Parabolic movement primitives and cortical states: merging optimality with geometric invariance

Previous studies have suggested that several types of rules govern the generation of complex arm movements. One class of rules consists of optimizing an objective function (e.g., maximizing motion smoothness). Another class consists of geometric and kinematic constraints, for instance the coupling between speed and curvature during drawing movements as expressed by the two-thirds power law. It has also been suggested that complex movements are composed of simpler elements or primitives. However, the ability to unify the different rules has remained an open problem. We address this issue by identifying movement paths whose generation according to the two-thirds power law yields maximally smooth trajectories. Using equi-affine differential geometry we derive a mathematical condition which these paths must obey. Among all possible solutions only parabolic paths minimize hand jerk, obey the two-thirds power law and are invariant under equi-affine transformations (which preserve the fit to the two-thirds power law). Affine transformations can be used to generate any parabolic stroke from an arbitrary parabolic template, and a few parabolic strokes may be concatenated to compactly form a complex path. To test the possibility that parabolic elements are used to generate planar movements, we analyze monkeys’ scribbling trajectories. Practiced scribbles are well approximated by long parabolic strokes. Of the motor cortical neurons recorded during scribbling more were related to equi-affine than to Euclidean speed. Unsupervised segmentation of simulta- neously recorded multiple neuron activity yields states related to distinct parabolic elements. We thus suggest that the cortical representation of movements is state-dependent and that parabolic elements are building blocks used by the motor system to generate complex movements.     

Motor primitives in vertebrates and invertebrates

In recent years different lines of evidence have led to the idea that motor actions and movements in both vertebrates and invertebrates are composed of elementary building blocks. The entire motor repertoire can be spanned by applying a well-defined set of operations and transformations to these primitives and by combining them in many different ways according to well-defined syntactic rules. Motor and movement primitives and modules might exist at the neural, dynamic and kinematic levels with complicated mapping among the elementary building blocks subserving these different levels of representation. Hence, while considerable progress has been made in recent years in unravelling the nature of these primitives, new experimental, computational and conceptual approaches are needed to further advance our understanding of motor compositionality.     

Architectonic constraints on the hyoid's optimal starting position for suction feeding of fish

During suction feeding teleost fish have to start mouth opening prior to other expansion movements of the head such as operculo-suspensorium abduction. The distribution of the input force over the various expansion movements is determined by the position of the hyoid in the expansion apparatus. Based on a three-dimensional (3-D) kinematic model of this apparatus it can be calculated at which positions of the hyoid operculo-suspensorial abduction is precluded. For 73 cichlid species from various African lakes and covering a wide array of feeding types and adult sizes, it is demonstrated that these optimal positions for the onset of suction feeding can be attained or closely approached by species whose regular diet only requires suction feeding but not by species whose regular diet is dominated by items requiring forceful biting. It is argued that the suboptimality of the biters is due to an architectonic constraint, viz. an increase in head width necessary to accommodate their enlarged m. adductor mandibulae. Although it is theoretically feasible to optimize the model's parameters for every head width, the biters apparently have not achieved such an adaptive change. As these parameters also feature in the execution of other functions, it is likely that conflicting demands on their optimal value overrule their optimization for the starting position of the hyoid of biters. The results hold for cichlids of independently evolved species flocks and therefore concern general rules for biter-sucker transformations in cichlids. © 1996 Wiley-Liss, Inc.     

Where the eye looks, the hand follows; limb-dependent magnetic misreaching in optic ataxia

The posterior parietal cortex (PPC) is thought to play an important role in the sensorimotor transformations associated with reaching movements. In humans, damage to the PPC, particularly bilateral lesions, leads to impairments of visually guided reaching movements (optic ataxia). Recent accounts of optic ataxia based upon electrophysiological recordings in monkeys have proposed that this disorder arises because of a breakdown in the tuning fields of parietal neurons responsible for integrating spatially congruent retinal, eye, and hand position signals to produce coordinated eye and hand movements . We present neurological evidence that forces a reconceptualization of this view. We report a detailed case study of a patient with a limb-dependent form of optic ataxia who can accurately reach with either hand to objects that he can foveate (thereby demonstrating coordinated eye-hand movements) but who cannot effectively decouple reach direction from gaze direction for movements executed using his right arm. The demonstration that our patient's misreaching is confined to movements executed using his right limb, and only for movements that are directed to nonfoveal targets, rules out explanations based upon simple perceptual or motor deficits but indicates an impairment in the ability to dissociate the eye and limb visuomotor systems when appropriate.     

