Functional significance of stiffness in adaptation of multijoint arm movements to stable and unstable dynamics.

This study compared the mechanisms of adaptation to stable and unstable dynamics from the perspective of changes in joint mechanics. Subjects were instructed to make point to point movements in force fields generated by a robotic manipulandum which interacted with the arm in either a stable or an unstable manner. After subjects adjusted to the initial disturbing effects of the force fields they were able to produce normal straight movements to the target. In the case of the stable interaction, subjects modified the joint torques in order to appropriately compensate for the force field. No change in joint torque or endpoint force was required or observed in the case of the unstable interaction. After adaptation, the endpoint stiffness of the arm was measured by applying displacements to the hand in eight different directions midway through the movements. This was compared to the stiffness measured similarly during movements in a null force field. After adaptation, the endpoint stiffness under both the stable and unstable dynamics was modified relative to the null field. Adaptation to unstable dynamics was achieved by selective modification of endpoint stiffness in the direction of the instability. To investigate whether the change in endpoint stiffness could be accounted for by change in joint torque or endpoint force, we estimated the change in stiffness on each trial based on the change in joint torque relative to the null field. For stable dynamics the change in endpoint stiffness was accurately predicted. However, for unstable dynamics the change in endpoint stiffness could not be reproduced. In fact, the predicted endpoint stiffness was similar to that in the null force field. Thus, the change in endpoint stiffness seen after adaptation to stable dynamics was directly related to changes in net joint torque necessary to compensate for the dynamics in contrast to adaptation to unstable dynamics, where a selective change in endpoint stiffness occurred without any modification of net joint torque.

Different mechanisms involved in adaptation to stable and unstable dynamics.

Recently, we demonstrated that humans can learn to make accurate movements in an unstable environment by controlling magnitude, shape, and orientation of the endpoint impedance. Although previous studies of human motor learning suggest that the brain acquires an inverse dynamics model of the novel environment, it is not known whether this control mechanism is operative in unstable environments. We compared learning of multijoint arm movements in a "velocity-dependent force field" (VF), which interacted with the arm in a stable manner, and learning in a "divergent force field" (DF), where the interaction was unstable. The characteristics of error evolution were markedly different in the 2 fields. The direction of trajectory error in the DF alternated to the left and right during the early stage of learning; that is, signed error was inconsistent from movement to movement and could not have guided learning of an inverse dynamics model. This contrasted sharply with trajectory error in the VF, which was initially biased and decayed in a manner that was consistent with rapid feedback error learning. EMG recorded before and after learning in the DF and VF are also consistent with different learning and control mechanisms for adapting to stable and unstable dynamics, that is, inverse dynamics model formation and impedance control. We also investigated adaptation to a rotated DF to examine the interplay between inverse dynamics model formation and impedance control. Our results suggest that an inverse dynamics model can function in parallel with an impedance controller to compensate for consistent perturbing force in unstable environments.

Adaptation to stable and unstable dynamics achieved by combined impedance control and inverse dynamics model.

This study compared adaptation in novel force fields where trajectories were initially either stable or unstable to elucidate the processes of learning novel skills and adapting to new environments. Subjects learned to move in a null force field (NF), which was unexpectedly changed either to a velocity-dependent force field (VF), which resulted in perturbed but stable hand trajectories, or a position-dependent divergent force field (DF), which resulted in unstable trajectories. With practice, subjects learned to compensate for the perturbations produced by both force fields. Adaptation was characterized by an initial increase in the activation of all muscles followed by a gradual reduction. The time course of the increase in activation was correlated with a reduction in hand-path error for the DF but not for the VF. Adaptation to the VF could have been achieved solely by formation of an inverse dynamics model and adaptation to the DF solely by impedance control. However, indices of learning, such as hand-path error, joint torque, and electromyographic activation and deactivation suggest that the CNS combined these processes during adaptation to both force fields. Our results suggest that during the early phase of learning there is an increase in endpoint stiffness that serves to reduce hand-path error and provides additional stability, regardless of whether the dynamics are stable or unstable. We suggest that the motor control system utilizes an inverse dynamics model to learn the mean dynamics and an impedance controller to assist in the formation of the inverse dynamics model and to generate needed stability.

