Linear Synergy Research Articles

Optimizing cultivated land under non-grain expansion in rural China: unveiling the spatial dynamics of trade-offs and synergies among ecosystem services

ABSTRACT Non-grain expansion in rural China has affected the stability of cultivated land structure and the sustainability of ecosystem services (ESs). Delving into the spatio-temporal heterogeneity of ES interactions is essential for refined and differentiated cultivated land management practices. Taking Tongxiang City as an example, this study mapped the variations of four ESs of cultivated land from 2000–2020, identified their socio-ecological drivers, explored the spatial non-stationarity characteristics of trade-off/synergy among different ESs, and proposed a zoning control framework for cultivated land. The results indicated that (1) food supply (FS) and habitat quality (HQ) decreased by 40.40% and 1.27%, respectively, while carbon sequestration (CS) and soil conservation (SC) increased by 8.5% and 26.21%, respectively. Areas of decreased ES were mainly concentrated in the southwest, while areas of increased ES supply were dispersed. (2) CS-SC and CS-FS ES pairs exhibited obvious trade-offs, with concave trade-offs dominating between 2000 and 2010, and convex trade-offs prevailing from 2010 to 2020. These ES trade-offs were mainly distributed in the southeast and northern regions. HQ-CS and FS-SC presented significant synergies, predominantly characterized by linear synergy and situated in the northern and central areas. (3) The spatial differentiation of ESs was mostly explained by landscape configuration drivers. (4) Different cultivated land zones were delineated based on the spatial non-stationarity of trade-offs/synergies and ES advantage areas. This study contributes to our understanding of the changes in ESs resulting from non-grain expansion and offers valuable guidance for implementing differentiated measures for cultivated land zoning and management.

The legacy of Gerald L. Gottlieb in human movement neuroscience.

In this paper, we review the legacy of Gerald (Gerry) Gottlieb in various fields related to the neural control of human movement. His studies on the myotatic (stretch) reflex and postmyotatic responses to ankle joint perturbations paved the way for current explorations of long-loop reflexes and their role in the control of movement. The dual-strategy hypothesis introduced order into a large body of literature on the triphasic muscle activation patterns seen over a variety of voluntary movements in healthy persons. The dual-strategy hypothesis continues to be important for understanding the performance of subjects with disordered motor control. The principle of linear synergy (covariance of joint torques) was an attempt to solve one of the notorious problems of motor redundancy, which remains an important topic in the field. Gerry's attitude toward the equilibrium-point hypothesis varied between rejection and using it to explore patterns of hypothetical control variables and movement variability. The discovery of reciprocal excitation in healthy neonates fostered other studies of changes in spinal cord physiology as motor skills develop. In addition, studies of people with spasticity and the effects of treatment with intrathecal baclofen were crucial in demonstrating the possibility of unmasking voluntary movements after suppression of the hyperreflexia of spasticity. Gerry Gottlieb contributed a significant body of knowledge that formed a solid foundation from which to study a variety of neurological diseases and their treatments, and a more comprehensive and parsimonious foundation to describe the neural control of human movement.

Variations in sustainable development goal interactions: Population, regional, and income disaggregation

AbstractTo fulfill the 2030 Agenda, the complexity of sustainable development goal (SDG) interactions needs to be disentangled. However, this understanding is currently limited. We conduct a cross‐sectional correlational analysis for 2016 to understand SDG interactions under the entire development spectrum. We apply several correlation methods to classify the interaction as synergy or trade‐off and characterize them according to their monotony and linearity. Simultaneously, we analyze SDG interactions considering population, location, income, and regional groups. Our findings highlight that synergies always outweigh trade‐offs and linear outweigh non‐linear interactions. SDG 1, 5, and 6 are associated with linear synergies, SDG 3, and 7 with non‐linear synergies. SDG interactions vary according to a country's income and region along with the gender, age, and location of its population. In summary, to achieve the 2030 Agenda the detected interactions and inequalities across countries need be tracked and leveraged to “leave no one behind.”

