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F A Mussa-Ivaldi

Publications and source records attributed to F A Mussa-Ivaldi.

9 recordsLinked to original sources
PubMed1992

From basis functions to basis fields: vector field approximation from sparse data.

Recent investigations (Poggio and Girosi 1990b) have pointed out the equivalence between a wide class of learning problems and the reconstruction of a real-valued function from a sparse set of data. However, in order to process sensory information and to generate purposeful actions living organisms must deal not only with real-valued functions but also with vector-valued mappings. Examples of such vector-valued mappings range from the optical flow fields associated with visual motion to the fields of mechanical forces produced by neuromuscular activation. In this paper, I discuss the issue of vector-field processing from a broad computational perspective. A variety of vector patterns can be efficiently represented by a combination of linearly independent vector fields that I call "basis fields". Basis fields offer in some cases a better alternative to treating each component of a vector as an independent scalar entity. In spite of its apparent simplicity, such a component-based representation is bound to change with any change of coordinates. In contrast, vector-valued primitives such as basis fields generate vector field representations that are invariant under coordinate transformations.

Animals↗
PubMed1992

Vector field approximation: a computational paradigm for motor control and learning.

Recent experiments in the spinalized frog (Bizzi et al. 1991) have shown that focal microstimulation of a site in the premotor layers in the lumbar grey matter of the spinal cord results in a field of forces acting on the frog's ankle and converging to a single equilibrium position. These experiments suggested that the neural circuits in the spinal cord are organized in a set of control modules that "store" a few limb postures in the form of convergent force fields acting on the limb's end-point. Here, we investigate how such postural modules can be combined by the central nervous system for generating and representing a wider repertoire of control patterns. Our work is related to some recent investigations by Poggio and Girosi (1990a, b) who have proposed to represent the task of learning scalar maps as a problem of surface approximation. Consistent both with this view and with our experimental findings in the spinal frog, we regard the issue of generating motor repertoires as a problem of vector-field approximation. To this end, we characterize the output of a control module as a "basis field" (Mussa-Ivaldi 1992), that is as the vectorial equivalent of a basis function. Our theoretical findings indicate that by combining basis fields, the central nervous system may achieve a number of goals such as (1) the generation of a wide repertoire of control patterns and (2) the representation of these control patterns with a set of coefficients that are invariant under coordinate transformations.

Animals↗
PubMed1991

Computations underlying the execution of movement: a biological perspective.

To execute voluntary movements, the central nervous system must transform the neural representation of the direction, amplitude, and velocity of the limb, represented by the activity of cortical and subcortical neurons, into signals that activate the muscles that move the limb. This task is equivalent to solving an "ill-posed" computational problem because the number of degrees of freedom of the musculoskeletal apparatus is much larger than that specified in the plan of action. Some of the mechanisms and circuitry underlying the transformation of motor plans into motor commands are described. A central feature of this transformation is a coarse map of limb postures in the premotor areas of the spinal cord. Vectorial combination of motor outputs among different areas of the spinal map may produce a large repertoire of motor behaviors.

Animals↗
PubMed1988

Do neurons in the motor cortex encode movement direction? An alternative hypothesis.

Previous investigations by Georgopoulos et al. of cell activities in the primate motor cortex during the execution of voluntary arm movements have shown that these cells are characterized by tuning properties related to the direction of hand trajectories. Here, it is demonstrated that these findings do not necessarily imply that cortical cells encode spatial features of hand movements and an alternative hypothesis is considered according to which cortical cells encode muscle state variables. It is shown that this hypothesis would lead both to the single-cell activities and to the population behaviors observed by Georgopoulos et al.

Animals↗
PubMed1987

Controlling multijoint motor behavior.

Much can be learned about the central nervous system from a study of motor coordination, but its true richness and complexity become evident only in a multiarticular system. Despite the intrinsic complexity of multiarticular actions, they offer an unparalleled opportunity to learn about the central nervous system in a quantitative and experimentally testable way. For example, the observation that unconstrained, unperturbed arm movements are coordinated in terms of hand motion shows that motor control is organized in a hierarchy of increasing levels of abstraction. These arm motions are organized as though a disembodied hand could be moved in space; the details of how this is to be achieved must then be supplied by a different level in the hierarchy. The essence of human behavior is its adaptability. Just as the true complexity of coordination is evident only in multiarticular actions, the sophistication and subtlety of adaptive behavior are evident only in dynamic, interactive tasks. A study of movement alone is not sufficient to understand this behavior. The dynamic response of the limbs becomes the overriding concern and must be controlled by the central nervous system. The dynamic response of a limb is usually associated with its posture, rather than its movement, but in a functional task such as the use of a tool, the postural dynamics are an integral part of the action. This perspective on motor behavior leads to some useful insights. Coordination is not a problem for movement alone; in a multiarticular system, even posture requires coordination and control. Muscles do not merely act reciprocally to generate forces about the joints; the net mechanical impedance of the limb may be controlled by synergistic activation of all muscles, including antagonists. Controlling dynamic behavior is a far more demanding task than controlling motion. Consequently, features of the neuromusculoskeletal system that appear to be redundant or unnecessary for movement control can play a functional role in controlling dynamic behavior. Polyarticular muscles contribute to the mechanical impedance in a unique way. Skeletal redundancies have a profound influence on all aspects of dynamic behavior, including the apparent inertia of the limbs. Redundancies are commonly perceived as a complicating factor in the control of motion, a problem that must be solved by the central nervous system. Rather than presenting a problem requiring solution, they may present a solution to a problem. Posture is not merely the outcome of a motor act; it is one of the important preparatory stages in the production of motor behavior.

Hand↗
PubMed1985

Neural, mechanical, and geometric factors subserving arm posture in humans.

When the hand is displaced from an equilibrium posture by an external disturbance, a force is generated to restore the original position. We developed a new experimental method to measure and represent the field of elastic forces associated with posture of the hand in the horizontal plane. While subjects maintained a given posture, small displacements of the hand along different directions were delivered by torque motors. The hand was held in the displaced positions and, at that time, we measured the corresponding restoring forces before the onset of any voluntary reaction. The stiffness in the vicinity of the hand equilibrium position was estimated by analyzing the force and displacement vectors. We chose to represent the stiffness both numerically, as a matrix, and graphically, as an ellipse characterized by three parameters: magnitude (the area), shape (the ratio of axis) and orientation (direction of the major axis). The latter representation captures the main geometrical features of the elastic force field associated with posture. We also evaluated the conservative and nonconservative components of this elastic force field. We found that the former were much larger than the latter and concluded that the behavior of the neuromuscular system of the multiarticular arm is predominantly spring-like. Our data indicated that the shape and orientation of the stiffness were invariant over subjects and over time. We also investigated the ability of our subjects to produce voluntary and adaptive changes in the stiffness. Our findings indicated that, when a disturbance acting along a fixed and predictable direction was imposed, the magnitude of the stiffness was increased but only minor changes in shape and orientation occurred. Taken together, all of these experiments represent a step toward the understanding of the interactions between geometrical and neural factors involved in maintaining hand posture and its interactions with the environment.

Adaptation, Physiological↗