Finger Modes Research Articles

Two classes of action-stabilizing synergies reflecting spinal and supraspinal circuitry.

We explored force-stabilizing synergies during accurate four-finger constant force production tasks in spaces of finger modes (commands to fingers computed to account for the finger interdependence) and of motor unit (MU) firing frequencies. The main specific hypothesis was that the multifinger synergies would disappear during unintentional force drifts without visual feedback on the force magnitude, whereas MU-based synergies would be robust to such drifts. Healthy participants performed four-finger accurate cyclical force production trials followed by trials of constant force production. Individual MUs were identified in the flexor digitorum superficialis (FDS) and extensor digitorum communis (EDC). Principal component analysis was applied to motor unit frequencies to identify robust MU groups (MU-modes) with parallel scaling of the firing frequencies in FDS, in EDC, and the combined MUs of FDS + EDC. The framework of the uncontrolled manifold hypothesis was used to quantify force-stabilizing synergies when visual feedback on the force magnitude was available and 15 s after turning the visual feedback off. Removing visual feedback led to a force drift toward lower magnitudes, accompanied by the disappearance of multifinger synergies. In contrast, MU-mode synergies were minimally affected by removing visual feedback off and continued to be robust for the FDS and for the EDC, while being absent for the (FDS + EDC) analysis. We interpret the findings within the theory of hierarchical control of action with spatial referent coordinates. The qualitatively different behavior of the multifinger and MU-mode-based synergies likely reflects the difference in the involved neural circuitry, supraspinal for the former and spinal for the latter.NEW & NOTEWORTHY Two types of synergies, in the space of commands to individual fingers and in the space of motor unit groups, show qualitatively different behaviors during accurate multifinger force-production tasks. After removing visual feedback, finger force synergies disappear, whereas motor unit-based synergies persist. These results point at different neural circuitry involved in these two basic classes of synergies: supraspinal for multieffector synergies, and spinal for motor unit-based synergies.

Finger interdependence and unintentional force drifts: Lessons from manipulations of visual feedback.

We explored the phenomenon of unintentional finger force drift by using visual feedback on the force produced either by explicitly instructed (master) finger pairs or by non-instructed (enslaved) finger pairs. In particular, we drew contrasting predictions from two hypotheses: that force drifts represented consequences of drifts in effector referent coordinates at the level of individual fingers vs. at the level of finger modes (hypothetical variables accounting for the finger force interdependence). Subjects performed accurate force production with two fingers of a hand, index-ring or middle-little. They received visual feedback on the force produced either by the master fingers or by the other two, enslaved, fingers. The feedback scale was adjusted to ensure that the subjects did not know the difference between these two, randomly presented, conditions. Under feedback on the master finger force, enslaved force showed a consistent drift upward. Under feedback on the enslaved finger force, master force showed a consistent drift downward. The subjects were unaware of the force drifts, which could reach over 35% of the initial force magnitude. The data support the hypothesis on drifts in the referent coordinate at the level of individual digits, not finger modes, as the origin of unintentional force drifts. The consistent increase in the relative amount of force produced by the enslaved fingers suggests that the commonly used methods to quantify enslaving should include relatively brief force production tasks.

Stability of steady hand force production explored across spaces and methods of analysis.

We used the framework of the uncontrolled manifold (UCM) hypothesis and explored the reliability of several outcome variables across different spaces of analysis during a very simple four-finger accurate force production task. Fourteen healthy, young adults performed the accurate force production task with each hand on 3 days. Small spatial finger perturbations were generated by the "inverse piano" device three times per trial (lifting the fingers 1cm/0.5s and lowering them). The data were analyzed using the following main methods: (1) computation of indices of the structure of inter-trial variance and motor equivalence in the space of finger forces and finger modes, and (2) analysis of referent coordinates and apparent stiffness values for the hand. Maximal voluntary force and the index of enslaving (unintentional finger force production) showed good to excellent reliability. Strong synergies stabilizing total force were reflected in both structure of variance and motor equivalence indices. Variance within the UCM and the index of motor equivalent motion dropped over the trial duration and showed good to excellent reliability. Variance orthogonal to the UCM and the index of non-motor equivalent motion dropped over the 3 days and showed poor to moderate reliability. Referent coordinate and apparent stiffness indices co-varied strongly and both showed good reliability. In contrast, the computed index of force stabilization showed poor reliability. The findings are interpreted within the scheme of neural control with referent coordinates involving the hierarchy of two basic commands, the r-command and c-command. The data suggest natural drifts in the finger force space, particularly within the UCM. We interpret these drifts as reflections of a trade-off between stability and optimization of action. The implications of these findings for the UCM framework and future clinical applications are explored in the discussion. Indices of the structure of variance and motor equivalence show good reliability and can be recommended for applied studies.

