Internal models in the cerebellum.

This review will focus on the possibility that the cerebellum contains an internal model or models of the motor apparatus. Inverse internal models can provide the neural command necessary to achieve some desired trajectory. First, we review the necessity of such a model and the evidence, based on the ocular following response, that inverse models are found within the cerebellar circuitry. Forward internal models predict the consequences of actions and can be used to overcome time delays associated with feedback control. Secondly, we review the evidence that the cerebellum generates predictions using such a forward model. Finally, we review a computational model that includes multiple paired forward and inverse models and show how such an arrangement can be advantageous for motor learning and control.

How are internal models of unstable tasks formed?

The results of recent studies suggest that humans can form internal models that they use in a feedforward manner to compensate for both stable and unstable dynamics. To examine how internal models are formed, we performed adaptation experiments in novel dynamics, and measured the endpoint force, trajectory and EMG during learning. Analysis of reflex feedback and change of feedforward commands between consecutive trials suggested a unified model of motor learning, which can coherently unify the learning processes observed in stable and unstable dynamics and reproduce available data on motor learning. To our knowledge, this algorithm, based on the concurrent minimization of (reflex) feedback and muscle activation, is also the first nonlinear adaptive controller able to stabilize unstable dynamics.

Internal Models, Vestibular Cognition, and Mental Imagery: Conceptual Considerations

Vestibular cognition has recently gained attention. Despite numerous experimental and clinical demonstrations, it is not yet clear what vestibular cognition really is. For future research in vestibular cognition, adopting a computational approach will make it easier to explore the underlying mech- anisms. Indeed, most modeling approaches in vestibular science include a top-down or a priori component. We review recent Bayesian optimal observer models, and discuss in detail the conceptual value of prior assumptions, likelihood and posterior estimates for research in vestibular cognition. We then consider forward models in vestibular processing, which are required in order to distinguish between sensory input that is induced by active self-motion, and sensory input that is due to passive self-motion. We suggest that forward models are used not only in the service of estimating sensory states but they can also be drawn upon in an offline mode (e.g., spatial perspective transformations), in which interaction with sensory input is not desired. A computational approach to vestibular cogni- tion will help to discover connections across studies, and it will provide a more coherent framework for investigating vestibular cognition.

Análisis del riesgo de contraparte a través del modelo estructural de Merton en el marco de Solvencia II

[ES] La entrada en vigor del proyecto de Solvencia II transformará por completo el sistema de determinación de las necesidades de capital del sector asegurador europeo. Recientemente se ha presentado el último estudio de impacto cuantitativo (QIS5), donde se establece la forma de cálculo del modelo estándar para la determinación de los requerimientos de capital. Este trabajo trata de analizar la adecuación de la calibración del riesgo de crédito de la contraparte mediante los modelos que se proponen en los últimos informes de impacto cuantitativo (cuarto y quinto). Para ello comparamos las necesidades de capital que se obtienen por ambas alternativas, frente a las que resultarían de aplicar un modelo de simulación basado en el enfoque estructural. Los resultados obtenidos muestran que el uso de probabilidades basadas en la metodología de Merton frente a aquellas basadas en ratings, dan lugar a requerimientos de capital sustancialmente mayores. Además, el modelo propuesto en QIS4 basado en la distribución de Vasicek no es adecuado cuando el número de contrapartes es reducido, situación habitual en el sector asegurador europeo. Por otra parte, la nueva propuesta (QIS5 o modelo de Ter Berg) es más versátil y adecuada que su antecesora pero requiere analizar con más detenimiento las hipótesis de calibración para de este modo aproximar mejor las estimaciones al riesgo realmente asumido.

Spinal circuits can accommodate interaction torques during multijoint limb movements

The dynamic interaction of limb segments during movements that involve multiple joints creates torques in one joint due to motion about another. Evidence shows that such interaction torques are taken into account during the planning or control of movement in humans. Two alternative hypotheses could explain the compensation of these dynamic torques. One involves the use of internal models to centrally compute predicted interaction torques and their explicit compensation through anticipatory adjustment of descending motor commands. The alternative, based on the equilibrium-point hypothesis, claims that descending signals can be simple and related to the desired movement kinematics only, while spinal feedback mechanisms are responsible for the appropriate creation and coordination of dynamic muscle forces. Partial supporting evidence exists in each case. However, until now no model has explicitly shown, in the case of the second hypothesis, whether peripheral feedback is really sufficient on its own for coordinating the motion of several joints while at the same time accommodating intersegmental interaction torques. Here we propose a minimal computational model to examine this question. Using a biomechanics simulation of a two-joint arm controlled by spinal neural circuitry, we show for the first time that it is indeed possible for the neuromusculoskeletal system to transform simple descending control signals into muscle activation patterns that accommodate interaction forces depending on their direction and magnitude. This is achieved without the aid of any central predictive signal. Even though the model makes various simplifications and abstractions compared to the complexities involved in the control of human arm movements, the finding lends plausibility to the hypothesis that some multijoint movements can in principle be controlled even in the absence of internal models of intersegmental dynamics or learned compensatory motor signals.