Generalization in Adaptation to Stable and Unstable Dynamics

Humans skillfully manipulate objects and tools despite the inherent instability. In order to succeed at these tasks, the sensorimotor control system must build an internal representation of both the force and mechanical impedance. As it is not practical to either learn or store motor commands for every possible future action, the sensorimotor control system generalizes a control strategy for a range of movements based on learning performed over a set of movements. Here, we introduce a computational model for this learning and generalization, which specifies how to learn feedforward muscle activity in a function of the state space. Specifically, by incorporating co-activation as a function of error into the feedback command, we are able to derive an algorithm from a gradient descent minimization of motion error and effort, subject to maintaining a stability margin. This algorithm can be used to learn to coordinate any of a variety of motor primitives such as force fields, muscle synergies, physical models or artificial neural networks. This model for human learning and generalization is able to adapt to both stable and unstable dynamics, and provides a controller for generating efficient adaptive motor behavior in robots. Simulation results exhibit predictions consistent with all experiments on learning of novel dynamics requiring adaptation of force and impedance, and enable us to re-examine some of the previous interpretations of experiments on generalization. © 2012 Kadiallah et al.

The Personal and Professional Selves of Teachers: Stable and Unstable Identities

In much educational literature it is recognised that the broader social conditions in which teachers live and work, and the personal and professional elements of teachers' lives, experiences, beliefs and practices are integral to one another, and that there are often tensions between these which impact to a greater or lesser extent upon teachers' sense of self or identity. If identity is a key influencing factor on teachers' sense of purpose, self‐efficacy, motivation, commitment, job satisfaction and effectiveness, then investigation of those factors which influence positively and negatively, the contexts in which these occur and the consequences for practice, is essential. Surprisingly, although notions of ‘self’ and personal identity are much used in educational research and theory, critical engagement with individual teachers' cognitive and emotional ‘selves’ has been relatively rare. Yet such engagement is important to all with an interest in raising and sustaining standards of teaching, particularly in centralist reform contexts which threaten to destabilise long‐held beliefs and practices. This article addresses the issue of teacher identities by drawing together research which examines the nature of the relationships between social structures and individual agency; between notions of a socially constructed, and therefore contingent and ever‐remade, ‘self’, and a ‘self’ with dispositions, attitudes and behavioural responses which are durable and relatively stable; and between cognitive and emotional identities. Drawing upon existing research literature and findings from a four‐year Department for Education and Skills funded project with 300 teachers in 100 schools which investigated variations in teachers' work and lives and their effects on pupils (VITAE), it finds that identities are neither intrinsically stable nor intrinsically fragmented, as earlier literature suggests. Rather, teacher identities may be more, or less, stable and more or less fragmented at different times and in different ways according to a number of life, career and situational factors.

A general stability criterion for switched linear systems having stable and unstable subsystems

We report conditions on a switching signal that guarantee that solutions of a switched linear systems converge asymptotically to zero. These conditions are apply to continuous, discrete-time and hybrid switched linear systems, both those having stable subsystems and mixtures of stable and unstable subsystems.

Epigenetic phenotypes distinguish microsatellite-stable and -unstable colorectal cancers

Aberrant DNA methylation is a common phenomenon in human cancer, but its patterns, causes, and consequences are poorly defined. Promoter methylation of the DNA mismatch repair gene MutL homologue (MLH1) has been implicated in the subset of colorectal cancers that shows microsatellite instability (MSI). The present analysis of four MspI/HpaII sites at the MLH1 promoter region in a series of 89 sporadic colorectal cancers revealed two main methylation patterns that closely correlated with the MSI status of the tumors. These sites were hypermethylated in tumor tissue relative to normal mucosa in most MSI(+) cases (31/51, 61%). By contrast, in the majority of MSI(−) cases (20/38, 53%) the same sites showed methylation in normal mucosa and hypomethylation in tumor tissue. Hypermethylation displayed a direct correlation with increasing age and proximal location in the bowel and was accompanied by immunohistochemically documented loss of MLH1 protein both in tumors and in normal tissue. Similar patterns of methylation were observed in the promoter region of the calcitonin gene that does not have a known functional role in tumorigenesis. We propose a model of carcinogenesis where different epigenetic phenotypes distinguish the colonic mucosa in individuals who develop MSI(+) and MSI(−) tumors. These phenotypes may underlie the different developmental pathways that are known to occur in these tumors.

