A theory for cursive handwriting based on the minimization principle

 We propose a trajectory planning and control theory which provides explanations at the computation, algorithm, representation, and hardware levels for continuous movement such as connected cursive handwriting. The hardware is based on our previously proposed forward-inverse-relaxation neural network. Computationally, the optimization principle is the minimum torque-change criterion. At the representation level, hard constraints satisfied by a trajectory are represented as a set of via-points extracted from handwritten characters. Accordingly, we propose a via-point estimation algorithm that estimates via-points by repeating trajectory formation of a character and via-point extraction from the character. It is shown experimentally that for movements with a single via-point target, the via-point estimation algorithm can assign a point near the actual via-point target. Good quantitative agreement is found between human movement data and the trajectories generated by the proposed model. Received: 23 June 1994 / Accepted in revised form: 3 February 1995     

Dynamic optimization of the sit-to-stand movement

The purpose of this study was to clarify criteria that can predict trajectories during the sit-to-stand movement. In particular, the minimum jerk and minimum torque-change models were examined. Three patterns of sit-to-stand movement from a chair, i.e., upright, natural, and leaning forward, were measured in five young participants using a 3-D motion analysis device (200 Hz). The trajectory of the center of mass and its smoothness were examined, and the optimal trajectories predicted by both models were evaluated. Trajectories of the center of mass predicted by the minimum torque-change model, rather than the minimum jerk model, resembled the measured movements in all rising movement patterns. The upright pattern required greater extension torque of the knee and ankle joints at the instant of seat-off. The leaning-forward pattern required greater extension hip torque and higher movement cost than the natural and upright patterns. These results indicate that the natural sit-to-stand movement might be a result of dynamic optimization.     

Trajectory formation of arm movement by cascade neural network model based on minimum torque-change criterion

We proposed that the trajectory followed by human subject arms tended to minimize the time integral of the square of the rate of change of torque (Uno et al. 1987). This minimum torque-change model predicted and reproduced human multi-joint movement data quite well (Uno et al. 1989). Here, we propose a neural network model for trajectory formation based on the minimum torque-change criterion. Basic ideas of information representation and algorithm are(i) spatial representation of time,(ii) learning of forward dynamics and kinetics model and(iii) relaxation computation based on the acquired model. The model can resolve ill-posed inverse kinematics and inverse dynamics problems for redundant controlled object as well as ill-posed trajectory formation problems. By computer simulation, we show that the model can produce a multi-joint arm trajectory while avoiding obstacles or passing through viapoints.     

Formation and control of optimal trajectory in human multijoint arm movement

In this paper, we study trajectory planning and control in voluntary, human arm movements. When a hand is moved to a target, the central nervous system must select one specific trajectory among an infinite number of possible trajectories that lead to the target position. First, we discuss what criterion is adopted for trajectory determination. Several researchers measured the hand trajectories of skilled movements and found common invariant features. For example, when moving the hand between a pair of targets, subjects tended to generate roughly straight hand paths with bell-shaped speed profiles. On the basis of these observations and dynamic optimization theory, we propose a mathematical model which accounts for formation of hand trajectories. This model is formulated by defining an objective function, a measure of performance for any possible movement: square of the rate of change of torque integrated over the entire movement. That is, the objective function CT is defined as follows: (formula; see text) We overcome this difficult by developing an iterative scheme, with which the optimal trajectory and the associated motor command are simultaneously computed. To evaluate our model, human hand trajectories were experimentally measured under various behavioral situations. These results supported the idea that the human hand trajectory is planned and controlled in accordance with the minimum torque-change criterion.     

Optimal control of antagonistic muscle stiffness during voluntary movements

This paper presents a study on the control of antagonist muscle stiffness during single-joint arm movements by optimal control theory with a minimal effort criterion. A hierarchical model is developed based on the physiology of the neuromuscular control system and the equilibrium point hypothesis. For point-to-point movements, the model provides predictions on (1) movement trajectory, (2) equilibrium trajectory, (3) muscle control inputs, and (4) antagonist muscle stiffness, as well as other variables. We compared these model predictions to the behavior observed in normal human subjects. The optimal movements capture the major invariant characteristics of voluntary movements, such as a sigmoidal movement trajectory with a bell-shaped velocity profile, an N-shaped equilibrium trajectory, a triphasic burst pattern of muscle control inputs, and a dynamically modulated joint stiffness. The joint stiffness is found to increase in the middle of the movement as a consequence of the triphasic muscle activities. We have also investigated the effects of changes in model parameters on movement control. We found that the movement kinematics and muscle control inputs are strongly influenced by the upper bound of the descending excitation signal that activates motoneuron pools in the spinal cord. Furthermore, a class of movements with scaled velocity profiles can be achieved by tuning the amplitude and duration of this excitation signal. These model predictions agree with a wide body of experimental data obtained from normal human subjects. The results suggest that the control of fast arm movements involves explicit planning for both the equilibrium trajectory and joint stiffness, and that the minimal effort criterion best characterizes the objective of movement planning and control.     

