Compensating time delays with neural predictions: are predictions sensory or motor?

The perceptual timescape: Perceptual history on the sub-second scale

There is a high-capacity store of brief time span (∼1000 ms) which information enters from perceptual processing, often called iconic memory or sensory memory. It is proposed that a main function of this store is to hold recent perceptual information in a temporally segregated representation, named the perceptual timescape. The perceptual timescape is a continually active representation of change and continuity over time that endows the perceived present with a perceived history. This is accomplished primarily by two kinds of time marking information: time distance information, which marks all items of information in the perceptual timescape according to how far in the past they occurred, and ordinal temporal information, which organises items of information in terms of their temporal order. Added to that is information about connectivity of perceptual objects over time. These kinds of information connect individual items over a brief span of time so as to represent change, persistence, and continuity over time. It is argued that there is a one-way street of information flow from perceptual processing either to the perceived present or directly into the perceptual timescape, and thence to working memory. Consistent with that, the information structure of the perceptual timescape supports postdictive reinterpretations of recent perceptual information. Temporal integration on a time scale of hundreds of milliseconds takes place in perceptual processing and does not draw on information in the perceptual timescape, which is concerned with temporal segregation, not integration.

Neural mechanisms of visual motion extrapolation

Because neural processing takes time, the brain only has delayed access to sensory information. When localising moving objects this is problematic, as an object will have moved on by the time its position has been determined. Here, we consider predictive motion extrapolation as a fundamental delay-compensation strategy. From a population-coding perspective, we outline how extrapolation can be achieved by a forwards shift in the population-level activity distribution. We identify general mechanisms underlying such shifts, involving various asymmetries which facilitate the targeted 'enhancement' and/or 'dampening' of population-level activity. We classify these on the basis of their potential implementation (intra- vs inter-regional processes) and consider specific examples in different visual regions. We consider how motion extrapolation can be achieved during inter-regional signaling, and how asymmetric connectivity patterns which support extrapolation can emerge spontaneously from local synaptic learning rules. Finally, we consider how more abstract 'model-based' predictive strategies might be implemented. Overall, we present an integrative framework for understanding how the brain determines the real-time position of moving objects, despite neural delays.

An Integrated Model of Collaborative Skill Acquisition: Anticipation, Control Tuning, and Role Adoption

We studied collaborative skill acquisition in a dynamic setting with the game Co-op Space Fortress. While gaining expertise, the majority of subjects became increasingly consistent in the role they adopted without being able to communicate. Moreover, they acted in anticipation of the future task state. We constructed a collaborative skill acquisition model in the cognitive architecture ACT-R that reproduced subject skill acquisition trajectory. It modeled role adoption through reinforcement learning and predictive processes through motion extrapolation and learned relevant control parameters using both a reinforcement learning procedure and a new to ACT-R supervised learning procedure. This is the first integrated cognitive model of collaborative skill acquisition and, as such, gives us valuable insights into the multiple cognitive processes that are involved in learning to collaborate.

Controlling stick balancing on a linear track: Delayed state feedback or delay-compensating predictor feedback?

A planar stick balancing task was investigated using stabilometry parameters (SP); a concept initially developed to assess the stability of human postural sway. Two subject groups were investigated: 6 subjects (MD) with many days of balancing a 90 cm stick on a linear track and 25 subjects (OD) with only one day of balancing experience. The underlying mechanical model is a pendulum-cart system. Two control force models were investigated by means of numerical simulations: (1) delayed state feedback (DSF); and (2) delay-compensating predictor feedback (PF). Both models require an internal model and are subject to certainty thresholds with delayed switching. Measured and simulated time histories were compared quantitatively using a cost function in terms of some essential SPs for all subjects. Minimization of the cost function showed that the control strategy of both OD and MD subjects can better be described by DSF. The control mechanism for the MD subjects was superior in two aspects: (1) they devoted less energy to controlling the cart's position; and (2) their perception threshold for the stick's angular velocity was found to be smaller. Findings support the concept that when sufficient sensory information is readily available, a delay-compensating PF strategy is not necessary.