THE CONTRIBUTION OF GENE MOVEMENT TO THE “TWO RULES OF SPECIATION”

The two “rules of speciation”—the Large X‐effect and Haldane's rule—hold throughout the animal kingdom, but the underlying genetic mechanisms that cause them are still unclear. Two predominant explanations—the “dominance theory” and faster male evolution—both have some empirical support, suggesting that the genetic basis of these rules is likely multifarious. We revisit one historical explanation for these rules, based on dysfunctional genetic interactions involving genes recently moved between chromosomes. We suggest that gene movement specifically off or onto the X chromosome is another mechanism that could contribute to the two rules, especially as X chromosome movements can be subject to unique sex‐specific and sex chromosome specific consequences in hybrids. Our hypothesis is supported by patterns emerging from comparative genomic data, including a strong bias in interchromosomal gene movements involving the X and an overrepresentation of male reproductive functions among chromosomally relocated genes. In addition, our model indicates that the contribution of gene movement to the two rules in any specific group will depend upon key developmental and reproductive parameters that are taxon specific. We provide several testable predictions that can be used to assess the importance of gene movement as a contributor to these rules in the future.     

Hippocampus: memory, habit and voluntary movement

A general method for studying monkeys' memories is to teach the animals memory-dependent performance rules: for example, to choose, out of two visual stimuli, the one that flashed last time the animal saw it. One may thus assess the animal's memory for any arbitrarily chosen event such as flashing even if the event itself has no intrinsic importance for the animal. The method also allows assessment of an animal's memory of the animal's own previous behaviour. The use of these methods has revealed a simple generalization about the function of the hippocampus in memory: hippocampal lesions impair memory of the voluntary movement that a stimulus previously elicited, but leave intact memory for relations between environmental events other than voluntary movements. The impairment in memory for voluntary movements produces deficits in exploration and in habit formation.     

Drug Guru: a computer software program for drug design using medicinal chemistry rules

Drug Guru (drug generation using rules) is a new web-based computer software program for medicinal chemists that applies a set of transformations, that is, rules, to an input structure. The transformations correspond to medicinal chemistry design rules-of-thumb taken from the historical lore of drug discovery programs. The output of the program is a list of target analogs that can be evaluated for possible future synthesis. A discussion of the features of the program is followed by an example of the software applied to sildenafil (Viagra) in generating ideas for target analogs for phosphodiesterase inhibition. Comparison with other computer-assisted drug design software is given.     

Pigment color patterns of molluscs as an autonomous process generated by asynchronous automata

Pigment color patterns of molluscs are studied from the viewpoint of autonomy. Brownian algebra developed by Spencer-Brown (1969) is extensively used for the expression of cellular-automaton rules. When asynchronous updating is introduced for the transition of cellular automata, various kinds of patterns such as traveling waves, kinks, oscillatory local patterns etc. are generated from the same transitional rule. The type of patterns depends more sensitively on the asynchronous updating relationship rather than the transitional rule itself. Therefore, pattern changes in ontogeny can be explained without any changes in transitional rules or reaction processes. It is proposed that asynchronousness is intrinsic to living systems and that recognition of the intrinsic time is essential in understanding living systems.     

