The delayed and noisy nervous system: implications for neural control

Aberrant decision-making as a risk factor for falls in aging

Neuromotor impairments resulting from natural aging and aging-related diseases are often accompanied by a heightened prevalence of falls and fall-related injuries. Conventionally, the study of factors contributing to falls focuses on intrinsic characteristics, such as sensorimotor processing delays and weakness, and extrinsic factors, such as environmental obstacles. However, the impact of these factors only becomes evident in response to people's decisions about how and where they will move in their environment. This decision-making process can be considered a behavioral risk factor, and it influences the extent to which a person engages in activities that place them near the limits of their capacity. While there are readily available tools for assessing intrinsic and extrinsic fall risk, our understanding of how to assess behavioral risk is limited. Measuring behavioral risk requires a systematic assessment of how people make decisions when walking in complex environments and how these decisions relate to their functional capacity. We propose that experimental methods and computational models derived from behavioral economics can stimulate the development of such assessments. Behavioral economics relies on theoretical models and empirical studies to characterize the factors that influence how people make decisions under risky conditions where a given decision can have variable outcomes. Applying a behavioral economic approach to walking can provide insight into how internal assessment of one's fall risk influences the tasks that one is willing to perform. Ultimately, these assessments will allow us to identify people who make choices that increase their likelihood of fall-related injuries.

Learning to stand with sensorimotor delays generalizes across directions and from hand to leg effectors

Humans receive sensory information from the past, requiring the brain to overcome delays to perform daily motor skills such as standing upright. Because delays vary throughout the body and change over a lifetime, it would be advantageous to generalize learned control policies of balancing with delays across contexts. However, not all forms of learning generalize. Here, we use a robotic simulator to impose delays into human balance. When delays are imposed in one direction of standing, participants are initially unstable but relearn to balance by reducing the variability of their motor actions and transfer balance improvements to untrained directions. Upon returning to normal standing, aftereffects from learning are observed as small oscillations in control, yet they do not destabilize balance. Remarkably, when participants train to balance with delays using their hand, learning transfers to standing with the legs. Our findings establish that humans use experience to broadly update their neural control to balance with delays.

Preparing to move: Setting initial conditions to simplify interactions with complex objects

Humans dexterously interact with a variety of objects, including those with complex internal dynamics. Even in the simple action of carrying a cup of coffee, the hand not only applies a force to the cup, but also indirectly to the liquid, which elicits complex reaction forces back on the hand. Due to underactuation and nonlinearity, the object's dynamic response to an action sensitively depends on its initial state and can display unpredictable, even chaotic behavior. With the overarching hypothesis that subjects strive for predictable object-hand interactions, this study examined how subjects explored and prepared the dynamics of an object for subsequent execution of the target task. We specifically hypothesized that subjects find initial conditions that shorten the transients prior to reaching a stable and predictable steady state. Reaching a predictable steady state is desirable as it may reduce the need for online error corrections and facilitate feed forward control. Alternative hypotheses were that subjects seek to reduce effort, increase smoothness, and reduce risk of failure. Motivated by the task of 'carrying a cup of coffee', a simplified cup-and-ball model was implemented in a virtual environment. Human subjects interacted with this virtual object via a robotic manipulandum that provided force feedback. Subjects were encouraged to first explore and prepare the cup-and-ball before initiating a rhythmic movement at a specified frequency between two targets without losing the ball. Consistent with the hypotheses, subjects increased the predictability of interaction forces between hand and object and converged to a set of initial conditions followed by significantly decreased transients. The three alternative hypotheses were not supported. Surprisingly, the subjects' strategy was more effortful and less smooth, unlike the observed behavior in simple reaching movements. Inverse dynamics of the cup-and-ball system and forward simulations with an impedance controller successfully described subjects' behavior. The initial conditions chosen by the subjects in the experiment matched those that produced the most predictable interactions in simulation. These results present first support for the hypothesis that humans prepare the object to minimize transients and increase stability and, overall, the predictability of hand-object interactions.