Predictor feedback models for stick balancing with delay mismatch and sensory dead zones

Human stick balancing is investigated in terms of reaction time delay and sensory dead zones for position and velocity perception using a special combination of delayed state feedback and mismatched predictor feedback as a control model. The corresponding mathematical model is a delay-differential equation with event-driven switching in the control action. Due to the sensory dead zones, initial conditions of the actual state cannot always be provided for an internal-model-based prediction, which indicates that (1) perfect prediction is not possible and (2) the delay in the switching condition cannot be compensated. The imperfection of the predictor is described by the delay mismatch, which is treated as a lumped parameter that creates a transition between perfect predictor feedback (zero delay mismatch) and delayed state feedback (mismatch equal to switching delay). The maximum admissible switching delay (critical delay) is determined numerically based on a practical stabilizability concept. This critical delay is compared to a realistic reference value of 230 ms in order to assess the possible regions of the threshold values for position and velocity perception. The ratio of the angular position and angular velocity for 44 successful balancing trials by 8 human subjects was used to validate the numerical results. Comparison of actual human stick balancing data and numerical simulations based on the mismatched predictor feedback model provided a plausible range of parameters: position detection threshold 1°, velocity detection threshold between 4.24 and 9.35°/s, and delay mismatch around 100-150 ms.

Virtual stick balancing: skill development in Newtonian and Aristotelian dynamics

Human reaction delay significantly limits manual control of unstable systems. It is more difficult to balance a short stick on a fingertip than a long one, because a shorter stick falls faster and therefore requires faster reactions. In this study, a virtual stick balancing environment was developed where the reaction delay can be artificially modulated and the law of motion can be changed between second-order (Newtonian) and first-order (Aristotelian) dynamics. Twenty-four subjects were separated into two groups and asked to perform virtual stick balancing programmed according to either Newtonian or Aristotelian dynamics. The shortest stick length (critical length, L_c) was determined for different added delays in six sessions of balancing trials performed on different days. The observed relation between L_c and the overall reaction delay τ reflected the feature of the underlying mathematical models: (i) for the Newtonian dynamics L_c is proportional to τ²; (ii) for the Aristotelian dynamics L_c is proportional to τ. Deviation of the measured L_c(τ) function from the theoretical one was larger for the Newtonian dynamics for all sessions, which suggests that, at least in virtually controlled tasks, it is more difficult to adopt second-order dynamics than first-order dynamics.

Perception in real-time: predicting the present, reconstructing the past

We feel that we perceive events in the environment as they unfold in real-time. However, this intuitive view of perception is impossible to implement in the nervous system due to biological constraints such as neural transmission delays. I propose a new way of thinking about real-time perception: at any given moment, instead of representing a single timepoint, perceptual mechanisms represent an entire timeline. On this timeline, predictive mechanisms predict ahead to compensate for delays in incoming sensory input, and reconstruction mechanisms retroactively revise perception when those predictions do not come true. This proposal integrates and extends previous work to address a crucial gap in our understanding of a fundamental aspect of our everyday life: the experience of perceiving the present.

The perceived present: What is it, and what is it there for?

It is proposed that the perceived present is not a moment in time, but an information structure comprising an integrated set of products of perceptual processing. All information in the perceived present carries an informational time marker identifying it as "present". This marker is exclusive to information in the perceived present. There are other kinds of time markers, such as ordinality ("this stimulus occurred before that one") and duration ("this stimulus lasted for 50 ms"). These are different from the "present" time marker and may be attached to information regardless of whether it is in the perceived present or not. It is proposed that the perceived present is a very short-term and very high-capacity holding area for perceptual information. The maximum holding time for any given piece of information is ~100 ms: This is affected by the need to balance the value of informational persistence for further processing against the problem of obsolescence of the information. The main function of the perceived present is to facilitate access by other specialized, automatic processes.

