Rethinking motor learning and savings in adaptation paradigms: model-free memory for successful actions combines with internal models

Although motor learning is likely to involve multiple processes, phenomena observed in error-based motor learning paradigms tend to be conceptualized in terms of only a single process: adaptation, which occurs through updating an internal model. Here we argue that fundamental phenomena like movement direction biases, savings (faster relearning), and interference do not relate to adaptation but instead are attributable to two additional learning processes that can be characterized as model-free: use-dependent plasticity and operant reinforcement. Although usually "hidden" behind adaptation, we demonstrate, with modified visuomotor rotation paradigms, that these distinct model-based and model-free processes combine to learn an error-based motor task. (1) Adaptation of an internal model channels movements toward successful error reduction in visual space. (2) Repetition of the newly adapted movement induces directional biases toward the?repeated movement. (3) Operant reinforcement through association of the adapted movement with successful error reduction is responsible for savings.     

Parallel Explicit and Implicit Control of Reaching

Background

Human movement can be guided automatically (implicit control) or attentively (explicit control). Explicit control may be engaged when learning a new movement, while implicit control enables simultaneous execution of multiple actions. Explicit and implicit control can often be assigned arbitrarily: we can simultaneously drive a car and tune the radio, seamlessly allocating implicit or explicit control to either action. This flexibility suggests that sensorimotor signals, including those that encode spatially overlapping perception and behavior, can be accurately segregated to explicit and implicit control processes.

Methodology/Principal Findings

We tested human subjects'' ability to segregate sensorimotor signals to parallel control processes by requiring dual (explicit and implicit) control of the same reaching movement and testing for interference between these processes. Healthy control subjects were able to engage dual explicit and implicit motor control without degradation of performance compared to explicit or implicit control alone. We then asked whether segregation of explicit and implicit motor control can be selectively disrupted by studying dual-control performance in subjects with no clinically manifest neurologic deficits in the presymptomatic stage of Huntington''s disease (HD). These subjects performed successfully under either explicit or implicit control alone, but were impaired in the dual-control condition.

Conclusion/Significance

The human nervous system can exert dual control on a single action, and is therefore able to accurately segregate sensorimotor signals to explicit and implicit control. The impairment observed in the presymptomatic stage of HD points to a possible crucial contribution of the striatum to the segregation of sensorimotor signals to multiple control processes.     

Interacting adaptive processes with different timescales underlie short-term motor learning

Multiple processes may contribute to motor skill acquisition, but it is thought that many of these processes require sleep or the passage of long periods of time ranging from several hours to many days or weeks. Here we demonstrate that within a timescale of minutes, two distinct fast-acting processes drive motor adaptation. One process responds weakly to error but retains information well, whereas the other responds strongly but has poor retention. This two-state learning system makes the surprising prediction of spontaneous recovery (or adaptation rebound) if error feedback is clamped at zero following an adaptation-extinction training episode. We used a novel paradigm to experimentally confirm this prediction in human motor learning of reaching, and we show that the interaction between the learning processes in this simple two-state system provides a unifying explanation for several different, apparently unrelated, phenomena in motor adaptation including savings, anterograde interference, spontaneous recovery, and rapid unlearning. Our results suggest that motor adaptation depends on at least two distinct neural systems that have different sensitivity to error and retain information at different rates.     

Flexible cognitive strategies during motor learning

Visuomotor rotation tasks have proven to be a powerful tool to study adaptation of the motor system. While adaptation in such tasks is seemingly automatic and incremental, participants may gain knowledge of the perturbation and invoke a compensatory strategy. When provided with an explicit strategy to counteract a rotation, participants are initially very accurate, even without on-line feedback. Surprisingly, with further testing, the angle of their reaching movements drifts in the direction of the strategy, producing an increase in endpoint errors. This drift is attributed to the gradual adaptation of an internal model that operates independently from the strategy, even at the cost of task accuracy. Here we identify constraints that influence this process, allowing us to explore models of the interaction between strategic and implicit changes during visuomotor adaptation. When the adaptation phase was extended, participants eventually modified their strategy to offset the rise in endpoint errors. Moreover, when we removed visual markers that provided external landmarks to support a strategy, the degree of drift was sharply attenuated. These effects are accounted for by a setpoint state-space model in which a strategy is flexibly adjusted to offset performance errors arising from the implicit adaptation of an internal model. More generally, these results suggest that strategic processes may operate in many studies of visuomotor adaptation, with participants arriving at a synergy between a strategic plan and the effects of sensorimotor adaptation.     