Multi-finger synergies and the muscular apparatus of the hand.

We explored whether the synergic control of the hand during multi-finger force production tasks depends on the hand muscles involved. Healthy subjects performed accurate force production tasks and targeted force pulses while pressing against loops positioned at the level of fingertips, middle phalanges, and proximal phalanges. This varied the involvement of the extrinsic and intrinsic finger flexors. The framework of the uncontrolled manifold (UCM) hypothesis was used to analyze the structure of inter-trial variance, motor equivalence, and anticipatory synergy adjustments prior to the force pulse in the spaces of finger forces and finger modes (hypothetical finger-specific control signals). Subjects showed larger maximal force magnitudes at the proximal site of force production. There were synergies stabilizing total force during steady-state phases across all three sites of force production; no differences were seen across the sites in indices of structure of variance, motor equivalence, or anticipatory synergy adjustments. Indices of variance, which did not affect the task (within the UCM), correlated with motor equivalent motion between the steady states prior to and after the force pulse; in contrast, variance affecting task performance did not correlate with non-motor equivalent motion. The observations are discussed within the framework of hierarchical control with referent coordinates for salient effectors at each level. The findings suggest that multi-finger synergies are defined at the level of abundant transformation between the low-dimensional hand level and higher dimensional finger level while being relatively immune to transformations between the finger level and muscle level. The results also support the scheme of control with two classes of neural variables that define referent coordinates and gains in back-coupling loops between hierarchical control levels.

Numerical study of convective sedimentation through a sharp density interface

We conduct numerical simulations using the Eulerian–Lagrangian approach to investigate the formation of the leaking, finger, and stable-settling modes in convective sedimentation when a sediment-laden fluid layer descends through a sharply stratified ambient flow. We show that the temporal evolution of the sedimentation process for the leaking mode can be divided into three stages, including (in temporal order) Rayleigh–Taylor instability, convection, and leaking stages. The presence of sheet-like descending plumes of suspended particles is an important characteristic of the leaking mode, which marks the existence of the leaking stage. For larger particles, the motion is more dominated by gravitational settling and less affected by buoyancy-induced flow motion. The resulting lack of the leaking stage for the larger-particle case leads to persistent finger-like plumes of suspended particles, known as the finger mode. The stable-settling mode occurs when the particles are large and the concentration is dilute such that flow motion due to Rayleigh–Taylor instability has no effect on the particle motion, and the convective motion of suspended particles is insignificant. For the third stage of the leaking mode, which is also the final stationary state, we derive the criterion for the occurrence of the leaking pattern from a scaling argument of the viscous boundary layer. The criterion is further confirmed by the present simulation results and previous laboratory experiments. Through analysis of the energy budget and the vertical flux, we show that although the settling of individual particles is accelerated, the presence of the sheet-like descending plumes in the leaking mode does not contribute to an efficient settling enhancement compared with the finger mode and the Rayleigh–Taylor instability, i.e., the cases with no background stratification. This implies a negative effect on the settling enhancement for small suspended particles when a stable background density stratification exists. In addition, simulations using the equilibrium Eulerian description for the suspended particles are also conducted to examine the difference between the present Lagrangian particle approach and the conventional Eulerian model.