Establishing metrics and control laws for the learning process: ball and beam balancing

Understanding how dexterity improves with practice is a fundamental challenge of motor control and neurorehabilitation. Here we investigate a ball and beam implementation of a dexterity puzzle in which subjects stabilize a ball at the mid-point of a beam by manipulating the angular position of the beam. Stabilizability analysis of different biomechanical models for the ball and beam task with time-delayed proportional-derivative feedback identified the angular position of the beam as the manipulated variable. Consequently, we monitored the changes in the dynamics with learning by measuring changes in the control parameters. Two types of stable motion are possible: node type (nonoscillatory) and spiral type (oscillatory). Both types of motion are observed experimentally and correspond to well-defined regions in the parameter space of the control gains. With practice the control gains for each subject move close to or on the portion of the boundary which separates the node-type and spiral-type solutions and which is associated with the rightmost characteristic exponent of smallest real part. These observations suggest that with learning the control gains for ball and beam balancing change in such a way that minimizes overshoot and the settling time. This study provides an example of how mathematical analysis together with careful experimental observations can shed light onto the early stages of skill acquisition. Since the difficulty of this task depends on the length of the beam, ball and beam balancing tasks may be useful for the rehabilitation of children with dyspraxia and those recovering from a stroke.

Effect of processing delay on bifurcation delay in a network of slow-fast oscillators

Bifurcation delay or slow passage effect occurs in dynamical systems with slow-fast time-varying parameters. In this work, we report the impact of processing delay on bifurcation delay in a network of locally coupled slow-fast systems with self-feedback delay. We report that the network exhibits coexisting coherent (synchronized) and incoherent (desynchronized) states among the oscillators as a function of various parameters like self-feedback delay, processing delay, and amplitude of the external current. In particular, we show the decrease of the synchronized region (control of synchronization) for (i) a fixed value of processing delay with varying self-feedback delay and (ii) fixed self-feedback delay with increasing processing delay. In contrast, we observe the increase of the synchronized region (control of desynchronization) for fixed processing delay and self-feedback delay while varying the amplitude of the external current. Finally, we have also analyzed the effect of processing delay on bifurcation delay with the presence of noise and we report that the inhomogeneity in the additional noise does not affect the asymmetry in a bifurcation delay.

Virtual stick balancing: sensorimotor uncertainties related to angular displacement and velocity

Sensory uncertainties and imperfections in motor control play important roles in neural control and Bayesian approaches to neural encoding. However, it is difficult to estimate these uncertainties experimentally. Here, we show that magnitude of the uncertainties during the generation of motor control force can be measured for a virtual stick balancing task by varying the feedback delay, τ. It is shown that the shortest stick length that human subjects are able to balance is proportional to τ  2. The proportionality constant can be related to a combined effect of the sensory uncertainties and the error in the realization of the control force, based on a delayed proportional-derivative (PD) feedback model of the balancing task. The neural reaction delay of the human subjects was measured by standard reaction time tests and by visual blank-out tests. Experimental observations provide an estimate for the upper boundary of the average sensorimotor uncertainty associated either with angular position or with angular velocity. Comparison of balancing trials with 27 human subjects to the delayed PD model suggests that the average uncertainty in the control force associated purely with the angular position is at most 14% while that associated purely with the angular velocity is at most 40%. In the general case when both uncertainties are present, the calculations suggest that the allowed uncertainty in angular velocity will always be greater than that in angular position.

Anticipatory Neural Activity Improves the Decoding Accuracy for Dynamic Head-Direction Signals

Insects and vertebrates harbor specific neurons that encode the animal's head direction (HD) and provide an internal compass for spatial navigation. Each HD cell fires most strongly in one preferred direction. As the animal turns its head, however, HD cells in rat anterodorsal thalamic nucleus (ADN) and other brain areas fire already before their preferred direction is reached, as if the neurons anticipated the future HD. This phenomenon has been explained at a mechanistic level, but a functional interpretation is still missing. To close this gap, we use a computational approach based on the movement statistics of male rats and a simple model for the neural responses within the ADN HD network. Network activity is read out using population vectors in a biologically plausible manner, so that only past spikes are taken into account. We find that anticipatory firing improves the representation of the present HD by reducing the motion-induced temporal bias inherent in causal decoding. The amount of anticipation observed in ADN enhances the precision of the HD compass read-out by up to 40%. More generally, our theoretical framework predicts that neural integration times not only reflect biophysical constraints, but also the statistics of behaviorally relevant stimuli; in particular, anticipatory tuning should be found wherever neurons encode sensory signals that change gradually in time.SIGNIFICANCE STATEMENT Across different brain regions, populations of noisy neurons encode dynamically changing stimuli. Decoding a time-varying stimulus from the population response involves a trade-off: For short read-out times, stimulus estimates are unreliable as the number of stochastic spikes is small; for long read-outs, estimates are biased because they lag behind the true stimulus. We show that optimal decoding of temporally correlated stimuli not only relies on finding the right read-out time window but requires neurons to anticipate future stimulus values. We apply this general framework to the rodent head-direction system and show that the experimentally observed anticipation of future head directions can be explained at a quantitative level from the neuronal tuning properties, network size, and the animal's head-movement statistics.