Grip force anticipation of nonlinear, underactuated load force

Feedforward internal model-based control enabled by efference copies of motor commands is the prevailing theoretical account of motor anticipation. Grip force control during object manipulation-a paradigmatic example of motor anticipation-is a key line of evidence for that account. However, the internal model approach has not addressed the computational challenges faced by the act of manipulating mechanically complex objects with nonlinear, underactuated degrees of freedom. These objects exhibit complex and unpredictable load force dynamics which cannot be encoded by efference copies of underlying motor commands, leading to the prediction from the perspective of an efference copy-enabled feedforward control scheme that grip force should either lag or fail to coordinate with changes in load force. In contrast to that prediction, we found evidence for strong, precise, anticipatory grip force control during manipulations of a complex object. The results are therefore inconsistent with the internal forward model approach and suggest that efference copies of motor commands are not necessary to enable anticipatory control during active object manipulation.NEW & NOTEWORTHY From the perspective of feedforward internal model-based control, precise, anticipatory grip force (GF) control when manipulating a complex object should not be possible as the object's changing load forces (LFs) cannot be encoded by efference copies of the underlying movements. However, we observed that GF exhibited strong, precise, anticipatory coupling with LF during extended manipulations of a complex object. These findings suggest that an alternative theoretical framework is needed to account for anticipatory GF control.

Scaling of inertial delays in terrestrial mammals

As part of its response to a perturbation, an animal often needs to reposition its body. Inertia acts to oppose the corrective motion, delaying the completion of the movement-we refer to this elapsed time as inertial delay. As animal size increases, muscle moment arms also increase, but muscles are proportionally weaker, and limb inertia is proportionally larger. Consequently, the scaling of inertial delays is complex. Our intent is to determine how quickly different sized animals can produce corrective movements when their muscles act at their force capacity, relative to the time within which those movements need to be performed. Here, we quantify inertial delay using two biomechanical models representing common scenarios in animal locomotion: a distributed mass pendulum approximating swing limb repositioning (swing task), and an inverted pendulum approximating whole body posture recovery (posture task). We parameterized the anatomical, muscular, and inertial properties of these models using literature scaling relationships, then determined inertial delay for each task across a large range of movement magnitudes and the full range of terrestrial mammal sizes. We found that inertial delays scaled with an average of M0.28 in the swing task and M0.35 in the posture task across movement magnitudes-larger animals require more absolute time to perform the same movement as small animals. The time available to complete a movement also increases with animal size, but less steeply. Consequently, inertial delays comprise a greater fraction of swing duration and other characteristic movement times in larger animals. We also compared inertial delays to the other component delays within the stimulus-response pathway. As movement magnitude increased, inertial delays exceeded these sensorimotor delays, and this occurred for smaller movements in larger animals. Inertial delays appear to be a challenge for motor control, particularly for bigger movements in larger animals.

Flexible organization of grip force control during movement frequency scaling

The grip force applied to maintain grasp of a handheld object has been typically reported as tightly coupled to the load force exerted by the object as it is actively manipulated, occurring proportionally and consistently in phase with changes in load force. However, continuous grip force-load force coupling breaks down when overall load force levels and oscillation amplitudes are lower (Grover F, Lamb M, Bonnette S, Silva PL, Lorenz T, Riley MA. Exp Brain Res 236: 2531–2544, 2018) or more predictable (Grover FM, Nalepka P, Silva PL, Lorenz T, Riley MA. Exp Brain Res 237: 687–703, 2019). Under these circumstances, grip force is instead only intermittently coupled to load force; continuous coupling is prompted only when load force levels or variations become sufficiently high or unpredictable. The current study investigated the nature of the transition between continuous and intermittent modes of grip force control by scaling the load force level and the oscillation amplitude continuously in time by means of scaling the required frequency of movement oscillations. Participants grasped a cylindrical object between the thumb and forefinger and oscillated their arm about the shoulder in the sagittal plane. Oscillation frequencies were paced with a metronome that scaled through an ascending or descending frequency progression. Due to greater accelerations, faster frequencies produced greater overall load force levels and more pronounced load oscillations. We observed smooth but nonlinear transitions between clear regimes of intermittent and continuous grip force-load force coordination, for both scaling directions, indicating that grip force control can flexibly reorganize as parameters affecting grasp (e.g., variations in load force) change over time.

NEW & NOTEWORTHY Grip force (GF) is synchronously coupled to changing load forces (LF) during object manipulation when LF levels are high or unpredictable, but only intermittently coupled to LF during less challenging grasp conditions. This study characterized the nature of transitions between synchronous and intermittent GF-LF coupling, revealing a smooth but nonlinear change in intermittent GF modulation in response to continuous scaling of LF amplitude. Intermittent, “drift-and-act” control may provide an alternative framework for understanding GF-LF coupling.