Task-specific stability of abundant systems: Structure of variance and motor equivalence

Our main goal was to test a hypothesis that transient changes in performance of a steady-state task would result in motor equivalence. We also estimated effects of visual feedback on the amount of reorganization of motor elements. Healthy subjects performed two variations of a four-finger pressing task requiring accurate production of total pressing force (FTOT) and total moment of force (MTOT). In the Jumping-Target task, a sequence of target jumps required transient changes in either FTOT or MTOT. In the Step-Perturbation task, the index finger was lifted by 1cm for 0.5s leading to a change in both FTOT and MTOT. Visual feedback could have been frozen for one of these two variables in both tasks. Deviations in the space of finger modes (hypothetical commands to individual fingers) were quantified in directions of unchanged FTOT and MTOT (motor equivalent – ME) and in directions that changed FTOT and MTOT (non-motor equivalence – nME). Both the ME and nME components increased when the performance changed. After transient target jumps leading to the same combination of FTOT and MTOT, the changes in finger modes had a large residual ME component with only a very small nME component. Without visual feedback, an increase in the nME component was observed without consistent changes in the ME component. Results from the Step-Perturbation task were qualitatively similar. These findings suggest that both external perturbations and purposeful changes in performance trigger a reorganization of elements of an abundant system, leading to large ME change. These results are consistent with the principle of motor abundance corroborating the idea that a family of solutions is facilitated to stabilize values of important performance variables.

Task-Specific Stability of Multifinger Steady-State Action

ABSTRACTThe authors explored task-specific stability during accurate multifinger force production tasks with different numbers of instructed fingers. Subjects performed steady-state isometric force production tasks and were instructed not to interfere voluntarily with transient lifting-and-lowering perturbations applied to the index finger. The main results were (a) intertrial variance in the space of finger modes at steady states was larger within the subspace that had no effect on the total force (the uncontrolled manifold [UCM]); (b) perturbations caused large deviations of finger modes within the UCM (motor equivalence); and (c) deviations caused by the perturbation showed larger variance within the UCM. No significant effects of the number of task fingers were noted in any of the 3 indicators. The results are discussed within the frameworks of the UCM and referent configuration hypotheses. The authors conclude, in particular, that all the tasks were effectively 4-finger tasks with different involvement of task and nontask fingers.

Learning to Combine High Variability With High Precision: Lack of Transfer to a Different Task

ABSTRACTThe authors studied effects of practicing a 4-finger accurate force production task on multifinger coordination quantified within the uncontrolled manifold hypothesis. During practice, task instability was modified by changing visual feedback gain based on accuracy of performance. The authors also explored the retention of these effects, and their transfer to a prehensile task. Subjects practiced the force production task for 2 days. After the practice, total force variability decreased and performance became more accurate. In contrast, variance of finger forces showed a tendency to increase during the first practice session while in the space of finger modes (hypothetical commands to fingers) the increase was under the significance level. These effects were retained for 2 weeks. No transfer of these effects to the prehensile task was seen, suggesting high specificity of coordination changes. The retention of practice effects without transfer to a different task suggests that further studies on a more practical method of improving coordination are needed.

Stability of multifinger action in different state spaces.

We investigated stability of action by a multifinger system with three methods: analysis of intertrial variance, application of transient perturbations, and analysis of the system's motion in different state spaces. The "inverse piano" device was used to apply transient (lifting-and-lowering) perturbations to individual fingers during single- and two-finger accurate force production tasks. In each trial, the perturbation was applied either to a finger explicitly involved in the task or one that was not. We hypothesized that, in one-finger tasks, task-specific stability would be observed in the redundant space of finger forces but not in the nonredundant space of finger modes (commands to explicitly involved fingers). In two-finger tasks, we expected that perturbations applied to a nontask finger would not contribute to task-specific stability in mode space. In contrast to our expectations, analyses in both force and mode spaces showed lower stability in directions that did not change total force output compared with directions that did cause changes in total force. In addition, the transient perturbations led to a significant increase in the enslaving index. We consider these results within a theoretical scheme of control with referent body configurations organized hierarchically, using multiple few-to-many mappings organized in a synergic way. The observed volatility of enslaving, greater equifinality of total force compared with elemental variables, and large magnitude of motor equivalent motion in both force and mode spaces provide support for the concept of task-specific stability of performance and the existence of multiple neural loops, which ensure this stability.