Muscle Synergies Obtained from Comprehensive Mapping of the Cortical Forelimb Representation Using Stimulus Triggered Averaging of EMG Activity

Neuromuscular control of voluntary movement may be simplified using muscle synergies similar to those found using non-negative matrix factorization. We recently identified synergies in electromyography (EMG) recordings associated with both voluntary movement and movement evoked by high-frequency long-duration intracortical microstimulation applied to the forelimb representation of the primary motor cortex (M1). The goal of this study was to use stimulus-triggered averaging (StTA) of EMG activity to investigate the synergy profiles and weighting coefficients associated with poststimulus facilitation, as synergies may be hard-wired into elemental cortical output modules and revealed by StTA. We applied StTA at low (LOW, ∼15 μA) and high intensities (HIGH, ∼110 μA) to 247 cortical locations of the M1 forelimb region in two male rhesus macaques while recording the EMG of 24 forelimb muscles. Our results show that 10-11 synergies accounted for 90% of the variation in poststimulus EMG facilitation peaks from the LOW-intensity StTA dataset while only 4-5 synergies were needed for the HIGH-intensity dataset. Synergies were similar across monkeys and current intensities. Most synergy profiles strongly activated only one or two muscles; all joints were represented and most, but not all, joint directions of motion were represented. Cortical maps of the synergy weighting coefficients suggest only a weak organization. StTA of M1 resulted in highly diverse muscle activations, suggestive of the limiting condition of requiring a synergy for each muscle to account for the patterns observed.SIGNIFICANCE STATEMENT Coordination of muscle activity and the neural origin of potential muscle synergies remains a fundamental question of neuroscience. We previously demonstrated that high-frequency long-duration intracortical microstimulation-evoked synergies were unrelated to voluntary movement synergies and were not clearly organized in the cortex. Here we present stimulus-triggered averaging facilitation-related muscle synergies, suggesting that when fundamental cortical output modules are activated, synergies approach the limit of single-muscle control. Thus, we conclude that if the CNS controls movement via linear synergies, those synergies are unlikely to be called from M1. This information is critical for understanding neural control of movement and the development of brain-machine interfaces.

On the Relationship Between Human Motor Control Performance and Kinematic Synergies in Upper Limb Prosthetics.

Current prosthesis command interfaces only allow for a single degree of freedom to be commanded at a time, making coordinated motion difficult to achieve. Thus it becomes crucial to develop methods that complement these interfaces to allow for intuitive coordinated arm motion. Kinematic synergies have been shown as an alternate method where the motion of the prosthetic device is coordinated with that of the residual limb. In this paper, the mapping between the parameters of a kinematic synergy model and a measure of task performance is established experimentally in order to test the applicability of online optimization methods for the identification of synergies. To achieve this, a cost function that captures the objective of the reaching task and a linear kinematic synergy model were chosen. A human experiment was developed in a Virtual Reality (VR) platform in order to determine the synergy-performance relationship. The experiments were performed on 10 able-bodied subjects. The relationship observed between the synergy parameter and the reaching task cost function suggests existing online optimization methods may be applicable.

52. Transmission detector with 3D dose reconstruction: compass system validation for patient specific dose verification

Introduction Methods used for external radiotherapy plan verification do not generally provide clinically relevant results. Compass 4.0 software combined with Dolphin (IBA) transmission detector is a plan verification system which reconstructs the delivered dose distribution inside the patient’s CT-dataset. This study aimed to evaluate this system for VMAT plans verification. Methods The transmission detector is a 2D array of 1513 ionization chambers. With an independent beam modeling and a collapsed cone dose engine, the system provides two ways for treatment plans verification [ Fig. 1 ]: a dose calculation verification with an independent dose calculation; a verification of the actual dose delivered by the linear accelerator (measurement-based dose reconstruction). VMAT plans, using 6 MV photons beams, were generated in Pinnacle v9.10 (Philips) TPS. Elekta linear accelerators Synergy and Versa HD, equipped with an Agility multi leaf collimator (MLC) were used for beams delivery. System validation was realized in two steps: (i) Verification of beam modelling and dose reconstruction method: both Compass calculated dose distribution and reconstructed dose distribution were compared to radiochromic films measurements (gamma index 2D, criteria 3% local/3 mm, threshold 30%) for 11 Head and Neck (H&N) plans. (ii) Evaluation of error detection abilities for two treatment plan complexities (prostate and H&N). Two kinds of error were introduced: MLC positional uncertainties from 1 to 5 mm (one leaf bank shift, two banks shifts in same and in opposite direction) and output errors (MU increase from 1% to 5%). The system was used for 17 clinical cases (nine H&N, eight lungs including SBRT). Measurement-based dose distributions ere compared with planned dose distributions (volume of PTV receiving at least 95% of prescribed dose, V95%, mean dose to organs at risks, Dmean). Results On average, Compass calculated dose distributions compared with film measurements showed a mean gamma value ( γ mean) of 0.422 (standard-deviation σ = 0.078) and a percentage of accepted points (%accepted pts) of 95.7% ( σ = 3.7%). Reconstructed dose distributions compared with film measurements showed a γ mean of 0.380 ( σ = 0.072) and a %accepted pts of 96.8 % ( σ = 2.1%). The system could detect 1 mm leaf bank shift for all the simulated leaf banks shifts, 1% and 3% MU increase for H&N and prostate plan respectively. For clinical cases, differences between planned dose and Compass reconstructed dose were on averaged 1.5% ( σ = 3.8%) for V95% and 53 cGy ( σ = 137 cGy) for the organs at risk. Conclusions The performances of Compass software combined with Dolphin transmission detector were validated for clinical implementation: Compass calculated and reconstructed doses were in agreement with film measurements, 1 mm leaf bank shift error was detected. The dose reconstruction on patient CT-dataset gives a relevant clinical meaning to patient quality assurance results. An interesting evolution of the product would be the delivered dose reconstruction on daily CBCT, for adaptative radiotherapy purpose.