Temporal pattern discrimination of impulse sequences in the computer-simulated nerve cells

This paper deals with some properties of temporal pattern discrimination performed by single digital-computer simulated synaptic cells. To clarify these properties, the Shannon's entropy method which is a basic notion in the information theory and a fundamental approach for the design of pattern classification system was applied to input-output relations of the digital computer simulated synaptic cells. We used the average mutual information per symbol as a measure for the temporal pattern sensitivity of the nerve cells, and the average response entropy per symbol as a measure for the frequency transfer characteristics. To use these measures, the probability of a post-synaptic spike as a function of the recent history of pre-synaptic intervals was examined in detail. As the results of such application, it was found that the EPSP size is closely related to the pattern of impulse sequences of the input, and the average mutual information per symbol for EPSP size is given by a bimodal curve with two maximum values. One is a small EPSP size and the other is a large EPSP size. In two maximum points, the structure of the temporal pattern discrimination reverses each other. In addition, the relation between the mean frequency, or the form of impulse sequences of the input, and the average mutual information per symbol has been examined. The EPSP size at one maximum point of average mutual information is in inverse proportion to the magnitude of input mean frequency which relates to the convergence number of input terminal, while that at the other maximum point is proportional to that of the mean frequency. Moreover, the temporal pattern discrimination is affected remarkably by whether successive interspike intervals of the input are independent or not in the statistical sense. Computer experiments were performed by the semi-Markov processes with three typical types of transition matrixes and these shuffling processes. The average mutual informations in the cases of these semi-Markov processes are in contrast to those of the shuffling processes which provide a control case. The temporal structure of successive interspike intervals of the input is thus a significant factor in pattern discrimination at synaptic level.     

Dynamic response properties of movement detectors: Theoretical analysis and electrophysiological investigation in the visual system of the fly

Dynamic aspects of the computation of visual motion information are analysed both theoretically and experimentally. The theoretical analysis is based on the type of movement detector which has been proposed to be realized in the visual system of insects (e.g. Hassenstein and Reichardt 1956; Reichardt 1957, 1961; Buchner 1984), but also of man (e.g. van Doorn and Koenderink 1982a, b; van Santen and Sperling 1984; Wilson 1985). The output of both a single movement detector and a one-dimensional array of detectors is formulated mathematically as a function of time. The resulting movement detector theory can be applied to a much wider range of moving stimuli than has been possible on the basis of previous formulations of the detector output. These stimuli comprise one-dimensional smooth detector input functions, i.e. functions which can be expanded into a time-dependent convergent Taylor series for any value of the spatial coordinate.The movement detector response can be represented by a power series. Each term of this series consists of one exclusively time-dependent component and of another component that depends, in addition, on the properties of the pattern. Even the exclusively time-dependent components of the movement detector output are not solely determined by the stimulus velocity. They rather depend in a non-linear way on the weighted sum of the instantaneous velocity and all its higher order time derivatives. The latter point represents another reason — not discussed so far in the literature — that movement detectors of the type analysed here do not represent pure velocity sensors.The significance of this movement detector theory is established for the visual system of the fly. This is done by comparing the spatially integrated movement detector response with the functional properties of the directionally-selective motion-sensitive. Horizontal Cells of the third visual ganglion of the fly's brain.These integrate local motion information over large parts of the visual field. The time course of the spatially integrated movement detector response is about proportional to the velocity of the stimulus pattern only as long as the pattern velocity and its time derivatives are sufficiently small. For large velocities and velocity changes of the stimulus pattern characteristic deviations of the response profiles from being proportional to pattern velocity are predicted on the basis of the detector theory developed here. These deviations are clearly reflected in the response of the wide-field Horizontal Cells, thus, providing very specific evidence that the movement detector theory developed here can be applied to motion detection in the fly. The characteristic dynamic features of the theoretically predicted and the experimentally determined cellular responses are exploited to estimate the time constant of the movement detector filter.     