Scaling of sensorimotor delays in terrestrial mammals

Whether an animal is trying to escape from a predator, avoid a fall or perform a more mundane task, the effectiveness of its sensory feedback is constrained by sensorimotor delays. Here, we combine electrophysiological experiments, systematic reviews of the literature and biophysical models to determine how delays associated with the fastest locomotor reflex scale with size in terrestrial mammals. Nerve conduction delay is one contributor, and increases strongly with animal size. Sensing, synaptic and neuromuscular junction delays also contribute, and we approximate each as a constant value independent of animal size. Muscle's electromechanical and force generation delays increase more moderately with animal size than nerve conduction delay, but their total contribution exceeds that of the four neural delays. The sum of these six component delays, termed total delay, increases with animal size in proportion to M0.21-large mammals experience total delays 17 times longer than small mammals. The slower movement times of large animals mostly offset their long delays resulting in a more modest, but perhaps still significant, doubling of their total delay relative to movement duration when compared with their smaller counterparts. Irrespective of size, sensorimotor delay is likely a challenge for all mammals, particularly during fast running.

Predictability, force, and (anti)resonance in complex object control

Manipulation of complex objects as in tool use is ubiquitous and has given humans an evolutionary advantage. This study examined the strategies humans choose when manipulating an object with underactuated internal dynamics, such as a cup of coffee. The dynamics of the object renders the temporal evolution complex, possibly even chaotic, and difficult to predict. A cart-and-pendulum model, loosely mimicking coffee sloshing in a cup, was implemented in a virtual environment with a haptic interface. Participants rhythmically manipulated the virtual cup containing a rolling ball; they could choose the oscillation frequency, whereas the amplitude was prescribed. Three hypotheses were tested: 1) humans decrease interaction forces between hand and object; 2) humans increase the predictability of the object dynamics; and 3) humans exploit the resonances of the coupled object-hand system. Analysis revealed that humans chose either a high-frequency strategy with antiphase cup-and-ball movements or a low-frequency strategy with in-phase cup-and-ball movements. Counter to hypothesis 1, they did not decrease interaction force; instead, they increased the predictability of the interaction dynamics, quantified by mutual information, supporting hypothesis 2. To address hypothesis 3, frequency analysis of the coupled hand-object system revealed two resonance frequencies separated by an antiresonance frequency. The low-frequency strategy exploited one resonance, whereas the high-frequency strategy afforded more choice, consistent with the frequency response of the coupled system; both strategies avoided the antiresonance. Hence, humans did not prioritize small interaction forces but rather strategies that rendered interactions predictable. These findings highlight that physical interactions with complex objects pose control challenges not present in unconstrained movements. NEW & NOTEWORTHY Daily actions involve manipulation of complex nonrigid objects, which present a challenge since humans have no direct control of the whole object. We used a virtual-reality experiment and simulations of a cart-and-pendulum system coupled to hand movements with impedance to analyze the manipulation of this underactuated object. We showed that participants developed strategies that increased the predictability of the object behavior by exploiting the resonance structure of the object but did not minimize the hand-object interaction force.

Aversive Behavior in the Nematode C. elegans Is Modulated by cGMP and a Neuronal Gap Junction Network

All animals rely on their ability to sense and respond to their environment to survive. However, the suitability of a behavioral response is context-dependent, and must reflect both an animal's life history and its present internal state. Based on the integration of these variables, an animal's needs can be prioritized to optimize survival strategies. Nociceptive sensory systems detect harmful stimuli and allow for the initiation of protective behavioral responses. The polymodal ASH sensory neurons are the primary nociceptors in C. elegans. We show here that the guanylyl cyclase ODR-1 functions non-cell-autonomously to downregulate ASH-mediated aversive behaviors and that ectopic cGMP generation in ASH is sufficient to dampen ASH sensitivity. We define a gap junction neural network that regulates nociception and propose that decentralized regulation of ASH signaling can allow for rapid correlation between an animal's internal state and its behavioral output, lending modulatory flexibility to this hard-wired nociceptive neural circuit.

Signal prediction by anticipatory relaxation dynamics

Real-time prediction of signals is a task often encountered in control problems as well as by living systems. Here, a parsimonious prediction approach based on the coupling of a linear relaxation-delay system to a smooth, stationary signal is described. The resulting anticipatory relaxation dynamics (ARD) is a frequency-dependent predictor of future signal values. ARD not only approximately predicts signals on average but can anticipate the occurrence of signal peaks, too. This can be explained by recognizing ARD as an input-output system with negative group delay. It is characterized, including its prediction horizon, by its analytically given frequency response function.