Delay-induced low-frequency modulation of the voice during sustained phonation

An important property of negative feedback systems is the tendency to oscillate when feedback is delayed. This paper evaluated this phenomenon in a sustained phonation task, where subjects prolonged a vowel with 0-600 ms delays in auditory feedback. This resulted in a delay-dependent vocal wow: from 0.4 to 1 Hz fluctuations in fundamental frequency and intensity that increased in period and amplitude as the delay increased. A similar modulation in low-frequency oscillations was not observed in the first two formant frequencies, although some subjects did display increased variability. Results suggest that delayed auditory feedback enhances an existing periodic fluctuation in the voice, with a more complex, possibly indirect, influence on supraglottal articulation. These findings have important implications for understanding how speech may be affected by artificially applied or disease-based delays in sensory feedback.

Eye-hand coordination during flexible manual interception of an abruptly appearing, moving target

As a vital skill in an evolving world, interception of moving objects relies on accurate prediction of target motion. In natural circumstances, active gaze shifts often accompany hand movements when exploring targets of interest, but how eye and hand movements are coordinated during manual interception and their dependence on visual prediction remain unclear. Here, we trained gaze-unrestrained monkeys to manually intercept targets appearing at random locations and circularly moving with random speeds. We found that well-trained animals were able to intercept the targets with adequate compensation for both sensory transmission and motor delays. Before interception, the animals' gaze followed the targets with adequate compensation for the sensory delay, but not for extra target displacement during the eye movements. Both hand and eye movements were modulated by target kinematics, and their reaction times were correlated. Moreover, retinal errors and reaching errors were correlated across different stages of reach execution. Our results reveal eye-hand coordination during manual interception, yet the eye and hand movements may show different levels of prediction based on the task context.

NEW & NOTEWORTHY Here we studied the eye-hand coordination of monkeys during flexible manual interception of a moving target. Eye movements were untrained and not explicitly associated with reward. We found that the initial saccades toward the moving target adequately compensated for sensory transmission delays, but not for extra target displacement, whereas the reaching arm movements fully compensated for sensorimotor delays, suggesting that the mode of eye-hand coordination strongly depends on behavioral context.

Control at stability's edge minimizes energetic costs: expert stick balancing

Stick balancing on the fingertip is a complex voluntary motor task that requires the stabilization of an unstable system. For seated expert stick balancers, the time delay is 0.23 s, the shortest stick that can be balanced for 240 s is 0.32 m and there is a [Formula: see text]° dead zone for the estimation of the vertical displacement angle in the saggital plane. These observations motivate a switching-type, pendulum-cart model for balance control which uses an internal model to compensate for the time delay by predicting the sensory consequences of the stick's movements. Numerical simulations using the semi-discretization method suggest that the feedback gains are tuned near the edge of stability. For these choices of the feedback gains, the cost function which takes into account the position of the fingertip and the corrective forces is minimized. Thus, expert stick balancers optimize control with a combination of quick manoeuvrability and minimum energy expenditures.

Effects of Badminton Expertise on Representational Momentum: A Combination of Cross-Sectional and Longitudinal Studies

Representational momentum (RM) has been found to be magnified in experts (e.g., sport players) with respect to both real and implied motion in expert-familiar domains. However, it remains unclear whether similar effects can be achieved in expert-unfamiliar domains, especially within the context of implied motion. To answer this question, we conducted two independent experiments using an implied motion paradigm and examined the expert effects of badminton training on RM in both adult and child players. In Experiment 1, we used a cross-sectional design and compared RM between adult professional badminton players and matched controls. The results revealed significantly enhanced RM for adult players, supporting the expert effect in expert-unfamiliar domains for implied motion. However, cross-sectional studies could not ascertain whether the observed expert effect was due to innate factors or expertise acquirement. Therefore, in Experiment 2, we used a longitudinal design and compared RM between two groups of child participants, naming child players who had enrolled professional badminton training program at a sports school and age-matched peer non-players who attended an ordinary primary school without sports training. Before training, there were no differences in RM among child players, their non-player peers, and adult non-players. However, after 4 years of badminton training, child players demonstrated significantly enhanced RM compared to themselves prior to training. The increased RM observed in both adult and child players suggests that badminton expertise modulates implied motion RM.