Multidisciplinary Views on Applying Explicit and Implicit Motor Learning in Practice: An International Survey

Background

A variety of options and techniques for causing implicit and explicit motor learning have been described in the literature. The aim of the current paper was to provide clearer guidance for practitioners on how to apply motor learning in practice by exploring experts’ opinions and experiences, using the distinction between implicit and explicit motor learning as a conceptual departure point.

Methods

A survey was designed to collect and aggregate informed opinions and experiences from 40 international respondents who had demonstrable expertise related to motor learning in practice and/or research. The survey was administered through an online survey tool and addressed potential options and learning strategies for applying implicit and explicit motor learning. Responses were analysed in terms of consensus (≥ 70%) and trends (≥ 50%). A summary figure was developed to illustrate a taxonomy of the different learning strategies and options indicated by the experts in the survey.

Results

Answers of experts were widely distributed. No consensus was found regarding the application of implicit and explicit motor learning. Some trends were identified: Explicit motor learning can be promoted by using instructions and various types of feedback, but when promoting implicit motor learning, instructions and feedback should be restricted. Further, for implicit motor learning, an external focus of attention should be considered, as well as practicing the entire skill. Experts agreed on three factors that influence motor learning choices: the learner’s abilities, the type of task, and the stage of motor learning (94.5%; n = 34/36). Most experts agreed with the summary figure (64.7%; n = 22/34).

Conclusion

The results provide an overview of possible ways to cause implicit or explicit motor learning, signposting examples from practice and factors that influence day-to-day motor learning decisions.     

Awareness of Sensorimotor Adaptation to Visual Rotations of Different Size

Previous studies on sensorimotor adaptation revealed no awareness of the nature of the perturbation after adaptation to an abrupt 30° rotation of visual feedback or after adaptation to gradually introduced perturbations. Whether the degree of awareness depends on the magnitude of the perturbation, though, has as yet not been tested. Instead of using questionnaires, as was often done in previous work, the present study used a process dissociation procedure to measure awareness and unawareness. A naïve, implicit group and a group of subjects using explicit strategies adapted to 20°, 40° and 60° cursor rotations in different adaptation blocks that were each followed by determination of awareness and unawareness indices. The awareness index differed between groups and increased from 20° to 60° adaptation. In contrast, there was no group difference for the unawareness index, but it also depended on the size of the rotation. Early adaptation varied between groups and correlated with awareness: The more awareness a participant had developed the more the person adapted in the beginning of the adaptation block. In addition, there was a significant group difference for savings but it did not correlate with awareness. Our findings suggest that awareness depends on perturbation size and that aware and strategic processes are differentially involved during adaptation and savings. Moreover, the use of the process dissociation procedure opens the opportunity to determine awareness and unawareness indices in future sensorimotor adaptation research.     

Erasing Sensorimotor Memories via PKMζ Inhibition

Sensorimotor cortex has a role in procedural learning. Previous studies suggested that this learning is subserved by long-term potentiation (LTP), which is in turn maintained by the persistently active kinase, protein kinase Mzeta (PKMζ). Whereas the role of PKMζ in animal models of declarative knowledge is established, its effect on procedural knowledge is not well understood. Here we show that PKMζ inhibition, via injection of zeta inhibitory peptide (ZIP) into the rat sensorimotor cortex, disrupts sensorimotor memories for a skilled reaching task even after several weeks of training. The rate of relearning the task after the memory disruption by ZIP was indistinguishable from the rate of initial learning, suggesting no significant savings after the memory loss. These results indicate a shared molecular mechanism of storage for declarative and procedural forms of memory.     