A stochastic mechanism for signal propagation in the brain: Force of rapid random fluctuations in membrane potentials of individual neurons

There are two functionally important factors in signal propagation in a brain structural network: the very first synaptic delay-a time delay about 1ms-from the moment when signals originate to the moment when observation on the signal propagation can begin; and rapid random fluctuations in membrane potentials of every individual neuron in the network at a timescale of microseconds. We provide a stochastic analysis of signal propagation in a general setting. The analysis shows that the two factors together result in a stochastic mechanism for the signal propagation as described below. A brain structural network is not a rigid circuit rather a very flexible framework that guides signals to propagate but does not guarantee success of the signal propagation. In such a framework, with the very first synaptic delay, rapid random fluctuations in every individual neuron in the network cause an "alter-and-concentrate effect" that almost surely forces signals to successfully propagate. By the stochastic mechanism we provide analytic evidence for the existence of a force behind signal propagation in a brain structural network caused by rapid random fluctuations in every individual neuron in the network at a timescale of microseconds with a time delay of 1ms.

Predictability and Robustness in the Manipulation of Dynamically Complex Objects

Manipulation of complex objects and tools is a hallmark of many activities of daily living, but how the human neuromotor control system interacts with such objects is not well understood. Even the seemingly simple task of transporting a cup of coffee without spilling creates complex interaction forces that humans need to compensate for. Predicting the behavior of an underactuated object with nonlinear fluid dynamics based on an internal model appears daunting. Hence, this research tests the hypothesis that humans learn strategies that make interactions predictable and robust to inaccuracies in neural representations of object dynamics. The task of moving a cup of coffee is modeled with a cart-and-pendulum system that is rendered in a virtual environment, where subjects interact with a virtual cup with a rolling ball inside using a robotic manipulandum. To gain insight into human control strategies, we operationalize predictability and robustness to permit quantitative theory-based assessment. Predictability is quantified by the mutual information between the applied force and the object dynamics; robustness is quantified by the energy margin away from failure. Three studies are reviewed that show how with practice subjects develop movement strategies that are predictable and robust. Alternative criteria, common for free movement, such as maximization of smoothness and minimization of force, do not account for the observed data. As manual dexterity is compromised in many individuals with neurological disorders, the experimental paradigm and its analyses are a promising platform to gain insights into neurological diseases, such as dystonia and multiple sclerosis, as well as healthy aging.

Sensorimotor control of tracking movements at various speeds for stroke patients as well as age-matched and young healthy subjects

There are aging- and stroke-induced changes on sensorimotor control in daily activities, but their mechanisms have not been well investigated. This study explored speed-, aging-, and stroke-induced changes on sensorimotor control. Eleven stroke patients (affected sides and unaffected sides) and 20 control subjects (10 young and 10 age-matched individuals) were enrolled to perform elbow tracking tasks using sinusoidal trajectories, which included 6 target speeds (15.7, 31.4, 47.1, 62.8, 78.5, and 94.2 deg/s). The actual elbow angle was recorded and displayed on a screen as visual feedback, and three indicators, the root mean square error (RMSE), normalized integrated jerk (NIJ) and integral of the power spectrum density of normalized speed (IPNS), were used to investigate the strategy of sensorimotor control. Both NIJ and IPNS had significant differences among the four groups (P<0.01), and the values were ranked in the following order: young controls < age-matched controls Collapse

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MESH Headings

• Adult
• Case-Control Studies
• Elbow/physiopathology
• Female
• Humans
• Male
• Middle Aged
• Movement/physiology
• Psychomotor Performance/physiology
• Stroke/physiopathology
• Young Adult

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Grants Collapse

Affiliation(s)

Di Ao School of Engineering, Sun Yat-sen University, Guangzhou, Guang Dong, P. R. China Key Laboratory of Sensing Technology and Biomedical Instrument of GuangDong province, Guangzhou, Guang Dong, P. R. China
Rong Song School of Engineering, Sun Yat-sen University, Guangzhou, Guang Dong, P. R. China Key Laboratory of Sensing Technology and Biomedical Instrument of GuangDong province, Guangzhou, Guang Dong, P. R. China
Kai-yu Tong Division of Biomedical Engineering, Department of Electronic Engineering, the Chinese University of Hong Kong, Hong Kong, China