δ13C signature of organic carbon in estuarine bottom sediment as an indicator of carbon export from adjacent marshes

The ¹³C signature of organic carbon in estuarine bottom sediment in Louisiana Barataria Basin was used for estimating carbon flux from adjacent marsh. The stable carbon isotope composition of plants, soils and sediments from the basin were determined. The ¹³C content of marsh vegetation ranged from -26.3 to -27.8% for C₃ freshwater vegetation in the upper basin to -13.0 to -13.3% for C₄ vegetation in the lower basin. The ¹³C content of the highly organic marsh soils were similar to ¹³C content of vegetation present. The ¹³C content of organic carbon from bottom sediment of open water bodies ranged from 27.3 in the upper basin (freshwater) to 16.4 in bottom sediment of salt marsh ponds. The¹³C signature of organic carbon in bottom sediment from saline regions corresponded to the size of the body of water. The smaller salt marsh ponds contain sediment with ¹³C values close to that of the C₄ plantSpartina alterniflora. Results suggest that phytoplankton rather thanSpartina alterniffora is the likely organic source in bottom sediment of the larger bay near the coast (e.g. Caminada Bay).     

End-point constraints in aiming movements: effects of approach angle and speed

 The present study focuses on two trajectory-formation models of point-to-point aiming movements, viz., the minimum-jerk and the minimum torque-change model. To date, few studies on minimum-jerk and minimum torque-change trajectories have incorporated self- or externally imposed end-point constraints, such as the direction and velocity with which a target area is approached. To investigate which model accounts best for the effects on movement trajectories of such – in many circumstances – realistic end-point constraints, we adjusted both the minimum-jerk and the minimum torque-change model so that they could generate trajectories of which the final part has a specific direction and speed. The adjusted models yield realistic trajectories with a high curvature near movement completion. Comparison of simulated and measured movement trajectories show that pointing movements that are constrained with respect to final movement direction and speed can be described in terms of minimization of joint-torque changes. Received: 7 July 1999 / Accepted in revised form: 8 January 2001     

A model for size- and rotation-invariant pattern processing in the visual system

The mapping of retinal space onto the striate cortex of some mammals can be approximated by a log-polar function. It has been proposed that this mapping is of functional importance for scale-and rotation-invariant pattern recognition in the visual system. An exact log-polar transform converts centered scaling and rotation into translations. A subsequent translation-invariant transform, such as the absolute value of the Fourier transform, thus generates overall size-and rotation-invariance. In our model, the translation-invariance is realized via the R-transform. This transform can be executed by simple neural networks, and it does not require the complex computations of the Fourier transform, used in Mellin-transform size-invariance models. The logarithmic space distortion and differentiation in the first processing stage of the model is realized via Mexican hat filters whose diameter increases linearly with eccentricity, similar to the characteristics of the receptive fields of retinal ganglion cells. Except for some special cases, the model can explain object recognition independent of size, orientation and position. Some general problems of Mellin-type size-invariance models-that also apply to our model-are discussed.     

Elementary pattern discrimination (behavioural experiments with the fly Musca domestica)

This paper investigates the problem of spontaneous pattern discrimination by the visual system of the fly. The indicator for discrimination and attractivity of a pattern is the yaw torque of a test fly. It is shown that the pattern discrimination process may be treated as a special (degenerate) case of figureground discrimination which has been described in detail in earlier publications. Decisive for the discrimination process is the fact that pattern discrimination by the fly is mediated by motion detectors which respond not only a pattern velocity but also to structural properties of pattern contrast. This is demonstrated by the transition from the existing twodimensional array of motion detectors to a continuous detector field which enabled us to calculate instantaneous detector responses to instationary pattern motion. The new approach, together with the special theory for figure-ground discrimination, is then applied to predict spontaneous discriminations of onedimensional periodic patterns. It is shown that predictions and experimental results are in good agreement. The second set of discrimination experiments deals with two dimensional dot patterns for which a quantitative theory is not yet available. However, it is shown that the attractivity of a dot pattern crucially depends on both the orientation and the direction of motion relative to the fly's eyes. If the contrast of a moving dot elicits an event in a motion detector which through the detector's time constant leads to an interference with an event received by a preceeding dot, the attractivity of the dot pattern is diminished. In the discussion relations are drawn between the concepts of pattern discrimination in honey bees and the theoretical aspects of discrimination put forward in this paper. It is briefly discussed why a two-dimensional motion detector theory might become the key for an understanding of pattern categories like figural intensity and figural quality.     

