From Parallel Sequence Representations to Calligraphic Control: A Conspiracy of Neural Circuits

Calligraphic writing presents a rich set of challenges to the human movement control system. These challenges include: initial learning, and recall from memory, of prescribed stroke sequences; critical timing of stroke onsets and durations; fine control of grip and contact forces; and letter-form invariance under voluntary size scaling, which entails fine control of stroke direction and amplitude during recruitment and derecruitment of musculoskeletal degrees of freedom. Experimental and computational studies in behavioral neuroscience have made rapid progress toward explaining the learning, planning and contTOl exercised in tasks that share features with calligraphic writing and drawing. This article summarizes computational neuroscience models and related neurobiological data that reveal critical operations spanning from parallel sequence representations to fine force control. Part one addresses stroke sequencing. It treats competitive queuing (CQ) models of sequence representation, performance, learning, and recall. Part two addresses letter size scaling and motor equivalence. It treats cursive handwriting models together with models in which sensory-motor tmnsformations are performed by circuits that learn inverse differential kinematic mappings. Part three addresses fine-grained control of timing and transient forces, by treating circuit models that learn to solve inverse dynamics problems.National Institutes of Health (R01 DC02852

A Dynamic Approach to Rhythm in Language: Toward a Temporal Phonology

It is proposed that the theory of dynamical systems offers appropriate tools to model many phonological aspects of both speech production and perception. A dynamic account of speech rhythm is shown to be useful for description of both Japanese mora timing and English timing in a phrase repetition task. This orientation contrasts fundamentally with the more familiar symbolic approach to phonology, in which time is modeled only with sequentially arrayed symbols. It is proposed that an adaptive oscillator offers a useful model for perceptual entrainment (or `locking in') to the temporal patterns of speech production. This helps to explain why speech is often perceived to be more regular than experimental measurements seem to justify. Because dynamic models deal with real time, they also help us understand how languages can differ in their temporal detail---contributing to foreign accents, for example. The fact that languages differ greatly in their temporal detail suggests that these effects are not mere motor universals, but that dynamical models are intrinsic components of the phonological characterization of language.Comment: 31 pages; compressed, uuencoded Postscrip

A Compact Representation of Drawing Movements with Sequences of Parabolic Primitives

Some studies suggest that complex arm movements in humans and monkeys may optimize several objective functions, while others claim that arm movements satisfy geometric constraints and are composed of elementary components. However, the ability to unify different constraints has remained an open question. The criterion for a maximally smooth (minimizing jerk) motion is satisfied for parabolic trajectories having constant equi-affine speed, which thus comply with the geometric constraint known as the two-thirds power law. Here we empirically test the hypothesis that parabolic segments provide a compact representation of spontaneous drawing movements. Monkey scribblings performed during a period of practice were recorded. Practiced hand paths could be approximated well by relatively long parabolic segments. Following practice, the orientations and spatial locations of the fitted parabolic segments could be drawn from only 2–4 clusters, and there was less discrepancy between the fitted parabolic segments and the executed paths. This enabled us to show that well-practiced spontaneous scribbling movements can be represented as sequences (“words”) of a small number of elementary parabolic primitives (“letters”). A movement primitive can be defined as a movement entity that cannot be intentionally stopped before its completion. We found that in a well-trained monkey a movement was usually decelerated after receiving a reward, but it stopped only after the completion of a sequence composed of several parabolic segments. Piece-wise parabolic segments can be generated by applying affine geometric transformations to a single parabolic template. Thus, complex movements might be constructed by applying sequences of suitable geometric transformations to a few templates. Our findings therefore suggest that the motor system aims at achieving more parsimonious internal representations through practice, that parabolas serve as geometric primitives and that non-Euclidean variables are employed in internal movement representations (due to the special role of parabolas in equi-affine geometry)

\u3cem\u3eGRASP News\u3c/em\u3e: Volume 9, Number 1

The past year at the GRASP Lab has been an exciting and productive period. As always, innovation and technical advancement arising from past research has lead to unexpected questions and fertile areas for new research. New robots, new mobile platforms, new sensors and cameras, and new personnel have all contributed to the breathtaking pace of the change. Perhaps the most significant change is the trend towards multi-disciplinary projects, most notable the multi-agent project (see inside for details on this, and all the other new and on-going projects). This issue of GRASP News covers the developments for the year 1992 and the first quarter of 1993

Movement Timing and Invariance Arise from Several Geometries

Human movements show several prominent features; movement duration is nearly independent of movement size (the isochrony principle), instantaneous speed depends on movement curvature (captured by the 2/3 power law), and complex movements are composed of simpler elements (movement compositionality). No existing theory can successfully account for all of these features, and the nature of the underlying motion primitives is still unknown. Also unknown is how the brain selects movement duration. Here we present a new theory of movement timing based on geometrical invariance. We propose that movement duration and compositionality arise from cooperation among Euclidian, equi-affine and full affine geometries. Each geometry posses a canonical measure of distance along curves, an invariant arc-length parameter. We suggest that for continuous movements, the actual movement duration reflects a particular tensorial mixture of these canonical parameters. Near geometrical singularities, specific combinations are selected to compensate for time expansion or compression in individual parameters. The theory was mathematically formulated using Cartan's moving frame method. Its predictions were tested on three data sets: drawings of elliptical curves, locomotion and drawing trajectories of complex figural forms (cloverleaves, lemniscates and limaçons, with varying ratios between the sizes of the large versus the small loops). Our theory accounted well for the kinematic and temporal features of these movements, in most cases better than the constrained Minimum Jerk model, even when taking into account the number of estimated free parameters. During both drawing and locomotion equi-affine geometry was the most dominant geometry, with affine geometry second most important during drawing; Euclidian geometry was second most important during locomotion. We further discuss the implications of this theory: the origin of the dominance of equi-affine geometry, the possibility that the brain uses different mixtures of these geometries to encode movement duration and speed, and the ontogeny of such representations

How Spinal Neural Networks Reduce Discrepancies between Motor Intention and Motor Realization

This paper attempts a rational, step-by-step reconstruction of many aspects of the mammalian neural circuitry known to be involved in the spinal cord's regulation of opposing muscles acting on skeletal segments. Mathematical analyses and local circuit simulations based on neural membrane equations are used to clarify the behavioral function of five fundamental cell types, their complex connectivities, and their physiological actions. These cell types are: α-MNs, γ-MNs, IaINs, IbINs, and Renshaw cells. It is shown that many of the complexities of spinal circuitry are necessary to ensure near invariant realization of motor intentions when descending signals of two basic types independently vary over large ranges of magnitude and rate of change. Because these two types of signal afford independent control, or Factorization, of muscle LEngth and muscle TEnsion, our construction was named the FLETE model (Bullock and Grossberg, 1988b, 1989). The present paper significantly extends the range of experimental data encompassed by this evolving model.National Science Foundation (IRI-87-16960, IRI-90-24877); Instituto Tecnológico y de Estudios Superiores de Monterre