An Adaptive Neural Mechanism for Acoustic Motion Perception with Varying Sparsity

Biological motion-sensitive neural circuits are quite adept in perceiving the relative motion of a relevant stimulus. Motion perception is a fundamental ability in neural sensory processing and crucial in target tracking tasks. Tracking a stimulus entails the ability to perceive its motion, i.e., extracting information about its direction and velocity. Here we focus on auditory motion perception of sound stimuli, which is poorly understood as compared to its visual counterpart. In earlier work we have developed a bio-inspired neural learning mechanism for acoustic motion perception. The mechanism extracts directional information via a model of the peripheral auditory system of lizards. The mechanism uses only this directional information obtained via specific motor behaviour to learn the angular velocity of unoccluded sound stimuli in motion. In nature however the stimulus being tracked may be occluded by artefacts in the environment, such as an escaping prey momentarily disappearing behind a cover of trees. This article extends the earlier work by presenting a comparative investigation of auditory motion perception for unoccluded and occluded tonal sound stimuli with a frequency of 2.2 kHz in both simulation and practice. Three instances of each stimulus are employed, differing in their movement velocities-0.5°/time step, 1.0°/time step and 1.5°/time step. To validate the approach in practice, we implement the proposed neural mechanism on a wheeled mobile robot and evaluate its performance in auditory tracking.

The Flash-Lag Effect as a Motion-Based Predictive Shift

Due to its inherent neural delays, the visual system has an outdated access to sensory information about the current position of moving objects. In contrast, living organisms are remarkably able to track and intercept moving objects under a large range of challenging environmental conditions. Physiological, behavioral and psychophysical evidences strongly suggest that position coding is extrapolated using an explicit and reliable representation of object’s motion but it is still unclear how these two representations interact. For instance, the so-called flash-lag effect supports the idea of a differential processing of position between moving and static objects. Although elucidating such mechanisms is crucial in our understanding of the dynamics of visual processing, a theory is still missing to explain the different facets of this visual illusion. Here, we reconsider several of the key aspects of the flash-lag effect in order to explore the role of motion upon neural coding of objects’ position. First, we formalize the problem using a Bayesian modeling framework which includes a graded representation of the degree of belief about visual motion. We introduce a motion-based prediction model as a candidate explanation for the perception of coherent motion. By including the knowledge of a fixed delay, we can model the dynamics of sensory information integration by extrapolating the information acquired at previous instants in time. Next, we simulate the optimal estimation of object position with and without delay compensation and compared it with human perception under a broad range of different psychophysical conditions. Our computational study suggests that the explicit, probabilistic representation of velocity information is crucial in explaining position coding, and therefore the flash-lag effect. We discuss these theoretical results in light of the putative corrective mechanisms that can be used to cancel out the detrimental effects of neural delays and illuminate the more general question of the dynamical representation at the present time of spatial information in the visual pathways.

Visual illusions are powerful tools to explore the limits and constraints of human perception. One of them has received considerable empirical and theoretical interests: the so-called “flash-lag effect”. When a visual stimulus moves along a continuous trajectory, it may be seen ahead of its veridical position with respect to an unpredictable event such as a punctuate flash. This illusion tells us something important about the visual system: contrary to classical computers, neural activity travels at a relatively slow speed. It is largely accepted that the resulting delays cause this perceived spatial lag of the flash. Still, after three decades of debates, there is no consensus regarding the underlying mechanisms. Herein, we re-examine the original hypothesis that this effect may be caused by the extrapolation of the stimulus’ motion that is naturally generated in order to compensate for neural delays. Contrary to classical models, we propose a novel theoretical framework, called parodiction, that optimizes this process by explicitly using the precision of both sensory and predicted motion. Using numerical simulations, we show that the parodiction theory subsumes many of the previously proposed models and empirical studies. More generally, the parodiction hypothesis proposes that neural systems implement generic neural computations that can systematically compensate the existing neural delays in order to represent the predicted visual scene at the present time. It calls for new experimental approaches to directly explore the relationships between neural delays and predictive coding.

