The composition of Event-B models

The transition from classical B [2] to the Event-B language and method [3] has seen the removal of some forms of model structuring and composition, with the intention of reinventing them in future. This work contributes to thatreinvention. Inspired by a proposed method for state-based decomposition and refinement [5] of an Event-B model, we propose a familiar parallel event composition (over disjoint state variable lists), and the less familiar event fusion (over intersecting state variable lists). A brief motivation is provided for these and other forms of composition of models, in terms of feature-based modelling. We show that model consistency is preserved under such compositions. More significantly we show that model composition preserves refinement

Integration of Gravitational Torques in Cerebellar Pathways Allows for the Dynamic Inverse Computation of Vertical Pointing Movements of a Robot Arm

Several authors suggested that gravitational forces are centrally represented in the brain for planning, control and sensorimotor predictions of movements. Furthermore, some studies proposed that the cerebellum computes the inverse dynamics (internal inverse model) whereas others suggested that it computes sensorimotor predictions (internal forward model).This study proposes a model of cerebellar pathways deduced from both biological and physical constraints. The model learns the dynamic inverse computation of the effect of gravitational torques from its sensorimotor predictions without calculating an explicit inverse computation. By using supervised learning, this model learns to control an anthropomorphic robot arm actuated by two antagonists McKibben artificial muscles. This was achieved by using internal parallel feedback loops containing neural networks which anticipate the sensorimotor consequences of the neural commands. The artificial neural networks architecture was similar to the large-scale connectivity of the cerebellar cortex. Movements in the sagittal plane were performed during three sessions combining different initial positions, amplitudes and directions of movements to vary the effects of the gravitational torques applied to the robotic arm. The results show that this model acquired an internal representation of the gravitational effects during vertical arm pointing movements.This is consistent with the proposal that the cerebellar cortex contains an internal representation of gravitational torques which is encoded through a learning process. Furthermore, this model suggests that the cerebellum performs the inverse dynamics computation based on sensorimotor predictions. This highlights the importance of sensorimotor predictions of gravitational torques acting on upper limb movements performed in the gravitational field

The Inactivation Principle: Mathematical Solutions Minimizing the Absolute Work and Biological Implications for the Planning of Arm Movements

An important question in the literature focusing on motor control is to determine which laws drive biological limb movements. This question has prompted numerous investigations analyzing arm movements in both humans and monkeys. Many theories assume that among all possible movements the one actually performed satisfies an optimality criterion. In the framework of optimal control theory, a first approach is to choose a cost function and test whether the proposed model fits with experimental data. A second approach (generally considered as the more difficult) is to infer the cost function from behavioral data. The cost proposed here includes a term called the absolute work of forces, reflecting the mechanical energy expenditure. Contrary to most investigations studying optimality principles of arm movements, this model has the particularity of using a cost function that is not smooth. First, a mathematical theory related to both direct and inverse optimal control approaches is presented. The first theoretical result is the Inactivation Principle, according to which minimizing a term similar to the absolute work implies simultaneous inactivation of agonistic and antagonistic muscles acting on a single joint, near the time of peak velocity. The second theoretical result is that, conversely, the presence of non-smoothness in the cost function is a necessary condition for the existence of such inactivation. Second, during an experimental study, participants were asked to perform fast vertical arm movements with one, two, and three degrees of freedom. Observed trajectories, velocity profiles, and final postures were accurately simulated by the model. In accordance, electromyographic signals showed brief simultaneous inactivation of opposing muscles during movements. Thus, assuming that human movements are optimal with respect to a certain integral cost, the minimization of an absolute-work-like cost is supported by experimental observations. Such types of optimality criteria may be applied to a large range of biological movements

Motion sickness induced by otolith stimulation is correlated with otolith-induced eye movements.

International audienceThis article addresses the relationships between motion sickness (MS) and three-dimensional (3D) ocular responses during otolith stimulation. A group of 19 healthy subjects was tested for motion sickness during a 16 min otolith stimulation induced by off-vertical axis rotation (OVAR) (constant velocity 60 degrees /s, frequency 0.16 Hz). For each subject, the MS induced during the session was quantified, and based on this quantification, the subjects were divided into two groups of less susceptible (MS-), and more susceptible (MS+) subjects. The angular eye velocity induced by the otolith stimulation was analyzed in order to identify a possible correlation between susceptibility to MS and 3D eye velocity. The main results show that: (1) MS significantly correlates in a multiple regression with several components of the horizontal vestibular eye movements i.e. positively with the velocity modulation (P<0.01) and bias (P<0.05) of the otolith ocular reflex and negatively with the time constant of the vestibulo-ocular reflex (P<0.01) and (2) the length of the resultant 3D eye velocity vector is significantly larger in the MS+ as compared with the MS- group. Based on these results we suggest that the CNS, including the velocity storage mechanism, reconstructs an eye velocity vector modulated by head position whose length might predict MS occurrence during OVAR

Trains with a view to sickness.

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Effect of gaze direction on neck muscle activity during cervical rotation

Control of the neck muscles is coordinated with the sensory organs of vision, hearing and balance. For instance, activity of splenius capitis (SC) is modified with gaze shift. This interaction between eye movement and neck muscle activity is likely to influence the control of neck movement. The aim of this study was to investigate the effect of eye position on neck muscle activity during cervical rotation. In eleven subjects we recorded electromyographic activity (EMG) of muscles that rotate the neck to the right [right obliquus capitis inferior (OI), multifides (MF), and SC, and left sternocleidomastoid (SCM)] with intramuscular or surface electrodes. In sitting, subjects rotated the neck in each direction to specific points in range that were held statically with gaze either fixed to a guide (at three different positions) that moved with the head to maintain a constant intra-orbit eye position or to a panel in front of the subject. Although right SC and left SCM EMG increased with rotation to the right, contrary to anatomical texts, OI EMG increased with both directions and MF EMG did not change from the activity recorded at rest. During neck rotation SCM and MF EMG was less when the eyes were maintained with a constant intra-orbit position that was opposite to the direction of rotation compared to trials in which the eyes were maintained in the same direction as the head movement. The inter-relationship between eye position and neck muscle activity may affect the control of neck posture and movement