Pattern of movement in and dispersal from a dutch forest of Carabus problematicus Hbst. (Coleoptera,Carabidae)

Summary Data in the literature that in the Netherlands Carabus problematicus is an autumn breeder with overwintering larvae and adults have been confirmed. Pitfall catches show two peaks of adult beetles. The first small peak of activity is realized in May, the significance of which is not yet understood. The second higher peak occurs from the end of August till the beginning of October: the reproduction period. In this period at least three age classes are present. Some females were shown to take part in reproduction for at least two seasons. Old females appeared to have less eggs in the ovaries than young ones. Larvae can be trapped throughout the winter. The new generation appears in July and in the beginning of August. They immediately take part in reproduction. C. problematicus shows noctural activity with a peak towards the end of the night.In field experiments the pattern of movement and the dispersal behaviour of marked individuals was investigated and related to the choice of habitat. It was shown that in the Netherlands C. problematicus prefers a forest habitat. Some individuals were found to disperse from their favoured habitat. The percentage of beetles that disperse out of the forest during the breeding season could be estimated at 4–8%. Dispersal increases in the second part of the breeding season. Females tend to disperse more frequently than males.The pattern of movement consists of two types: a random walk and a directed movement. It is suggested that the pattern of movement of individuals dispersing out of the forest is the directed movement. It could be shown that individuals released outside the forest were able to walk towards a forest silhouette. The significance of both the pattern of movement and the dispersal behaviour for the survival of the species is discuussed.Communication no. 212 of the Biological Station of the Agricultural University (Wageningen), Wijster (Drente), The Netherlands     

A three-dimensional data visualization technique for reporting movement pattern deviations

Relative motion plots are the most prevalent method for displaying interjoint coupling. The method, however, is limited when amplitude and timing comparisons of like data are of interest. Another limitation of relative motion plots is that the second parameter (e.g., angle) is included at the expense of a continuous time reference. In this paper, we present a novel method for displaying three-dimensional movement pattern deviations. Parameter-parameter-time data (e.g., knee and hip angle as a function of time) are color-coded based on the magnitude and direction of the deviation. The color-coded deviations are mapped to an individual's three-dimensional parameter-parameter-time trajectory, resulting in a multi-color, three-dimensional curve depicting how an individual's parameter-parameter-time pattern differs relative to a reference pattern. The algorithmic development of the color-coded parameter-parameter-time display is presented and comparative patient and normative data are reported.     

Independent pathways for water and solute movement across the cell membrane

Summary In published studies of the relationship between movement of nonelectrolytes across cell membranes and the lipid solubility of these test molecules, it is generally found that a number of the smaller, more water-soluble molecules deviate significantly from the general pattern relating permeability (or reflection coefficient) to lipid solubility. This is often true of the amides, for example, whose reflection coefficients are considerably lower than expected on the basis of lipid solubility. While this has been interpretep in terms of the movement of these solutes through aqueous channels in the membrane, it now appears that many of these deviant molecules may cross the membrane by means of carrier-mediated diffusion, independent of osmotic water flow. This has important implications for studies in which equivalent pore radius has been estimated from the reflection coefficients of small hydrophilic molecules, and for our present concepts of membrane structure.     

A novel model of motor learning capable of developing an optimal movement control law online from scratch

A computational model of a learning system (LS) is described that acquires knowledge and skill necessary for optimal control of a multisegmental limb dynamics (controlled object or CO), starting from knowing only the dimensionality of the objects state space. It is based on an optimal control problem setup different from that of reinforcement learning. The LS solves the optimal control problem online while practicing the manipulation of CO. The systems functional architecture comprises several adaptive components, each of which incorporates a number of mapping functions approximated based on artificial neural nets. Besides the internal model of the COs dynamics and adaptive controller that computes the control law, the LS includes a new type of internal model, the minimal cost (IM_mc) of moving the controlled object between a pair of states. That internal model appears critical for the LSs capacity to develop an optimal movement trajectory. The IM_mc interacts with the adaptive controller in a cooperative manner. The controller provides an initial approximation of an optimal control action, which is further optimized in real time based on the IM_mc. The IM_mc in turn provides information for updating the controller. The LSs performance was tested on the task of center-out reaching to eight randomly selected targets with a 2DOF limb model. The LS reached an optimal level of performance in a few tens of trials. It also quickly adapted to movement perturbations produced by two different types of external force field. The results suggest that the proposed design of a self-optimized control system can serve as a basis for the modeling of motor learning that includes the formation and adaptive modification of the plan of a goal-directed movement.     