Forward Prediction in the Posterior Parietal Cortex and Dynamic Brain-Machine Interface

While remarkable progress has been made in brain-machine interfaces (BMIs) over the past two decades, it is still difficult to utilize neural signals to drive artificial actuators to produce predictive movements in response to dynamic stimuli. In contrast to naturalistic limb movements largely based on forward planning, brain-controlled neuroprosthetics mainly rely on feedback without prior trajectory formation. As an important sensorimotor interface integrating multisensory inputs and efference copy, the posterior parietal cortex (PPC) might play a proactive role in predictive motor control. Here it is proposed that predictive neural activity in PPC could be decoded to provide prosthetic control signals for guiding BMI systems in dynamic environments.

Neurología de la anticipación y sus implicaciones en el deporte

<p>El movimiento es una acción que involucra interconexiones complejas, por lo cual se requiere profundizar en los procesos de adaptación, predicción y anticipación que permiten entender la importancia de estos aspectos desde sus bases filogenéticas y ontogenéticas hasta su implicación en movimientos complejos. Parte de la optimización de los procesos descritos se haya en la calidad de información aferente, la cual permite la relación con el entorno —especialmente la entrada visual— que reconoce un flujo de imágenes y una proyección al contexto en el que se está inmerso. Las estructuras e interconexiones implicadas en la anticipación y predicción de movimientos son descritas de modo que se evidencia la congruencia y continuidad del flujo de información que caracteriza esta especialidad neuromecánica de movimiento. Por otro lado, se aborda la integración de centros puntuales del sistema nervioso central y redes neuronales que permiten el entramado de procesos de aprendizaje por observación, además de proveer equilibrio y eficiencia al sistema en la recepción de estímulos y su relación con la generación de eferencias motoras que cumplan con objetivos específicos. En el ámbito deportivo estos procesos favorecen la eficiencia del gesto optimizando el movimiento.</p>

LRP predicts smooth pursuit eye movement onset during the ocular tracking of self-generated movements

Several studies have indicated that human observers are very efficient at tracking self-generated hand movements with their gaze, yet it is not clear whether this is simply a by-product of the predictability of self-generated actions or if it results from a deeper coupling of the somatomotor and oculomotor systems. In a first behavioral experiment we compared pursuit performance as observers either followed their own finger or tracked a dot whose motion was externally generated but mimicked their finger motion. We found that even when the dot motion was completely predictable in terms of both onset time and kinematics, pursuit was not identical to that produced as the observers tracked their finger, as evidenced by increased rate of catch-up saccades and by the fact that in the initial phase of the movement gaze was lagging behind the dot, whereas it was ahead of the finger. In a second experiment we recorded EEG in the attempt to find a direct link between the finger motor preparation, indexed by the lateralized readiness potential (LRP) and the latency of smooth pursuit. After taking into account finger movement onset variability, we observed larger LRP amplitudes associated with earlier smooth pursuit onset across trials. The same held across subjects, where average LRP onset correlated with average eye latency. The evidence from both experiments concurs to indicate that a strong coupling exists between the motor systems leading to eye and finger movements and that simple top-down predictive signals are unlikely to support optimal coordination.

Perceived temporal asynchrony between sinusoidally modulated luminance and depth

Simultaneously presented visual events lead to temporally asynchronous percepts. This has led some researchers to conclude that the asynchronous experience is a manifestation of differences in neural processing time for different visual attributes. Others, however, have suggested that the asynchronous experience is due to differences in temporal markers for changes of different visual attributes. Here, two sets of bars were presented, one to each eye. Either the bars were moving or their luminance was gradually changing. Bars moved horizontally in counterphase at low frequencies along short trajectories and were presented stereoscopically, such that the horizontal movements were perceived as back-and-forth motion on a sagittal plane, or monocularly to a dominant eye, preserving a perception of the horizontal movements on a frontal plane. In a control condition, bars were stationary and their luminance was modulated. The changes in stimulus speed or luminance occurred sinusoidally. When asked to adjust the phase of one stimulus to the other to achieve synchronous perception, participants showed a constant phase offset at the lowest frequencies used. Given the absence of abrupt transitions and the presence of similar gradual turning points in our stimuli to control for attentional effects, it can be concluded that asynchronous percepts in multimodal stimuli may at least in part be a manifestation of difference in neural processing time of visual attributes rather than solely a difference in the temporal markers (transitions versus turning points).