Linear and non-linear evolution of the vertical shear instability in accretion discs

We analyse the stability and non-linear dynamics of power-law accretion disc models. These have mid-plane densities that follow radial power laws and have either temperature or entropy distributions that are strict power-law functions of cylindrical radius, R. We employ two different hydrodynamic codes to perform high-resolution 2D axisymmetric and 3D simulations that examine the long-term evolution of the disc models as a function of the power-law indices of the temperature or entropy, the disc scaleheight, the thermal relaxation time of the fluid and the disc viscosity. We present an accompanying stability analysis of the problem, based on asymptotic methods, that we use to guide our interpretation of the simulation results. We find that axisymmetric disc models whose temperature or entropy profiles cause the equilibrium angular velocity to vary with height are unstable to the growth of perturbations whose most obvious character is modes with horizontal and vertical wavenumbers that satisfy |kR/kZ| ≫ 1. Instability occurs only when the thermodynamic response of the fluid is isothermal, or the thermal evolution time is comparable to or shorter than the local dynamical time-scale. These discs appear to exhibit the Goldreich–Schubert–Fricke or ‘vertical shear’ linear instability. Closer inspection of the simulation results uncovers the growth of two distinct modes. The first are characterized by very short radial wavelength perturbations that grow rapidly at high latitudes in the disc, and descend down towards the mid-plane on longer time-scales. We refer to these as ‘finger modes’ because they display kR/kZ ≫ 1. The second appear at slightly later times in the main body of the disc, including near the mid-plane. These ‘body modes’ have somewhat longer radial wavelengths. Early on they manifest themselves as fundamental breathing modes, but quickly become corrugation modes as symmetry about the mid-plane is broken. The corrugation modes are a prominent feature of the non-linear saturated state, leading to strong vertical oscillation of the disc mid-plane. In a viscous disc with aspect ratio H/r = 0.05, instability is found to operate when the viscosity parameter α < 4 × 10−4. In three dimensions the instability generates a quasi-turbulent flow, and the associated Reynolds stress produces a fluctuating effective viscosity coefficient whose mean value reaches α ∼ 10−3 by the end of the simulation. The evolution and saturation of the vertical shear instability in astrophysical disc models which include realistic treatments of the thermal physics has yet to be examined. Should it occur on either global or local scales, however, our results suggest that it will have significant consequences for their internal dynamics, transport properties and observational appearance.

Equifinality and its violations in a redundant system: multifinger accurate force production

We explored a hypothesis that transient perturbations applied to a redundant system result in equifinality in the space of task-related performance variables but not in the space of elemental variables. The subjects pressed with four fingers and produced an accurate constant total force level. The "inverse piano" device was used to lift and lower one of the fingers smoothly. The subjects were instructed "not to intervene voluntarily" with possible force changes. Analysis was performed in spaces of finger forces and finger modes (hypothetical neural commands to fingers) as elemental variables. Lifting a finger led to an increase in its force and a decrease in the forces of the other three fingers; the total force increased. Lowering the finger back led to a drop in the force of the perturbed finger. At the final state, the sum of the variances of finger forces/modes computed across repetitive trials was significantly higher than the variance of the total force/mode. Most variance of the individual finger force/mode changes between the preperturbation and postperturbation states was compatible with constant total force. We conclude that a transient perturbation applied to a redundant system leads to relatively small variance in the task-related performance variable (equifinality), whereas in the space of elemental variables much more variance occurs that does not lead to total force changes. We interpret the results within a general theoretical scheme that incorporates the ideas of hierarchically organized control, control with referent configurations, synergic control, and the uncontrolled manifold hypothesis.

Optimization and Variability of Motor Behavior in Multifinger Tasks: What Variables Does the Brain Use?