Representations of uncertainty in sensorimotor control.

Uncertainty is ubiquitous in our sensorimotor interactions, arising from factors such as sensory and motor noise and ambiguity about the environment. Setting it apart from previous theories, a quintessential property of the Bayesian framework for making inference about the state of world so as to select actions, is the requirement to represent the uncertainty associated with inferences in the form of probability distributions. In the context of sensorimotor control and learning, the Bayesian framework suggests that to respond optimally to environmental stimuli the central nervous system needs to construct estimates of the sensorimotor transformations, in the form of internal models, as well as represent the structure of the uncertainty in the inputs, outputs and in the transformations themselves. Here we review Bayesian inference and learning models that have been successful in demonstrating the sensitivity of the sensorimotor system to different forms of uncertainty as well as recent studies aimed at characterizing the representation of the uncertainty at different computational levels.

Fault-tolerant aspects of MPC

The various aspects of fault-tolerant control systems that have the ability to survive major equipment failures or damages are discussed. Model predictive control (MPC) offers a promising basis for fault-tolerant control. Failures can be dealt with by updating internal models and letting the on-line optimizer control the system in its new condition. Fault detection and isolation (FDI) and the management of complex models are two emerging technologies in this field.

Short- and long-term changes in joint co-contraction associated with motor learning as revealed from surface EMG.

In the field of motor control, two hypotheses have been controversial: whether the brain acquires internal models that generate accurate motor commands, or whether the brain avoids this by using the viscoelasticity of musculoskeletal system. Recent observations on relatively low stiffness during trained movements support the existence of internal models. However, no study has revealed the decrease in viscoelasticity associated with learning that would imply improvement of internal models as well as synergy between the two hypothetical mechanisms. Previously observed decreases in electromyogram (EMG) might have other explanations, such as trajectory modifications that reduce joint torques. To circumvent such complications, we required strict trajectory control and examined only successful trials having identical trajectory and torque profiles. Subjects were asked to perform a hand movement in unison with a target moving along a specified and unusual trajectory, with shoulder and elbow in the horizontal plane at the shoulder level. To evaluate joint viscoelasticity during the learning of this movement, we proposed an index of muscle co-contraction around the joint (IMCJ). The IMCJ was defined as the summation of the absolute values of antagonistic muscle torques around the joint and computed from the linear relation between surface EMG and joint torque. The IMCJ during isometric contraction, as well as during movements, was confirmed to correlate well with joint stiffness estimated using the conventional method, i.e., applying mechanical perturbations. Accordingly, the IMCJ during the learning of the movement was computed for each joint of each trial using estimated EMG-torque relationship. At the same time, the performance error for each trial was specified as the root mean square of the distance between the target and hand at each time step over the entire trajectory. The time-series data of IMCJ and performance error were decomposed into long-term components that showed decreases in IMCJ in accordance with learning with little change in the trajectory and short-term interactions between the IMCJ and performance error. A cross-correlation analysis and impulse responses both suggested that higher IMCJs follow poor performances, and lower IMCJs follow good performances within a few successive trials. Our results support the hypothesis that viscoelasticity contributes more when internal models are inaccurate, while internal models contribute more after the completion of learning. It is demonstrated that the CNS regulates viscoelasticity on a short- and long-term basis depending on performance error and finally acquires smooth and accurate movements while maintaining stability during the entire learning process.

Learning the dynamics of the external world: Brain inspired learning for robotic applications

Humans have exceptional abilities to learn new skills, manipulate tools and objects, and interact with our environment. In order to be successful at these tasks, our brain has become exceptionally well adapted to learning to deal not only with the complex dynamics of our own limbs but also with novel dynamics in the external world. While learning of these dynamics includes learning the complex time-varying forces at the end of limbs through the updating of internal models, it must also include learning the appropriate mechanical impedance in order to stabilize both the limb and any objects contacted in the environment. This article reviews the field of human learning by examining recent experimental evidence about adaptation to novel unstable dynamics and explores how this knowledge about the brain and neuro-muscular system can expand the learning capabilities of robotics and prosthetics. © 2006.