Fluctuation-response relation unifies dynamical behaviors in neural fields

Anticipation is a strategy used by neural fields to compensate for transmission and processing delays during the tracking of dynamical information and can be achieved by slow, localized, inhibitory feedback mechanisms such as short-term synaptic depression, spike-frequency adaptation, or inhibitory feedback from other layers. Based on the translational symmetry of the mobile network states, we derive generic fluctuation-response relations, providing unified predictions that link their tracking behaviors in the presence of external stimuli to the intrinsic dynamics of the neural fields in their absence.

Visual motion modulates pattern sensitivity ahead, behind, and beside motion

Retinal motion can modulate visual sensitivity. For instance, low contrast drifting waveforms (targets) can be easier to detect when abutting the leading edges of movement in adjacent high contrast waveforms (inducers), rather than the trailing edges. This target-inducer interaction is contingent on the adjacent waveforms being consistent with one another - in-phase as opposed to out-of-phase. It has been suggested that this happens because there is a perceptually explicit predictive signal at leading edges of motion that summates with low contrast physical input - a 'predictive summation'. Another possible explanation is a phase sensitive 'spatial summation', a summation of physical inputs spread across the retina (not predictive signals). This should be non-selective in terms of position - it should be evident at leading, adjacent, and at trailing edges of motion. To tease these possibilities apart, we examined target sensitivity at leading, adjacent, and trailing edges of motion. We also examined target sensitivity adjacent to flicker, and for a stimulus that is less susceptible to spatial summation, as it sums to grey across a small retinal expanse. We found evidence for spatial summation in all but the last condition. Finally, we examined sensitivity to an absence of signal at leading and trailing edges of motion, finding greater sensitivity at leading edges. These results are inconsistent with the existence of a perceptually explicit predictive signal in advance of drifting waveforms. Instead, we suggest that phase-contingent target-inducer modulations of sensitivity are explicable in terms of a directionally modulated spatial summation.

Sensory uncertainty and stick balancing at the fingertip

The effects of sensory input uncertainty, [Formula: see text], on the stability of time-delayed human motor control are investigated by calculating the minimum stick length, [Formula: see text], that can be stabilized in the inverted position for a given time delay, [Formula: see text]. Five control strategies often discussed in the context of human motor control are examined: three time-invariant controllers [proportional-derivative, proportional-derivative-acceleration (PDA), model predictive (MP) controllers] and two time-varying controllers [act-and-wait (AAW) and intermittent predictive controllers]. The uncertainties of the sensory input are modeled as a multiplicative term in the system output. Estimates based on the variability of neural spike trains and neural population responses suggest that [Formula: see text]-13 %. It is found that for this range of uncertainty, a tapped delay-line type of MP controller is the most robust controller. In particular, this controller can stabilize inverted sticks of the length balanced by expert stick balancers (0.25-0.5 m when [Formula: see text] s). However, a PDA controller becomes more effective when [Formula: see text]. A comparison between [Formula: see text] for human stick balancing at the fingertip and balancing on the rubberized surface of a table tennis racket suggest that friction likely plays a role in balance control. Measurements of [Formula: see text], and a variability of the fluctuations in the vertical displacement angle, an estimate of [Formula: see text], may make it possible to study the changes in control strategy as motor skill develops.