ABSTRACT The neural control of movement has been described using different sets of elemental variables. Two possible sets of elemental variables have been suggested for finger pressing tasks: the forces of individual fingers and the finger commands (also called finger modes or central commands). The authors analyzed which of the 2 sets of the elemental variables is more likely used in the optimization of the finger force sharing and which set is used for the stabilization of performance. They used two recently developed techniques—the analytical inverse optimization (ANIO) and the uncontrolled manifold (UCM) analysis—to evaluate each set of elemental variables with respect to both aspects of performance. The results of the UCM analysis favored the finger commands as the elemental variables used for performance stabilization, while ANIO worked equally well on both sets of elemental variables. A simple scheme is suggested as to how the CNS could optimize a cost function dependent on the finger forces, but for the sake of facilitation of the feed forward control it substitutes the original cost function by a cost function, which is convenient to optimize in the space of finger commands.

Contrasting effects of fatigue on multifinger coordination in young and older adults.

We investigated the effects of fatigue produced by timed maximal voluntary contraction (MVC) of the index finger of the right hand on performance in MVC and accurate cyclic force production tasks in right-handed young (Young group) and strength-matched elderly (Elderly group) participants. We hypothesized that, before fatigue, the Elderly group would show weaker force-stabilizing synergies and smaller adaptive changes in the synergy index during fatigue. Synergies were defined as covaried adjustments of neural commands to fingers (finger modes) across trials that stabilize total force. Fatigue caused a significant reduction in the MVC, which was larger in the Young group compared with the Elderly group for both fatigued finger (index finger) and four fingers (index, middle, ring, and little fingers pressing together). Indexes of finger enslaving (lack of individuation) increased with fatigue in both groups. The index of force-stabilizing synergies was similar for the two groups before fatigue, while its increase with fatigue was significantly larger in the Elderly group compared with the Young group. We infer that changes in the indexes of finger interaction (enslaving) and coordination (synergy) with age seem to be correlated with changes in muscle strength. This correlation may be causally related to the progressive death of neurons at different levels of the neuromotor hierarchy. The surprisingly large changes in the synergy index with fatigue in older adults suggest that, by itself, aging does not necessarily lead to impairment in synergic control. Strength training may be a method to avoid age-related decrement in finger interaction and coordination.

Multi-finger interaction during involuntary and voluntary single finger force changes

Two types of finger interaction are characterized by positive co-variation (enslaving) or negative co-variation (error compensation) of finger forces. Enslaving reflects mechanical and neural connections among fingers, while error compensation results from synergic control of fingers to stabilize their net output. Involuntary and voluntary force changes by a finger were used to explore these patterns. We hypothesized that synergic mechanisms will dominate during involuntary force changes, while enslaving will dominate during voluntary finger force changes. Subjects pressed with all four fingers to match a target force that was 10% of their maximum voluntary contraction (MVC). One of the fingers was unexpectedly raised 5.0 mm at a speed of 30.0 mm/s. During finger raising the subject was instructed "not to intervene voluntarily". After the finger was passively lifted and a new steady-state achieved, subjects pressed down with the lifted finger, producing a pulse of force voluntarily. The data were analyzed in terms of finger forces and finger modes (hypothetical commands to fingers reflecting their intended involvement). The target finger showed an increase in force during both phases. In the involuntary phase, the target finger force changes ranged between 10.71 ± 1.89% MVC (I-finger) and 16.60 ± 2.26% MVC (L-finger). Generally, non-target fingers displayed a force decrease with a maximum amplitude of -1.49 ± 0.43% MVC (L-finger). Thus, during the involuntary phase, error compensation was observed--non-lifted fingers showed a decrease in force (as well as in mode magnitude). During the voluntary phase, enslaving was observed--non-target fingers showed an increase in force and only minor changes in mode magnitude. The average change in force of non-target fingers ranged from 21.83 ± 4.47% MVC for R-finger (M-finger task) to 0.71 ± 1.10% MVC for L-finger (I-finger task). The average change in mode of non-target fingers was between -7.34 ± 19.27% MVC for R-finger (L-finger task) and 7.10 ± 1.38% MVC for M-finger (I-finger task). We discuss a range of factors affecting force changes, from purely mechanical effects of finger passive lifting to neural synergic adjustments of commands to individual fingers. The data fit a recently suggested scheme that merges the equilibrium-point hypothesis (control with referent configurations) with the idea of hierarchical synergic control of multi-element systems.