Synergistic valuations and efficiency in spectrum auctions

In spectrum auctions, bidders typically have synergistic values for combinations of licenses. This has been the key argument for the use of combinatorial auctions in the recent years. Considering synergistic valuations turns the allocation problem into a computationally hard optimization problem that generally cannot be approximated to a constant factor in polynomial time. Ascending auction designs such as the Simultaneous Multiple Round Auction (SMRA) and the single-stage or two-stage Combinatorial Clock Auction (CCA) can be seen as simple heuristic algorithms to solve this problem. Such heuristics do not necessarily compute the optimal solution, even if bidders are truthful. We study the average efficiency loss that can be attributed to the simplicity of the auction algorithm with different levels of synergies. Our simulations are based on realistic instances of bidder valuations we inferred from bid data from the 2014 Canadian 700 MHz auction. The goal of the paper is not to reproduce the results of the Canadian auction but rather to perform “out-of-sample” counterfactuals comparing SMRA and CCA under different synergy conditions when bidders maximize payoff in each round. With “linear” synergies, a bidder's marginal value for a license grows linearly with the total number of licenses won, while with the “extreme national” synergies, this marginal value is independent of the number of licenses won unless the bidder wins all licenses in a national package. We find that with the extreme national synergy model, the CCA is indeed more efficient than SMRA. However, for the more realistic case of linear synergies, SMRA outperforms various versions of CCA that have been implemented in the field including the one used in the Canadian 700 MHz auction. Overall, the efficiency loss of all ascending auction algorithms is small even with high synergies, which is remarkable given the simplicity of the algorithms.

Are muscle synergies useful for neural control?

The observation that the activity of multiple muscles can be well approximated by a few linear synergies is viewed by some as a sign that such low-dimensional modules constitute a key component of the neural control system. Here, we argue that the usefulness of muscle synergies as a control principle should be evaluated in terms of errors produced not only in muscle space, but also in task space. We used data from a force-aiming task in two dimensions at the wrist, using an electromyograms (EMG)-driven virtual biomechanics technique that overcomes typical errors in predicting force from recorded EMG, to illustrate through simulation how synergy decomposition inevitably introduces substantial task space errors. Then, we computed the optimal pattern of muscle activation that minimizes summed-squared muscle activities, and demonstrated that synergy decomposition produced similar results on real and simulated data. We further assessed the influence of synergy decomposition on aiming errors (AEs) in a more redundant system, using the optimal muscle pattern computed for the elbow-joint complex (i.e., 13 muscles acting in two dimensions). Because EMG records are typically not available from all contributing muscles, we also explored reconstructions from incomplete sets of muscles. The redundancy of a given set of muscles had opposite effects on the goodness of muscle reconstruction and on task achievement; higher redundancy is associated with better EMG approximation (lower residuals), but with higher AEs. Finally, we showed that the number of synergies required to approximate the optimal muscle pattern for an arbitrary biomechanical system increases with task-space dimensionality, which indicates that the capacity of synergy decomposition to explain behavior depends critically on the scope of the original database. These results have implications regarding the viability of muscle synergy as a putative neural control mechanism, and also as a control algorithm to restore movements.

