited by each pair of points. The experimental results show that our approach draw the symmetry line accurately, provided that the observed centroid point is true.     

The saccadic and neurological deficits in type 3 Gaucher disease

Our objective was to characterize the saccadic eye movements in patients with type 3 Gaucher disease (chronic neuronopathic) in relationship to neurological and neurophysiological abnormalities. For approximately 4 years, we prospectively followed a cohort of 15 patients with Gaucher type 3, ages 8-28 years, by measuring saccadic eye movements using the scleral search coil method. We found that patients with type 3 Gaucher disease had a significantly higher regression slope of duration vs amplitude and peak duration vs amplitude compared to healthy controls for both horizontal and vertical saccades. Saccadic latency was significantly increased for horizontal saccades only. Downward saccades were more affected than upward saccades. Saccade abnormalities increased over time in some patients reflecting the slowly progressive nature of the disease. Phase plane plots showed individually characteristic patterns of abnormal saccade trajectories. Oculo-manual dexterity scores on the Purdue Pegboard test were low in virtually all patients, even in those with normal cognitive function. Vertical saccade peak duration vs amplitude slope significantly correlated with IQ and with the performance on the Purdue Pegboard but not with the brainstem and somatosensory evoked potentials. We conclude that, in patients with Gaucher disease type 3, saccadic eye movements and oculo-manual dexterity are representative neurological functions for longitudinal studies and can probably be used as endpoints for therapeutic clinical trials. TRIAL REGISTRATION: ClinicalTrials.gov NCT00001289.     

Encoding mechanisms for sensory neurons studied with a multielectrode array in the cat dorsal root ganglion

Recent advances in microelectrode array technology now permit a direct examination of the way populations of sensory neurons encode information about a limb's position in space. To address this issue, we recorded nerve impulses from about 100 single units simultaneously in the L6 and L7 dorsal root ganglia (DRG) of the anesthetized cat. Movement sensors, placed near the hip, knee, ankle, and foot, recorded passive movements of the cat's limb while it was moved pseudo-randomly. The firing rate of the neurons was correlated with the position of the limb in various coordinate systems. The firing rates were less correlated to the position of the foot in Cartesian coordinates (x, y) than in joint angular coordinates (hip, knee, ankle), or in polar coordinates. A model was developed in which position and its derivatives are encoded linearly, followed by a nonlinear spike-generating process. Adding the nonlinear portion significantly increased the correlations in all coordinate systems, and the full models were able to accurately predict the firing rates of various types of sensory neurons. The observed residual variability is captured by a simple stochastic model. Our results suggest that compact encoding models for primary afferents recorded at the DRG are well represented in polar coordinates, as has previously been suggested for the cortical and spinal representation of movement. This study illustrates how sensory receptors encode a sense of limb position, and it provides a general framework for modeling sensory encoding by populations of neurons.     

Collinear effects on 3-Gabor alignment as a function of spacing, orientation and detectability.

Our ability to align three Gabor patches depends upon their internal carrier orientation; we are better at aligning vertical or horizontal patches than oblique patches (Keeble and Hess, 1998). However, the tuning of alignment to patch orientation has not studied in detail. We measured the alignment of a vertical target with reference patches varying in orientation and found it tuned to vertical (collinear) patches at centre-to-centre separation of three carrier periods, with a steep increase for oblique references and slight downturn for horizontal (orthogonal) references. Next, we increased separation between the patches, testing collinear, side-by-side, orthogonal and oblique configurations. Surprisingly, we found that the tuning for collinear patches was preserved. All ten observers tested had lower alignment thresholds for collinear patches. This effect extended to an inter-patch separation of 10 carrier periods (20 envelope standard deviations). Additionally, we measured contrast detection thresholds for the reference patches using the same stimuli. The collinear facilitation of alignment was even greater than the collinear facilitation of detection.     