Adaptive increase in force variance during fatigue in tasks with low redundancy

We tested a hypothesis that fatigue of an element (a finger) leads to an adaptive neural strategy that involves an increase in force variability in the other finger(s) and an increase in co-variation of commands to fingers to keep total force variability relatively unchanged. We tested this hypothesis using a system with small redundancy (two fingers) and a marginally redundant system (with an additional constraint related to the total moment of force produced by the fingers, unstable condition). The subjects performed isometric accurate rhythmic force production tasks by the index (I) finger and two fingers (I and middle, M) pressing together before and after a fatiguing exercise by the I finger. Fatigue led to a large increase in force variance in the I-finger task and a smaller increase in the IM-task. We quantified two components of variance in the space of hypothetical commands to fingers, finger modes. Under both stable and unstable conditions, there was a large increase in the variance component that did not affect total force and a much smaller increase in the component that did. This resulted in an increase in an index of the force-stabilizing synergy. These results indicate that marginal redundancy is sufficient to allow the central nervous system to use adaptive increase in variability to shield important variables from effects of fatigue. We offer an interpretation of these results based on a recent development of the equilibrium-point hypothesis known as the referent configuration hypothesis.

Variance components in discrete force production tasks

The study addresses the relationships between task parameters and two components of variance, "good" and "bad", during multi-finger accurate force production. The variance components are defined in the space of commands to the fingers (finger modes) and refer to variance that does ("bad") and does not ("good") affect total force. Based on an earlier study of cyclic force production, we hypothesized that speeding-up an accurate force production task would be accompanied by a drop in the regression coefficient linking the "bad" variance and force rate such that variance of the total force remains largely unaffected. We also explored changes in parameters of anticipatory synergy adjustments with speeding-up the task. The subjects produced accurate ramps of total force over different times and in different directions (force-up and force-down) while pressing with the four fingers of the right hand on individual force sensors. The two variance components were quantified, and their normalized difference was used as an index of a total force stabilizing synergy. "Good" variance scaled linearly with force magnitude and did not depend on force rate. "Bad" variance scaled linearly with force rate within each task, and the scaling coefficient did not change across tasks with different ramp times. As a result, a drop in force ramp time was associated with an increase in total force variance, unlike the results of the study of cyclic tasks. The synergy index dropped 100-200 ms prior to the first visible signs of force change. The timing and magnitude of these anticipatory synergy adjustments did not depend on the ramp time. Analysis of the data within an earlier model has shown adjustments in the variance of a timing parameter, although these adjustments were not as pronounced as in the earlier study of cyclic force production. Overall, we observed qualitative differences between the discrete and cyclic force production tasks: Speeding-up the cyclic tasks was associated with better adjustments of the timing accuracy, which helps achieve comparable force variance in tasks with different rates of force production. This does not happen in discrete tasks. The lack of scaling of the anticipatory changes in the synergy index with ramp time is the first reported feature that distinguishes anticipatory synergy adjustments from anticipatory postural adjustments. We discuss the differences between the cyclic and discrete tasks within a hierarchical control scheme offered by Schöner.

Fatigue and Motor Redundancy: Adaptive Increase in Finger Force Variance in Multi-Finger Tasks

We studied the effects of fatigue of the index finger on indices of force variability in discrete and rhythmic accurate force production tasks performed by the index finger and by all four fingers pressing in parallel. An increase in the variance of the force produced by the fatigued index finger was expected. We hypothesized that the other fingers would also show increased variance of their forces, which would be accompanied by co-variation among the finger forces resulting in relatively preserved accuracy of performance. The subjects performed isometric tasks including maximal voluntary contraction (MVC) and accurate force production before and after a 1-min MVC fatiguing exercise by the index finger. During fatigue, there was a significant increase in the root mean square index of force variability during accurate force production by the index finger. In the four-finger tasks, the variance of the individual finger force increased for all four fingers, while the total force variance showed only a modest change. We quantified two components of variance in the space of hypothetical commands to fingers, finger modes. There was a large increase in the variance component that did not affect total force and a much smaller increase in the component that did. The results suggest an adaptive increase in force variance by nonfatigued elements as a strategy to attenuate effects of fatigue on accuracy of multi-element performance. These effects were unlikely to originate at the level of synchronization of motor units across muscle compartments but rather involved higher control levels.

