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.

The VITEWRITE Model of Handwriting Production

This article describes the VITEWRITE model for generating handwriting movements. The model consists of a sequential controller, or motor program, that interacts with a trajectory generator to move a hand with redundant degrees of freedom. The neural trajectory generator is the Vector Integration to Endpoint (VITE) model for synchronous variable-speed control of multijoint movements. VITE properties enable a simple control strategy to generate complex handwritten script if the hand model contains redundant degrees of freedom. The controller launches transient directional commands to independent hand synergies at times when the hand begins to move, or when a velocity peak in the outflow command to a given synergy occurs. The VITE model translates these temporally disjoint synergy commands into smooth curvilinear trajectories among temporally overlapping synergetic movements. Each synergy exhibits a unimodal velocity profile during any stroke, generates letters that are invariant under speed and size rescaling, and enables effortless connection of letter shapes into words. Speed and size rescaling are achieved by scalar GO and GRO signals that express computationally simple volitional commands. Psychophysical data such as the isochrony principle, asymmetric velocity profiles, and the two-thirds power law relating movement curvature and velocity arise as emergent properties of model interactions.

A Self-Organizing Neural Model of Motor Equivalent Reaching and Tool Use by a Multijoint Arm

This paper describes a self-organizing neural model for eye-hand coordination. Called the DIRECT model, it embodies a solution of the classical motor equivalence problem. Motor equivalence computations allow humans and other animals to flexibly employ an arm with more degrees of freedom than the space in which it moves to carry out spatially defined tasks under conditions that may require novel joint configurations. During a motor babbling phase, the model endogenously generates movement commands that activate the correlated visual, spatial, and motor information that are used to learn its internal coordinate transformations. After learning occurs, the model is capable of controlling reaching movements of the arm to prescribed spatial targets using many different combinations of joints. When allowed visual feedback, the model can automatically perform, without additional learning, reaches with tools of variable lengths, with clamped joints, with distortions of visual input by a prism, and with unexpected perturbations. These compensatory computations occur within a single accurate reaching movement. No corrective movements are needed. Blind reaches using internal feedback have also been simulated. The model achieves its competence by transforming visual information about target position and end effector position in 3-D space into a body-centered spatial representation of the direction in 3-D space that the end effector must move to contact the target. The spatial direction vector is adaptively transformed into a motor direction vector, which represents the joint rotations that move the end effector in the desired spatial direction from the present arm configuration. Properties of the model are compared with psychophysical data on human reaching movements, neurophysiological data on the tuning curves of neurons in the monkey motor cortex, and alternative models of movement control.

Quantum Monte Carlo in the Interaction Representation --- Application to a Spin-Peierls Model

A quantum Monte Carlo algorithm is constructed starting from the standard perturbation expansion in the interaction representation. The resulting configuration space is strongly related to that of the Stochastic Series Expansion (SSE) method, which is based on a direct power series expansion of exp(-beta*H). Sampling procedures previously developed for the SSE method can therefore be used also in the interaction representation formulation. The new method is first tested on the S=1/2 Heisenberg chain. Then, as an application to a model of great current interest, a Heisenberg chain including phonon degrees of freedom is studied. Einstein phonons are coupled to the spins via a linear modulation of the nearest-neighbor exchange. The simulation algorithm is implemented in the phonon occupation number basis, without Hilbert space truncations, and is exact. Results are presented for the magnetic properties of the system in a wide temperature regime, including the T-->0 limit where the chain undergoes a spin-Peierls transition. Some aspects of the phonon dynamics are also discussed. The results suggest that the effects of dynamic phonons in spin-Peierls compounds such as GeCuO3 and NaV2O5 must be included in order to obtain a correct quantitative description of their magnetic properties, both above and below the dimerization temperature.

Tracking Human Body Pose on a Learned Smooth Space

Particle filtering is a popular method used in systems for tracking human body pose in video. One key difficulty in using particle filtering is caused by the curse of dimensionality: generally a very large number of particles is required to adequately approximate the underlying pose distribution in a high-dimensional state space. Although the number of degrees of freedom in the human body is quite large, in reality, the subset of allowable configurations in state space is generally restricted by human biomechanics, and the trajectories in this allowable subspace tend to be smooth. Therefore, a framework is proposed to learn a low-dimensional representation of the high-dimensional human poses state space. This mapping can be learned using a Gaussian Process Latent Variable Model (GPLVM) framework. One important advantage of the GPLVM framework is that both the mapping to, and mapping from the embedded space are smooth; this facilitates sampling in the low-dimensional space, and samples generated in the low-dimensional embedded space are easily mapped back into the original highdimensional space. Moreover, human body poses that are similar in the original space tend to be mapped close to each other in the embedded space; this property can be exploited when sampling in the embedded space. The proposed framework is tested in tracking 2D human body pose using a Scaled Prismatic Model. Experiments on real life video sequences demonstrate the strength of the approach. In comparison with the Multiple Hypothesis Tracking and the standard Condensation algorithm, the proposed algorithm is able to maintain tracking reliably throughout the long test sequences. It also handles singularity and self occlusion robustly.

A Neural Network Model for Cursive Script Production

This article describes a neural network model, called the VITEWRITE model, for generating handwriting movements. The model consists of a sequential controller, or motor program, that interacts with a trajectory generator to move a. hand with redundant degrees of freedom. The neural trajectory generator is the Vector Integration to Endpoint (VITE) model for synchronous variable-speed control of multijoint movements. VITE properties enable a simple control strategy to generate complex handwritten script if the hand model contains redundant degrees of freedom. The proposed controller launches transient directional commands to independent hand synergies at times when the hand begins to move, or when a velocity peak in a given synergy is achieved. The VITE model translates these temporally disjoint synergy commands into smooth curvilinear trajectories among temporally overlapping synergetic movements. The separate "score" of onset times used in most prior models is hereby replaced by a self-scaling activity-released "motor program" that uses few memory resources, enables each synergy to exhibit a unimodal velocity profile during any stroke, generates letters that are invariant under speed and size rescaling, and enables effortless. connection of letter shapes into words. Speed and size rescaling are achieved by scalar GO and GRO signals that express computationally simple volitional commands. Psychophysical data concerning band movements, such as the isochrony principle, asymmetric velocity profiles, and the two-thirds power law relating movement curvature and velocity arise as emergent properties of model interactions.