Human stick balancing: an intermittent control explanation

There are two issues in balancing a stick pivoting on a finger tip (or mechanically on a moving cart): maintaining the stick angle near to vertical and maintaining the horizontal position within the bounds of reach or cart track. The (linearised) dynamics of the angle are second order (although driven by pivot acceleration), and so, as in human standing, control of the angle is not, by itself very difficult. However, once the angle is under control, the position dynamics are, in general, fourth order. This makes control quite difficult for humans (and even an engineering control system requires careful design). Recently, three of the authors have experimentally demonstrated that humans control the stick angle in a special way: the closed-loop inverted pendulum behaves as a non-inverted pendulum with a virtual pivot somewhere between the stick centre and tip and with increased gravity. Moreover, they suggest that the virtual pivot lies at the radius of gyration (about the mass centre) above the mass centre. This paper gives a continuous-time control-theoretical interpretation of the virtual-pendulum approach. In particular, by using a novel cascade control structure, it is shown that the horizontal control of the virtual pivot becomes a second-order problem which is much easier to solve than the generic fourth-order problem. Hence, the use of the virtual pivot approach allows the control problem to be perceived by the subject as two separate second-order problems rather than a single fourth-order problem, and the control problem is therefore simplified. The theoretical predictions are verified using the data previously presented by three of the authors and analysed using a standard parameter estimation method. The experimental data indicate that although all subjects adopt the virtual pivot approach, the less expert subjects exhibit larger amplitude angular motion and poorly controlled translational motion. It is known that human control systems are delayed and intermittent, and therefore, the continuous-time strategy cannot be correct. However, the model of intermittent control used in this paper is based on the virtual pivot continuous-time control scheme, handles time delays and moreover masquerades as the underlying continuous-time controller. In addition, the event-driven properties of intermittent control can explain experimentally observed variability.

Motion extrapolation in the central fovea

Neural transmission latency would introduce a spatial lag when an object moves across the visual field, if the latency was not compensated. A visual predictive mechanism has been proposed, which overcomes such spatial lag by extrapolating the position of the moving object forward. However, a forward position shift is often absent if the object abruptly stops moving (motion-termination). A recent "correction-for-extrapolation" hypothesis suggests that the absence of forward shifts is caused by sensory signals representing 'failed' predictions. Thus far, this hypothesis has been tested only for extra-foveal retinal locations. We tested this hypothesis using two foveal scotomas: scotoma to dim light and scotoma to blue light. We found that the perceived position of a dim dot is extrapolated into the fovea during motion-termination. Next, we compared the perceived position shifts of a blue versus a green moving dot. As predicted the extrapolation at motion-termination was only found with the blue moving dot. The results provide new evidence for the correction-for-extrapolation hypothesis for the region with highest spatial acuity, the fovea.

The delayed and noisy nervous system: implications for neural control

Recent advances in the study of delay differential equations draw attention to the potential benefits of the interplay between random perturbations ('noise') and delay in neural control. The phenomena include transient stabilizations of unstable steady states by noise, control of fast movements using time-delayed feedback and the occurrence of long-lived delay-induced transients. In particular, this research suggests that the interplay between noise and delay necessitates the use of intermittent, discontinuous control strategies in which corrective movements are made only when controlled variables cross certain thresholds. A potential benefit of such strategies is that they may be optimal for minimizing energy expenditures associated with control. In this paper, the concepts are made accessible by introducing them through simple illustrative examples that can be readily reproduced using software packages, such as XPPAUT.

Visual motion induces a forward prediction of spatial pattern

Cortical motion analysis continuously encodes image velocity but might also be used to predict future patterns of sensory input along the motion path. We asked whether this predictive aspect of motion is exploited by the human visual system. Targets can be more easily detected at the leading as compared to the trailing edge of motion [1], but this effect has been attributed to a nonspecific boost in contrast gain at the leading edge, linked to motion-induced shifts in spatial position [1–4]. Here we show that the detectability of a local sinusoidal target presented at the ends of a region containing motion is phase dependent at the leading edge, but not at the trailing edge. These two observations rule out a simple gain control mechanism that modulates contrast energy and passive filtering explanations, respectively. By manipulating the relative orientation of the moving pattern and target, we demonstrate that the resulting spatial variation in detection threshold along the edge closely resembles the superposition of sensory input and an internally generated predicted signal. These findings show that motion induces a forward prediction of spatial pattern that combines with the cortical representation of the future stimulus.

Delay effects in brain dynamics. Introduction

This brief introductory paper reviews the methods and the results presented in the special issue. The general destabilizing effects of time delays in nonlinear dynamical systems are summarized and some similarities in the philosophical approaches of neural systems research in distinct disciplines are pointed out. All the invited papers focus on the central role of time delays in the dynamics of neural systems. The research contributions are set in order according to the increasing number of neurons involved in the corresponding study from a couple of neurons through neural fields to populations and clusters of neurons.