Ganzfeld Stimulation or Sleep Enhance Long Term Motor Memory Consolidation Compared to Normal Viewing in Saccadic Adaptation Paradigm

Adaptation of saccade amplitude in response to intra-saccadic target displacement is a type of implicit motor learning which is required to compensate for physiological changes in saccade performance. Once established trials without intra-saccadic target displacement lead to de-adaptation or extinction, which has been attributed either to extra-retinal mechanisms of spatial constancy or to the influence of the stable visual surroundings. Therefore we investigated whether visual deprivation (“Ganzfeld”-stimulation or sleep) can partially maintain this motor learning compared to free viewing of the natural surroundings. Thirty-five healthy volunteers performed two adaptation blocks of 100 inward adaptation trials – interspersed by an extinction block – which were followed by a two-hour break with or without visual deprivation (VD). Using additional adaptation and extinction blocks short and long (4 weeks) term memory of this implicit motor learning were tested. In the short term, motor memory tested immediately after free viewing was superior to adaptation performance after VD. In the long run, however, effects were opposite: motor memory and relearning of adaptation was superior in the VD conditions. This could imply independent mechanisms that underlie the short-term ability of retrieving learned saccadic gain and its long term consolidation. We suggest that subjects mainly rely on visual cues (i.e., retinal error) in the free viewing condition which makes them prone to changes of the visual stimulus in the extinction block. This indicates the role of a stable visual array for resetting adapted saccade amplitudes. In contrast, visual deprivation (GS and sleep), might train subjects to rely on extra-retinal cues, e.g., efference copy or prediction to remap their internal representations of saccade targets, thus leading to better consolidation of saccadic adaptation.     

Interference and Shaping in Sensorimotor Adaptations with Rewards

When a perturbation is applied in a sensorimotor transformation task, subjects can adapt and maintain performance by either relying on sensory feedback, or, in the absence of such feedback, on information provided by rewards. For example, in a classical rotation task where movement endpoints must be rotated to reach a fixed target, human subjects can successfully adapt their reaching movements solely on the basis of binary rewards, although this proves much more difficult than with visual feedback. Here, we investigate such a reward-driven sensorimotor adaptation process in a minimal computational model of the task. The key assumption of the model is that synaptic plasticity is gated by the reward. We study how the learning dynamics depend on the target size, the movement variability, the rotation angle and the number of targets. We show that when the movement is perturbed for multiple targets, the adaptation process for the different targets can interfere destructively or constructively depending on the similarities between the sensory stimuli (the targets) and the overlap in their neuronal representations. Destructive interferences can result in a drastic slowdown of the adaptation. As a result of interference, the time to adapt varies non-linearly with the number of targets. Our analysis shows that these interferences are weaker if the reward varies smoothly with the subject''s performance instead of being binary. We demonstrate how shaping the reward or shaping the task can accelerate the adaptation dramatically by reducing the destructive interferences. We argue that experimentally investigating the dynamics of reward-driven sensorimotor adaptation for more than one sensory stimulus can shed light on the underlying learning rules.     

Differences in Context and Feedback Result in Different Trajectories and Adaptation Strategies in Reaching

Computational models of motor control have often explained the straightness of horizontal planar reaching movements as a consequence of optimal control. Departure from rectilinearity is thus regarded as sub-optimal. Here we examine if subjects may instead select to make curved trajectories following adaptation to force fields and visuomotor rotations. Separate subjects adapted to force fields with or without visual feedback of their hand trajectory and were retested after 24 hours. Following adaptation, comparable accuracies were achieved in two ways: with visual feedback, adapted trajectories in force fields were straight whereas without it, they remained curved. The results suggest that trajectory shape is not always straight, but is also influenced by the calibration of available feedback signals for the state estimation required by the task. In a follow-up experiment, where additional subjects learned a visuomotor rotation immediately after force field, the trajectories learned in force fields (straight or curved) were transferred when directions of the perturbations were similar but not when directions were opposing. This demonstrates a strong bias by prior experience to keep using a recently acquired control policy that continues to produce successful performance inspite of differences in tasks and feedback conditions. On relearning of force fields on the second day, facilitation by intervening visuomotor rotations occurred only when required motor adjustments and calibration of feedback signals were similar in both tasks. These results suggest that both the available feedback signals and prior history of learning influence the choice and maintenance of control policy during adaptations.     

Visual feedback is not necessary for the learning of novel dynamics

Background

When learning to perform a novel sensorimotor task, humans integrate multi-modal sensory feedback such as vision and proprioception in order to make the appropriate adjustments to successfully complete the task. Sensory feedback is used both during movement to control and correct the current movement, and to update the feed-forward motor command for subsequent movements. Previous work has shown that adaptation to stable dynamics is possible without visual feedback. However, it is not clear to what degree visual information during movement contributes to this learning or whether it is essential to the development of an internal model or impedance controller.