THE EVOLUTION OF VIRULENCE IN PATHOGENS WITH VERTICAL AND HORIZONTAL TRANSMISSION

The idea that vertical transmission of parasites selects for lower virulence is widely accepted. However, little theoretical work has considered the evolution of virulence for parasites with mixed horizontal plus vertical transmission. Many human, animal, and plant parasites are transmitted both vertically and horizontally, and some horizontal transmission is generally necessary to maintain parasites at all. We present a population-dynamical model for the evolution of virulence when both vertical and horizontal transmission are present. In the simplest such model, up to two infectious strains can coexist within one host population. Virulent, vertically transmitted pathogens can persist in a population when they provide protection against more virulent, horizontally transmitted strains. When virulence is maintained by a correlation with horizontal transmission rates, increased levels of vertical transmission always lower the evolutionarily stable (ESS) level of virulence. Contrary to existing theory, however, increases in opportunities for horizontal transmission also lower the ESS level of virulence. We explain these findings in light of earlier work and confirm them in simulations including imperfect vertical transmission. We describe further simulations, in which both vertical and horizontal transmission rates are allowed to evolve. The outcome of these simulations depends on whether high levels of vertical transmission are possible with low virulence. Finally, we argue against the notion of a virulence-avirulence continuum between horizontal and vertical transmission, and discuss our results in relation to empirical studies of transmission and virulence.     

Spatial symmetries in vestibular projections to the uvula-nodulus

The discharge of secondary vestibular neurons relays the activity of the vestibular endorgans, occasioned by movements in three-dimensional physical space. At a slightly higher level of analysis, the discharge of each secondary vestibular neuron participates in a multifiber projection or pathway from primary afferents via the secondary neurons to another neuronal population. The logical organization of this projection determines whether characteristics of physical space are retained or lost. The logical structure of physical space is standardly expressed in terms of the mathematics of group theory. The logical organization of a projection can be compared to that of physical space by evaluating its symmetry group. The direct projection from the semicircular canal nerves via the vestibular nuclei to neck motor neurons has a full three-dimensional symmetry group, allowing it to maintain a three-dimensional coordinate frame. However, a projection may embed only a subgroup of the symmetry group of physical space, which incompletely mirrors the properties of physical space. The major visual and vestibular projections in the rabbit via the inferior olive to the uvula-nodulus carry three degrees of freedom—rotations about one vertical and two horizontal axes—but do not have full three dimensional symmetry. Instead, the vestibulo-olivo-nodular projection has symmetries corresponding to a product of two-dimensional vestibular and one-dimensional optokinetic spaces. This combination of projection symmetries provides the foundation for distinguishing horizontal from vertical rotations within a three dimensional space. In this study, we evaluate the symmetry group given by the physiological organization of the vestibulo-olivo-nodular projection. Although it acts on the same sets of elements and mirrors the rotations that occur in physical space, the physiological transformation group is distinct from the spatial group. We identify symmetries as products of physiological and spatial transformations. The symmetry group shapes the information the projection conveys to the uvula-nodulus; this shaping may depend on a physiological choice of generators, in the same way that function depends on the physiological choice of coordinates. We discuss the implications of the symmetry group for uvula-nodulus function, evolution, and functions of the vestibular system in general.     

Testing Neuronal Accounts of Anisotropic Motion Perception with Computational Modelling

There is an over-representation of neurons in early visual cortical areas that respond most strongly to cardinal (horizontal and vertical) orientations and directions of visual stimuli, and cardinal- and oblique-preferring neurons are reported to have different tuning curves. Collectively, these neuronal anisotropies can explain two commonly-reported phenomena of motion perception – the oblique effect and reference repulsion – but it remains unclear whether neuronal anisotropies can simultaneously account for both perceptual effects. We show in psychophysical experiments that reference repulsion and the oblique effect do not depend on the duration of a moving stimulus, and that brief adaptation to a single direction simultaneously causes a reference repulsion in the orientation domain, and the inverse of the oblique effect in the direction domain. We attempted to link these results to underlying neuronal anisotropies by implementing a large family of neuronal decoding models with parametrically varied levels of anisotropy in neuronal direction-tuning preferences, tuning bandwidths and spiking rates. Surprisingly, no model instantiation was able to satisfactorily explain our perceptual data. We argue that the oblique effect arises from the anisotropic distribution of preferred directions evident in V1 and MT, but that reference repulsion occurs separately, perhaps reflecting a process of categorisation occurring in higher-order cortical areas.