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Double-well dynamics of noise-driven control activation in human intermittent control: the case of stick balancing

When facing a task of balancing a dynamic system near an unstable equilibrium, humans often adopt intermittent control strategy: Instead of continuously controlling the system, they repeatedly switch the control on and off. Paradigmatic example of such a task is stick balancing. Despite the simplicity of the task itself, the complexity of human intermittent control dynamics in stick balancing still puzzles researchers in motor control. Here we attempt to model one of the key mechanisms of human intermittent control, control activation, using as an example the task of overdamped stick balancing. In doing so, we focus on the concept of noise-driven activation, a more general alternative to the conventional threshold-driven activation. We describe control activation as a random walk in an energy potential, which changes in response to the state of the controlled system. By way of numerical simulations, we show that the developed model captures the core properties of human control activation observed previously in the experiments on overdamped stick balancing. Our results demonstrate that the double-well potential model provides tractable mathematical description of human control activation at least in the considered task and suggest that the adopted approach can potentially aid in understanding human intermittent control in more complex processes.

Perceptual and motor learning underlies human stick-balancing skill

We investigated the acquisition of skill in balancing a stick (52 cm, 34 g) on the fingertip in nine participants using three-dimensional motion analysis. After 3.5 h of practice over 6 wk, the participants could more consistently balance the stick for longer durations with greatly reduced magnitude and speed of stick and finger movements. Irrespective of level of skill, the balanced stick behaved like a normal noninverted pendulum oscillating under greater-than-gravity torque with simple harmonic motion about a virtual pivot located at the radius of gyration above the center of mass. The control input parameter was the magnitude ratio between the torque applied on the stick by the participant and the torque due to gravity. The participants utilized only a narrow range of this parameter, which did not change with practice, to rotate the stick like a linear mass-spring system. With increased skill, the stick therefore maintained the same period of oscillation but showed marked reductions in magnitude of both oscillation and horizontal translation. Better balancing was associated with 1) more accurate visual localization of the stick and proprioceptive localization of the finger and 2) reduced cross-coupling errors between finger and stick movements in orthogonal directions; i.e., finger movements in the anteroposterior plane became less coupled with stick tip movements in the mediolateral plane, and vice versa. Development of this fine motor skill therefore depended on perceptual and motor learning to provide improved estimation of sensorimotor state and precision of motor commands to an unchanging internal model of the rotational dynamics.

Rhythmic manipulation of objects with complex dynamics: predictability over chaos

The study of object manipulation has been largely confined to discrete tasks, where accuracy, mechanical effort, or smoothness were examined to explain subjects' preferred movements. This study investigated a rhythmic manipulation task, which involved continuous interaction with a nonlinear object that led to unpredictable object behavior. Using a simplified virtual version of the task of carrying a cup of coffee, we studied how this unpredictable object behavior affected the selected strategies. The experiment was conducted in a virtual set-up, where subjects moved a cup with a ball inside, modeled by cart-and-pendulum dynamics. Inverse dynamics calculations of the system showed that performing the task with different amplitudes and relative phases required different force profiles and rendered the object's dynamics with different degrees of predictability (quantified by Mutual Information between the applied force and the cup kinematics and its sensitivity). Subjects (n = 8) oscillated the virtual cup between two targets via a robotic manipulandum, paced by a metronome at 1 Hz for 50 trials, each lasting 45 s. They were free to choose their movement amplitude and relative phase between the ball and cup. Experimental results showed that subjects increased their movement amplitudes, which rendered the interactions with the object more predictable and with lower sensitivity to the execution variables. These solutions were associated with higher average exerted force and lower object smoothness, contradicting common expectations from studies on discrete object manipulation and unrestrained movements. Instead, the findings showed that humans selected strategies with higher predictability of interaction dynamics. This finding expressed that humans seek movement strategies where force and kinematics synchronize to repeatable patterns that may require less sensorimotor information processing.