Methodology/Principle Findings

We examined the effects of the removal of visual feedback during movement on the learning of both stable and unstable dynamics in comparison with the case when both vision and proprioception are available. Subjects were able to learn to make smooth movements in both types of novel dynamics after learning with or without visual feedback. By examining the endpoint stiffness and force after learning it could be shown that subjects adapted to both types of dynamics in the same way whether they were provided with visual feedback of their trajectory or not. The main effects of visual feedback were to increase the success rate of movements, slightly straighten the path, and significantly reduce variability near the end of the movement.

Conclusions/Significance

These findings suggest that visual feedback of the hand during movement is not necessary for the adaptation to either stable or unstable novel dynamics. Instead vision appears to be used to fine-tune corrections of hand trajectory at the end of reaching movements.     

Expressions of multiple neuronal dynamics during sensorimotor learning in the motor cortex of behaving monkeys

Previous studies support the notion that sensorimotor learning involves multiple processes. We investigated the neuronal basis of these processes by recording single-unit activity in motor cortex of non-human primates (Macaca fascicularis), during adaptation to force-field perturbations. Perturbed trials (reaching to one direction) were practiced along with unperturbed trials (to other directions). The number of perturbed trials relative to the unperturbed ones was either low or high, in two separate practice schedules. Unsurprisingly, practice under high-rate resulted in faster learning with more pronounced generalization, as compared to the low-rate practice. However, generalization and retention of behavioral and neuronal effects following practice in high-rate were less stable; namely, the faster learning was forgotten faster. We examined two subgroups of cells and showed that, during learning, the changes in firing-rate in one subgroup depended on the number of practiced trials, but not on time. In contrast, changes in the second subgroup depended on time and practice; the changes in firing-rate, following the same number of perturbed trials, were larger under high-rate than low-rate learning. After learning, the neuronal changes gradually decayed. In the first subgroup, the decay pace did not depend on the practice rate, whereas in the second subgroup, the decay pace was greater following high-rate practice. This group shows neuronal representation that mirrors the behavioral performance, evolving faster but also decaying faster at learning under high-rate, as compared to low-rate. The results suggest that the stability of a new learned skill and its neuronal representation are affected by the acquisition schedule.     

Multiple Motor Learning Strategies in Visuomotor Rotation

Background

When exposed to a continuous directional discrepancy between movements of a visible hand cursor and the actual hand (visuomotor rotation), subjects adapt their reaching movements so that the cursor is brought to the target. Abrupt removal of the discrepancy after training induces reaching error in the direction opposite to the original discrepancy, which is called an aftereffect. Previous studies have shown that training with gradually increasing visuomotor rotation results in a larger aftereffect than with a suddenly increasing one. Although the aftereffect difference implies a difference in the learning process, it is still unclear whether the learned visuomotor transformations are qualitatively different between the training conditions.

Methodology/Principal Findings

We examined the qualitative changes in the visuomotor transformation after the learning of the sudden and gradual visuomotor rotations. The learning of the sudden rotation led to a significant increase of the reaction time for arm movement initiation and then the reaching error decreased, indicating that the learning is associated with an increase of computational load in motor preparation (planning). In contrast, the learning of the gradual rotation did not change the reaction time but resulted in an increase of the gain of feedback control, suggesting that the online adjustment of the reaching contributes to the learning of the gradual rotation. When the online cursor feedback was eliminated during the learning of the gradual rotation, the reaction time increased, indicating that additional computations are involved in the learning of the gradual rotation.

Conclusions/Significance

The results suggest that the change in the motor planning and online feedback adjustment of the movement are involved in the learning of the visuomotor rotation. The contributions of those computations to the learning are flexibly modulated according to the visual environment. Such multiple learning strategies would be required for reaching adaptation within a short training period.     