Inflammation, complement activation and endothelial function in stable and unstable coronary artery disease

Background: Endothelial dysfunction plays an important role in the pathogenesis of coronary artery disease (CAD). Apart from traditional risk factors complement activation and inflammation may trigger and sustain endothelial dysfunction. We sought to assess the association between endothelial function, high sensitivity C-reactive protein (hs-CRP) and markers of complement activation in patients with either stable or unstable coronary artery disease. Methods: We prospectively recruited 78 patients, 35 patients with stable angina pectoris (SAP) and 43 patients with unstable angina pectoris (UAP). Endothelial function was assessed as brachial artery reactivity (BAR). Hs-CRP, C3a, C5a, and C1-Inhibitor (C1 inh.) were measured enzymatically. Results: Patients with IJAP showed higher median levels of hs-CRP and C3a compared to patients with SAP, while BAR was not significantly different between patient groups. In UAP patients, hs-CRP was significantly correlated with cholesterol (r = 0.27, p < 0.02), C3a (r = 0.32, p < 0.001) and C1 INH.(r = 0.41, p < 0.003), but not with flow mediated dilatation (r = 0.09, P = 0.41). Hs-CRP and C1 INH.were found to be independant predictors of IJAP in a backward stepwise logistic regression model. Conclusions: We conclude that both hs-CRP, a marker of inflammation and C3a, a marker of complement activation are elevated in patients with UAP, but not in patients with SAP. (c) 2005 Elsevier B.V. All rights reserved.

A method to find unstable periodic orbits for the diamagnetic Kepler problem

A method to determine the admissibility of symbolic sequences and to find the unstable periodic orbits corresponding to allowed symbolic sequences for the diamagnetic Kepler problem is proposed by using the ordering of stable and unstable manifolds. By investigating the unstable periodic orbits up to length 6, a one to one correspondence between the unstable periodic orbits and their corresponding symbolic sequences is shown under the system symmetry decomposition.

The Construction of Arbitrary Stable Dynamics in Non-Linear Neural Networks

In this paper, two methods for constructing systems of ordinary differential equations realizing any fixed finite set of equilibria in any fixed finite dimension are introduced; no spurious equilibria are possible for either method. By using the first method, one can construct a system with the fewest number of equilibria, given a fixed set of attractors. Using a strict Lyapunov function for each of these differential equations, a large class of systems with the same set of equilibria is constructed. A method of fitting these nonlinear systems to trajectories is proposed. In addition, a general method which will produce an arbitrary number of periodic orbits of shapes of arbitrary complexity is also discussed. A more general second method is given to construct a differential equation which converges to a fixed given finite set of equilibria. This technique is much more general in that it allows this set of equilibria to have any of a large class of indices which are consistent with the Morse Inequalities. It is clear that this class is not universal, because there is a large class of additional vector fields with convergent dynamics which cannot be constructed by the above method. The easiest way to see this is to enumerate the set of Morse indices which can be obtained by the above method and compare this class with the class of Morse indices of arbitrary differential equations with convergent dynamics. The former set of indices are a proper subclass of the latter, therefore, the above construction cannot be universal. In general, it is a difficult open problem to construct a specific example of a differential equation with a given fixed set of equilibria, permissible Morse indices, and permissible connections between stable and unstable manifolds. A strict Lyapunov function is given for this second case as well. This strict Lyapunov function as above enables construction of a large class of examples consistent with these more complicated dynamics and indices. The determination of all the basins of attraction in the general case for these systems is also difficult and open.

Dynamics of a spacecraft and normalization around Lagrangian points in the Neptune-Triton system

The problem of a spacecraft orbiting the Neptune-Triton system is presented. The new ingredients in this restricted three body problem are the Neptune oblateness and the high inclined and retrograde motion of Triton. First we present some interesting simulations showing the role played by the oblateness on a Neptune's satellite, disturbed by Triton. We also give an extensive numerical exploration in the case when the spacecraft orbits Triton, considering Sun, Neptune and its planetary oblateness as disturbers. In the plane a x I (a = semi-major axis, I = inclination), we give a plot of the stable regions where the massless body can survive for thousand of years. Retrograde and direct orbits were considered and as usual, the region of stability is much more significant for the case of direct orbit of the spacecraft (Triton's orbit is retrograde). Next we explore the dynamics in a vicinity of the Lagrangian points. The Birkhoff normalization is constructed around L-2, followed by its reduction to the center manifold. In this reduced dynamics, a convenient Poincare section shows the interplay of the Lyapunov and halo periodic orbits, Lissajous and quasi-halo tori as well as the stable and unstable manifolds of the planar Lyapunov orbit. To show the effect of the oblateness, the planar Lyapunov family emanating from the Lagrangian points and three-dimensional halo orbits are obtained by the numerical continuation method. Published by Elsevier Ltd. on behalf of COSPAR.