Visual reliance for balance control in older adults persists when visual information is disrupted by artificial feedback delays

Sensory information from our eyes, skin and muscles helps guide and correct balance. Less appreciated, however, is that delays in the transmission of sensory information between our eyes, limbs and central nervous system can exceed several 10s of milliseconds. Investigating how these time-delayed sensory signals influence balance control is central to understanding the postural system. Here, we investigate how delayed visual feedback and cognitive performance influence postural control in healthy young and older adults. The task required that participants position their center of pressure (COP) in a fixed target as accurately as possible without visual feedback about their COP location (eyes-open balance), or with artificial time delays imposed on visual COP feedback. On selected trials, the participants also performed a silent arithmetic task (cognitive dual task). We separated COP time series into distinct frequency components using low and high-pass filtering routines. Visual feedback delays affected low frequency postural corrections in young and older adults, with larger increases in postural sway noted for the group of older adults. In comparison, cognitive performance reduced the variability of rapid center of pressure displacements in young adults, but did not alter postural sway in the group of older adults. Our results demonstrate that older adults prioritize vision to control posture. This visual reliance persists even when feedback about the task is delayed by several hundreds of milliseconds.

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.

Learning an intermittent control strategy for postural balancing using an EMG-based human-computer interface

It has been considered that the brain stabilizes unstable body dynamics by regulating co-activation levels of antagonist muscles. Here we critically reexamined this established theory of impedance control in a postural balancing task using a novel EMG-based human-computer interface, in which subjects were asked to balance a virtual inverted pendulum using visual feedback information on the pendulum's position. The pendulum was actuated by a pair of antagonist joint torques determined in real-time by activations of the corresponding pair of antagonist ankle muscles of subjects standing upright. This motor-task raises a frustrated environment; a large feedback time delay in the sensorimotor loop, as a source of instability, might favor adopting the non-reactive, preprogrammed impedance control, but the ankle muscles are relatively hard to co-activate, which hinders subjects from adopting the impedance control. This study aimed at discovering how experimental subjects resolved this frustrated environment through motor learning. One third of subjects adapted to the balancing task in a way of the impedance-like control. It was remarkable, however, that the majority of subjects did not adopt the impedance control. Instead, they acquired a smart and energetically efficient strategy, in which two muscles were inactivated simultaneously at a sequence of optimal timings, leading to intermittent appearance of periods of time during which the pendulum was not actively actuated. Characterizations of muscle inactivations and the pendulum¡Çs sway showed that the strategy adopted by those subjects was a type of intermittent control that utilizes a stable manifold of saddle-type unstable upright equilibrium that appeared in the state space of the pendulum when the active actuation was turned off.

Acceleration feedback improves balancing against reflex delay

A model for human postural balance is considered in which the time-delayed feedback depends on position, velocity and acceleration (proportional-derivative-acceleration (PDA) feedback). It is shown that a PDA controller is equivalent to a predictive controller, in which the prediction is based on the most recent information of the state, but the control input is not involved into the prediction. A PDA controller is superior to the corresponding proportional-derivative controller in the sense that the PDA controller can stabilize systems with approximately 40 per cent larger feedback delays. The addition of a sensory dead zone to account for the finite thresholds for detection by sensory receptors results in highly intermittent, complex oscillations that are a typical feature of human postural sway.

Neuronal avalanches, epileptic quakes and other transient forms of neurodynamics

Power-law behaviors in brain activity in healthy animals, in the form of neuronal avalanches, potentially benefit the computational activities of the brain, including information storage, transmission and processing. In contrast, power-law behaviors associated with seizures, in the form of epileptic quakes, potentially interfere with the brain's computational activities. This review draws attention to the potential roles played by homeostatic mechanisms and multistable time-delayed recurrent inhibitory loops in the generation of power-law phenomena. Moreover, it is suggested that distinctions between health and disease are scale-dependent. In other words, what is abnormal and defines disease it is not the propagation of neural activity but the propagation of activity in a neural population that is large enough to interfere with the normal activities of the brain. From this point of view, epilepsy is a disease that results from a failure of mechanisms, possibly located in part in the cortex itself or in the deep brain nuclei and brainstem, which truncate or otherwise confine the spatiotemporal scales of these power-law phenomena.

Spectral solution of delayed random walks

We develop a spectral method for computing the probability density function for delayed random walks; for such problems, the method is exact to machine precision and faster than existing approaches. In conjunction with a step function approximation and the weak Euler-Maruyama discretization, the spectral method can be applied to nonlinear stochastic delay differential equations (SDDE). In essence, this means approximating the SDDE by a delayed random walk, which is then solved using the spectral method. We carry out tests for a particular nonlinear SDDE that show that this method captures the solution without the need for Monte Carlo sampling.