Dynamics of Dual Prism Adaptation: Relating Novel Experimental Results to a Minimalistic Neural Model

In everyday life, humans interact with a dynamic environment often requiring rapid adaptation of visual perception and motor control. In particular, new visuo–motor mappings must be learned while old skills have to be kept, such that after adaptation, subjects may be able to quickly change between two different modes of generating movements (‘dual–adaptation’). A fundamental question is how the adaptation schedule determines the acquisition speed of new skills. Given a fixed number of movements in two different environments, will dual–adaptation be faster if switches (‘phase changes’) between the environments occur more frequently? We investigated the dynamics of dual–adaptation under different training schedules in a virtual pointing experiment. Surprisingly, we found that acquisition speed of dual visuo–motor mappings in a pointing task is largely independent of the number of phase changes. Next, we studied the neuronal mechanisms underlying this result and other key phenomena of dual–adaptation by relating model simulations to experimental data. We propose a simple and yet biologically plausible neural model consisting of a spatial mapping from an input layer to a pointing angle which is subjected to a global gain modulation. Adaptation is performed by reinforcement learning on the model parameters. Despite its simplicity, the model provides a unifying account for a broad range of experimental data: It quantitatively reproduced the learning rates in dual–adaptation experiments for both direct effect, i.e. adaptation to prisms, and aftereffect, i.e. behavior after removal of prisms, and their independence on the number of phase changes. Several other phenomena, e.g. initial pointing errors that are far smaller than the induced optical shift, were also captured. Moreover, the underlying mechanisms, a local adaptation of a spatial mapping and a global adaptation of a gain factor, explained asymmetric spatial transfer and generalization of prism adaptation, as observed in other experiments.     

Auditory-motor learning during speech production in 9-11-year-old children

Background

Hearing ability is essential for normal speech development, however the precise mechanisms linking auditory input and the improvement of speaking ability remain poorly understood. Auditory feedback during speech production is believed to play a critical role by providing the nervous system with information about speech outcomes that is used to learn and subsequently fine-tune speech motor output. Surprisingly, few studies have directly investigated such auditory-motor learning in the speech production of typically developing children.

Methodology/Principal Findings

In the present study, we manipulated auditory feedback during speech production in a group of 9–11-year old children, as well as in adults. Following a period of speech practice under conditions of altered auditory feedback, compensatory changes in speech production and perception were examined. Consistent with prior studies, the adults exhibited compensatory changes in both their speech motor output and their perceptual representations of speech sound categories. The children exhibited compensatory changes in the motor domain, with a change in speech output that was similar in magnitude to that of the adults, however the children showed no reliable compensatory effect on their perceptual representations.

Conclusions

The results indicate that 9–11-year-old children, whose speech motor and perceptual abilities are still not fully developed, are nonetheless capable of auditory-feedback-based sensorimotor adaptation, supporting a role for such learning processes in speech motor development. Auditory feedback may play a more limited role, however, in the fine-tuning of children''s perceptual representations of speech sound categories.     

When Money Is Not Enough: Awareness,Success, and Variability in Motor Learning

When performing a skill such as throwing a dart, many different combinations of joint motions suffice to hit the target. The motor system adapts rapidly to reduce bias in the desired outcome (i.e., the first-order moment of the error); however, the essence of skill is to produce movements with less variability (i.e., to reduce the second-order moment). It is easy to see how feedback about success or failure could sculpt performance to achieve this aim. However, it is unclear whether the dimensions responsible for success or failure need to be known explicitly by the subjects, or whether learning can proceed without explicit awareness of the movement parameters that need to change. Here, we designed a redundant, two-dimensional reaching task in which we could selectively manipulate task success and the variability of action outcomes, whilst also manipulating awareness of the dimension along which performance could be improved. Variability was manipulated either by amplifying natural errors, leaving the correlation between the executed movement and the visual feedback intact, or by adding extrinsic noise, decorrelating movement and feedback. We found that explicit, binary, feedback about success or failure was only sufficient for learning when participants were aware of the dimension along which motor behavior had to change. Without such awareness, learning was only present when extrinsic noise was added to the feedback, but not when task success or variability was manipulated in isolation; learning was also much slower. Our results highlight the importance of conscious awareness of the relevant dimension during motor learning, and suggest that higher-order moments of outcome signals are likely to play a significant role in skill learning in complex tasks.     

Ignored Faces Produce Figural Face Aftereffects

Following adaptation to faces with contracted (or expanded) internal features, faces previously perceived as normal appear distorted in the opposite direction. This figural face aftereffect suggests face-coding mechanisms adapt to changes in the spatial relations of features and/or the global structure of faces. Here, we investigated whether the figural aftereffect requires spatial attention. Participants ignored a distorted adapting face and performed a highly demanding letter-count task. Before and after adaptation, participants rated the normality of morphed distorted faces ranging from 50% contracted through undistorted to 50% expanded. A robust aftereffect was observed. These results suggest that the figural face aftereffect can occur in the absence of spatial attention, even when the attentional demands of the relevant task are high.     