Finger interaction in a three-dimensional pressing task

Accurate control of forces produced by the fingers is essential for performing object manipulation. This study examines the indices of finger interaction when accurate time profiles of force are produced in different directions, while using one of the fingers or all four fingers of the hand. We hypothesized that patterns of unintended force production among shear force components may involve features not observed in the earlier studies of vertical force production. In particular, we expected to see unintended forces generated by non-task fingers not in the direction of the instructed force but in the opposite direction as well as substantial force production in directions orthogonal to the instructed direction. We also tested a hypothesis that multi-finger synergies, quantified using the framework of the uncontrolled manifold hypothesis, will help reduce across-trials variance of both total force magnitude and direction. Young, healthy subjects were required to produce accurate ramps of force in five different directions by pressing on force sensors with the fingers of the right (dominant) hand. The index finger induced the smallest unintended forces in non-task fingers. The little finger showed the smallest unintended forces when it was a non-task finger. Task fingers showed substantial force production in directions orthogonal to the intended force direction. During four-finger tasks, individual force vectors typically pointed off the task direction, with these deviations nearly perfectly matched to produce a resultant force in the task direction. Multi-finger synergy indices reflected strong co-variation in the space of finger modes (commands to fingers) that reduced variability of the total force magnitude and direction across trials. The synergy indices increased in magnitude over the first 30% of the trial time and then stayed at a nearly constant level. The synergy index for stabilization of total force magnitude was higher for shear force components when compared to the downward pressing force component. The results suggest complex interactions between enslaving and synergic force adjustments, possibly reflecting the experience with everyday prehensile tasks. For the first time, the data document multi-finger synergies stabilizing both shear force magnitude and force vector direction. These synergies may play a major role in stabilizing the hand action during object manipulation.

Anticipatory covariation of finger forces during self-paced and reaction time force production

We tested a hypothesis that humans can change patterns of finger force covariation in a task-specific manner in preparation to a change in the total force. Subjects performed quick targeted force pulses by pressing with four fingers on force sensors from a certain background force level to a target level. In self-paced trials, finger force modes (hypothetical commands to fingers) showed changes in covariation, computed across trials, more than 100 ms before changes in the total force. Half of the subjects showed large early changes in force mode covariation, while in the other half these changes were much smaller and were followed by a larger positive covariation of finger modes potentially destabilizing the total force profile. Such early covariation changes were absent under the simple reaction time instruction. We conclude that anticipatory covariation reflects control processes that can be expressed differently in different persons and modified depending on the available time for action preparation.

Laboratory experiments on the formation of salt fingers after the decay of turbulence

Previous laboratory experiments have shown that salt fingers are easily disrupted by turbulence. However, in the interior of the ocean, turbulence is both patchy and intermittent, so that there may be sufficient time for the fingers to form between turbulent events. The growth of salt fingers after disruption by turbulence was examined in an experiment in which an oceanic turbulent event was simulated by a grid falling through fingers set up in a laboratory tank. Both horizontal conductivity and temperature profiles showed that after the grid turbulence had decayed the fingers grew rapidly, and that the time scale for growth was of the same order as the e‐folding time for the fastest‐growing long salt finger modes that have been described previously by several authors. This time scale is consistent with the observation that the peak in the temperature gradient spectrum was close to the predicted wave number for fastest‐growing fingers. On the other hand, visualization of the fingers suggests that the period of exponential growth of the finger amplitudes was short, of the order of one e‐folding period. Finally, the results of these experiments suggest that with the typical intermittency of turbulence in the interior of the ocean, salt fingers should have sufficient time to grow between events.