A theory of the pattern induced flight orientation of the fly Musca domestica

The theory presented here describes the visual orientation behavior of fixed flying insects (the fly Musca domestica) in the presence of elementary patterns. The theory, which is based on a number of experimental results, Reichardt (1973), is a phenomenological one whose main purpose is to provide an organizational framework for treating a complex phenomenon without the need of detailed assumptions about the neural mechanisms actually involved.A simple hypothesis concerning the basic structure of the pattern fixation process leads to an equivalent stochastic equation of the Langevin type, which can be linearized for simple single-stripe panoramas. A critical experiment supports these theoretical assumptions. In addition, the effect on pattern fixation behavior of adding contrast noise to the background of the panorama, is quantitatively predicted by the theory.In the more general case of a panorama consisting of many vertical stripes, the Fokker-Planck equation associated with the Langevin equation, no longer linear, is solved. Making use of an experimentally proven superposition principle, the stationary pattern fixation behavior of the fly in an arbitrary panorama consisting of a collection of vertical stripes is predicted. In this context, concepts like pseudo-invariance and phase-transition can be applied to the insects orientation behavior. The theory presented here seems to contain rich classification properties, which might provide the foundations for an understanding of more complex pattern discrimination processes.Possible extensions of the theory, as well as some similarities to human eye fixation, are also discussed.     

Observation of yeast cell movement and aggregation in a small-scale MHz-ultrasonic standing wave field

Aggregation of suspended yeast cells in a small-scale ultrasonic standing wave field has been monitored and quantified. The aggregation effect is based on the acoustic radiation force, which concentrates the cells in clumps. The ultrasonic chamber employed (1.9 MHz, one wavelength pathlength) had a sonication volume of 60 l. The aggregation process was observed from above the transducer through a transparent glass reflector. A distinct, reproducible, pattern of clumps formed rapidly in the sound field. The sound pressure was estimated experimentally to be of the order of 1 MPa. Microscopic observations of the formation of a single clump were recorded onto a PC. The time dependent movement patterns and travelling velocities of the cells during the aggregation process were extracted by particle image velocimetry analysis. A time dependent change was seen in the particle motion pattern during approach to its completion of clump formation after 45 s. Streaming eddies were set-up during the first couple of seconds. The scale of the eddies was consistent with Rayleigh micro-streaming theory. An increase in the travelling velocity of the cells was observed after 30 s from initially about 400 m s^–1 to about 1 mm s^–1. The influence of a number of mechanisms on particle behaviour (e.g. micro-streaming, particle interactions and convective flow) is considered. The experimental set-up introduced here is a powerful tool for aggregation studies in ultrasonic standing waves and lays the foundation for future quantitative experiments on the individual contributions of the different mechanisms.     

Pac-Man does not resolve the enduring problem of anaphase chromosome movement

Summary The Pac-Man hypothesis suggests that poleward movement of chromosomes during anaphase A is brought about by: disassembly of kinetochore microtubules (MTs) at the kinetochore; generation of the poleward force exclusively at or very close to the kinetochore; and the required energy coming from coupled disassembly of these MTs. This model has become widely accepted and cited as the sole or major mechanism of anaphase A. Rarely acknowledged are several significant phenomena that refute some or all of these postulates. We summarise these anomalies as follows: poleward movement of chromosomes occurring without insertion of any MTs at the kinetochore; anaphase shortening of kinetochore fibres in spindles entirely devoid of chromosomes and, presumably, kinetochores; continued movement of chromosomes while their severed kinetochore stub elongated poleward after treatment with UV microbeams; and fluxing of tubulin subunits through kinetochore MTs during anaphase A, indicating that during anaphase, kinetochore MTs disassemble partly or solely at the poles.Dedicated to Professor Brian E. S. Gunning on the occasion of his 65th birthday