Eye-Hand Coordination during Visuomotor Adaptation with Different Rotation Angles: Effects of Terminal Visual Feedback

This study examined adaptive changes of eye-hand coordination during a visuomotor rotation task under the use of terminal visual feedback. Young adults made reaching movements to targets on a digitizer while looking at targets on a monitor where the rotated feedback (a cursor) of hand movements appeared after each movement. Three rotation angles (30°, 75° and 150°) were examined in three groups in order to vary the task difficulty. The results showed that the 30° group gradually reduced direction errors of reaching with practice and adapted well to the visuomotor rotation. The 75° group made large direction errors of reaching, and the 150° group applied a 180° reversal shift from early practice. The 75°and 150° groups, however, overcompensated the respective rotations at the end of practice. Despite these group differences in adaptive changes of reaching, all groups gradually adapted gaze directions prior to reaching from the target area to the areas related to the final positions of reaching during the course of practice. The adaptive changes of both hand and eye movements in all groups mainly reflected adjustments of movement directions based on explicit knowledge of the applied rotation acquired through practice. Only the 30° group showed small implicit adaptation in both effectors. The results suggest that by adapting gaze directions from the target to the final position of reaching based on explicit knowledge of the visuomotor rotation, the oculomotor system supports the limb-motor system to make precise preplanned adjustments of reaching directions during learning of visuomotor rotation under terminal visual feedback.     

Remapping auditory-motor representations in voice production

Evidence regarding visually guided limb movements suggests that the motor system learns and maintains neural maps between motor commands and sensory feedback. Such systems are hypothesized to be used in a feed-forward control strategy that permits precision and stability without the delays of direct feedback control. Human vocalizations involve precise control over vocal and respiratory muscles. However, little is known about the sensorimotor representations underlying speech production. Here, we manipulated the heard fundamental frequency of the voice during speech to demonstrate learning of auditory-motor maps. Mandarin speakers repeatedly produced words with specific pitch patterns (tone categories). On each successive utterance, the frequency of their auditory feedback was increased by 1/100 of a semitone until they heard their feedback one full semitone above their true pitch. Subjects automatically compensated for these changes by lowering their vocal pitch. When feedback was unexpectedly returned to normal, speakers significantly increased the pitch of their productions beyond their initial baseline frequency. This adaptation was found to generalize to the production of another tone category. However, results indicate that a more robust adaptation was produced for the tone that was spoken during feedback alteration. The immediate aftereffects suggest a global remapping of the auditory-motor relationship after an extremely brief training period. However, this learning does not represent a complete transformation of the mapping; rather, it is in part target dependent.     

Learning the dynamics of reaching movements results in the modification of arm impedance and long-latency perturbation responses

 Some characteristics of arm movements that humans exhibit during learning the dynamics of reaching are consistent with a theoretical framework where training results in motor commands that are gradually modified to predict and compensate for novel forces that may act on the hand. As a first approximation, the motor control system behaves as an adapting controller that learns an internal model of the dynamics of the task. It approximates inverse dynamics and predicts motor commands that are appropriate for a desired limb trajectory. However, we had previously noted that subtle motion characteristics observed during changes in task dynamics challenged this simple model and raised the possibility that adaptation also involved sensory–motor feedback pathways. These pathways reacted to sensory feedback during the course of the movement. Here we hypothesize that adaptation to dynamics might also involve a modification of how the CNS responds to sensory feedback. We tested this through experiments that quantified how the motor system's response to errors during voluntary movements changed as it adapted to dynamics of a force field. We describe a nonlinear approach that approximates the impedance of the arm, i.e., force response as a function of arm displacement trajectory. We observe that after adaptation, the impedance function changes in a way that closely matches and counters the effect of the force field. This is particularly prominent in the long-latency (>100 ms) component of response to perturbations. Therefore, it appears that practice not only modifies the internal model with which the brain generates motor commands that initiate a movement, but also the internal model with which sensory feedback is integrated with the ongoing descending commands in order to respond to error during the movement. Received: 10 January 2001 / Accepted in revised form: 30 May 2001