The Role of the Caudal Superior Parietal Lobule in Updating Hand Location in Peripheral Vision: Further Evidence from Optic Ataxia

Patients with optic ataxia (OA), who are missing the caudal portion of their superior parietal lobule (SPL), have difficulty performing visually-guided reaches towards extra-foveal targets. Such gaze and hand decoupling also occurs in commonly performed non-standard visuomotor transformations such as the use of a computer mouse. In this study, we test two unilateral OA patients in conditions of 1) a change in the physical location of the visual stimulus relative to the plane of the limb movement, 2) a cue that signals a required limb movement 180° opposite to the cued visual target location, or 3) both of these situations combined. In these non-standard visuomotor transformations, the OA deficit is not observed as the well-documented field-dependent misreach. Instead, OA patients make additional eye movements to update hand and goal location during motor execution in order to complete these slow movements. Overall, the OA patients struggled when having to guide centrifugal movements in peripheral vision, even when they were instructed from visual stimuli that could be foveated. We propose that an intact caudal SPL is crucial for any visuomotor control that involves updating ongoing hand location in space without foveating it, i.e. from peripheral vision, proprioceptive or predictive information.     

Evidence for actin transformation during the contraction-relaxation cycle of cytoplasmic actomyosin: Cycle blockade by Phalloidin injection

1) The injection of a mushroom drug, Phalloidin (750 microgram -1 mg/ml), into the endoplasmic channel of Physarum veins induces an irreversible blockade of the intrinsic contraction-relaxation automaticity of the ectoplasmic tube wall, as measured by tensiometrical methods. 2) The morphological responses to Phalloidin injection include an increase and condensation of cytoplasmic actomyosin sheets bordering the plasmalemma invaginations within the ectoplasmic tube and a more pronounced dense layer of "groundplasm" in the cell cortex. This is in accordance with experiments with other cells as well as with Physarum. 3) The addition of marker particles to the injection solution revealed that the injected substances can be brought into direct contact with the contractile substrate, before newly formed membranes separate off the injection fluid. 4) Since Phalloidin irreversibly transforms oligomeric actin into a filamentous "Phalloidin-actin complex" and because this transformation does not hinder the actin in activating myosin ATPase, it is concluded that the contraction-relaxation cycle of cytoplasmic actomyosin in Physarum involves actin transformations. If these transformations are hindered, e.g. by Phalloidin, one stage and thereby the whole cycle is sustained which results in a blockade of the intrinsic contraction automaticity. 5) The functional importance of actin transformations in the congraction physiology of cytoplasmic actomyosins and cell motility phenomena is discussed.     

Perception of Social Interactions for Spatially Scrambled Biological Motion

It is vitally important for humans to detect living creatures in the environment and to analyze their behavior to facilitate action understanding and high-level social inference. The current study employed naturalistic point-light animations to examine the ability of human observers to spontaneously identify and discriminate socially interactive behaviors between two human agents. Specifically, we investigated the importance of global body form, intrinsic joint movements, extrinsic whole-body movements, and critically, the congruency between intrinsic and extrinsic motions. Motion congruency is hypothesized to be particularly important because of the constraint it imposes on naturalistic action due to the inherent causal relationship between limb movements and whole body motion. Using a free response paradigm in Experiment 1, we discovered that many naïve observers (55%) spontaneously attributed animate and/or social traits to spatially-scrambled displays of interpersonal interaction. Total stimulus motion energy was strongly correlated with the likelihood that an observer would attribute animate/social traits, as opposed to physical/mechanical traits, to the scrambled dot stimuli. In Experiment 2, we found that participants could identify interactions between spatially-scrambled displays of human dance as long as congruency was maintained between intrinsic/extrinsic movements. Violating the motion congruency constraint resulted in chance discrimination performance for the spatially-scrambled displays. Finally, Experiment 3 showed that scrambled point-light dancing animations violating this constraint were also rated as significantly less interactive than animations with congruent intrinsic/extrinsic motion. These results demonstrate the importance of intrinsic/extrinsic motion congruency for biological motion analysis, and support a theoretical framework in which early visual filters help to detect animate agents in the environment based on several fundamental constraints. Only after satisfying these basic constraints could stimuli be evaluated for high-level social content. In this way, we posit that perceptual animacy may serve as a gateway to higher-level processes that support action understanding and social inference.     

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).     

Transformation and ‘Human Values’ in the Landless Workers' Movement of Brazil

Social movements often seek transformation in wider society, but they are also themselves subject to the fluidity and ephemerality of the environments in which they operate. Academic literature has long held the view that social movements inevitably come to be beset by institutionalisation and a loss of relevance, and in Brazil, where socio-economic change has been so dynamic, the future of the Landless Workers’ Movement (Movimento dos Sem Terra (MST)) has been called into question. This article argues that the MST is responding to changes in its membership, and transformation more widely in Brazil, in a measured way, by drawing upon a familiar repertoire of cooperativisation to boost production. The article suggests that decline is not necessarily certain, but as a case study for movements more generally, current MST leadership decisions may be significant in understanding how social movements can best react to unpredictable transformations in wider society.     

Bayesian inference for identifying interaction rules in moving animal groups

The emergence of similar collective patterns from different self-propelled particle models of animal groups points to a restricted set of "universal" classes for these patterns. While universality is interesting, it is often the fine details of animal interactions that are of biological importance. Universality thus presents a challenge to inferring such interactions from macroscopic group dynamics since these can be consistent with many underlying interaction models. We present a Bayesian framework for learning animal interaction rules from fine scale recordings of animal movements in swarms. We apply these techniques to the inverse problem of inferring interaction rules from simulation models, showing that parameters can often be inferred from a small number of observations. Our methodology allows us to quantify our confidence in parameter fitting. For example, we show that attraction and alignment terms can be reliably estimated when animals are milling in a torus shape, while interaction radius cannot be reliably measured in such a situation. We assess the importance of rate of data collection and show how to test different models, such as topological and metric neighbourhood models. Taken together our results both inform the design of experiments on animal interactions and suggest how these data should be best analysed.     

Decision-making processes: The case of collective movements

Besides focusing on the adaptive significance of collective movements, it is crucial to study the mechanisms and dynamics of decision-making processes at the individual level underlying the higher-scale collective movements. It is now commonly admitted that collective decisions emerge from interactions between individuals, but how individual decisions are taken, i.e. how far they are modulated by the behaviour of other group members, is an under-investigated question. Classically, collective movements are viewed as the outcome of one individual's initiation (the leader) for departure, by which all or some of the other group members abide. Individuals assuming leadership have often been considered to hold a specific social status. This hierarchical or centralized control model has been challenged by recent theoretical and experimental findings, suggesting that leadership can be more distributed. Moreover, self-organized processes can account for collective movements in many different species, even in those that are characterized by high cognitive complexity. In this review, we point out that decision-making for moving collectively can be reached by a combination of different rules, i.e. individualized (based on inter-individual differences in physiology, energetic state, social status, etc.) and self-organized (based on simple response) ones for any species, context and group size.     

A common reference frame for movement plans in the posterior parietal cortex

Orchestrating a movement towards a sensory target requires many computational processes, including a transformation between reference frames. This transformation is important because the reference frames in which sensory stimuli are encoded often differ from those of motor effectors. The posterior parietal cortex has an important role in these transformations. Recent work indicates that a significant proportion of parietal neurons in two cortical areas transforms the sensory signals that are used to guide movements into a common reference frame. This common reference frame is an eye-centred representation that is modulated by eye-, head-, body- or limb-position signals. A common reference frame might facilitate communication between different areas that are involved in coordinating the movements of different effectors. It might also be an efficient way to represent the locations of different sensory targets in the world.     

Stabilisation of walking by intrinsic muscle properties revealed in a three-dimensional muscle-driven simulation

A fundamental question in movement science is how humans perform stable movements in the presence of disturbances such as contact with objects. It remains unclear how the nervous system, with delayed responses to disturbances, maintains the stability of complex movements. We hypothesised that intrinsic muscle properties (i.e. the force–length–velocity properties of muscle fibres and tendon elasticity) may help stabilise human walking by responding instantaneously to a disturbance and providing forces that help maintain the movement trajectory. To investigate this issue, we generated a 3D muscle-driven simulation of walking and analysed the changes in the simulation's motion when a disturbance was applied to models with and without intrinsic muscle properties. Removing the intrinsic properties reduced the stability; this was true when the disturbing force was applied at a variety of times and in different directions. Thus, intrinsic muscle properties play a unique role in stabilising walking, complementing the delayed response of the central nervous system.