The effect of movement direction on joint torque covariation

It has been proposed that unconstrained upper limb movements are coordinated via a kinetic constraint that produces dynamic muscle torques at each moving joint that are a linear function of a single torque command. This constraint has been termed linear synergy (Gottlieb et al. J Neurophysiol 75:1760-1764, 1996). The current study tested two hypotheses: (1) that the extent of covariation between dynamic muscle torques at the shoulder and elbow varied with the direction of movement and (2) that the extent to which muscle torques deviated from linear synergy would be reproduced by a simulation of pointing movements in which the path of the hand was constrained to be straight. Dynamic muscle torques were calculated from sagittal plane pointing movements performed by 12 participants to targets in eight different directions. The results of principal component analyses performed on the muscle torque data demonstrated direction-dependent variation in the extent to which dynamic muscle torques covaried at the shoulder and elbow. Linear synergy was deviated from substantially in movement directions for which the magnitude of muscle torque was low at one joint. A simulation of movements with straight hand paths was able to accurately estimate the amount of covariation between muscle torques at the two joints in many directions. These results support the idea that a kinematic constraint is imposed by the central nervous system during unconstrained pointing movements. Linear synergy may also be applied as a coordinating constraint in circumstances where its application allows the path of the moving endpoint to remain close to a straight line.

Electromyographic and kinetic strategies to control movements

Introduction: This paper is a literature review on the electromyographic and kinetic strategies used by the central nervous system to control voluntary movement. Such strategies have been identified from carrying out simple and complex movements, with and without direction reversal. Objective: To discuss the set of rules used to modulate the muscle activity patterns and muscle torque generated during voluntary movements involving one and two joints. Electromyographic strategies used to control simple movements involving one or two joints are dealt with first. Kinetic strategies are discussed in terms of the generation and modulation of muscle torque to carry out simple and complex movements. Linear synergy between muscle activity and muscle torque and the correlation of the muscle torque generated between chain-linked joints are then discussed. The role of interactive forces in the control of movements is also discussed. Conclusion: Physical therapy practice requires a theoretical framework based on technical-scientific knowledge to guide it. Motor control theories are powerful tools for this. Such knowledge could be used towards understanding the adaptations and modifications in motor control mechanisms that occur as a result of disorders or disease.

Horizontal-plane arm movements with direction reversals performed by normal individuals and individuals with down syndrome.

We examined the systematic variation in shoulder and elbow torque, as well as movement kinematics, for horizontal-plane arm movements with direction reversals performed by normal individuals and individuals with Down syndrome. Eight neurologically normal individuals and eight individuals with Down syndrome performed horizontal, planar reversal movements to four different target locations. The four locations of the targets were chosen such that there is a systematic increase in elbow interaction torque for each of the four different target locations. This systematic increase in interaction torque has previously been shown to lead to progressively larger movement reversal errors, and trajectories that do not show a sharp reversal of direction, for movements to and from the target in patients who have proprioceptive abnormalities. We computed joint torques at the elbow and shoulder and found a high correlation between elbow and shoulder torque for the neurologically normal subjects. The ratio of joint torques varied systematically with target location. These findings extend previously reported findings of a linear synergy between shoulder and elbow joints for a variety of point-to-point movements. There was also a correlation between elbow and shoulder torque in individuals with Down syndrome, but the magnitude of the correlation was less. The ratio of joint torques changed systematically with target direction in individuals with Down syndrome but was slightly different from the ratio observed for neurologically normal individuals. The difference in the ratio was caused by the generation of proportionately more elbow torque than shoulder torque. The fingertip path of individuals with Down syndrome showed a sharp reversal in moving toward and then away from the target. In this respect, they were similar to neurologically normal individuals but dissimilar to individuals with proprioceptive deficits. Finally, we observed that individuals with Down syndrome spend proportionately more time in the vicinity of the target than normal individuals. Collectively these results show that there is a systematic relationship between joint torques at the elbow and shoulder. This relationship is present for reversal movements and is also present in individuals with Down syndrome.

An unlearned principle for controlling natural movements.

Recently, Gottlieb and colleagues discovered a linear relation between elbow and shoulder dynamic torque in natural pointing movements in the sagittal plane. The present study investigates if the process of learning to reach involves discovering this linearity principle. We inspected torque data from four infants who were learning to reach and grab a toy in front of them. In a longitudinal study, we collected data both in the period before and after they performed their first successful reaches. Torque profiles at the shoulder and elbow were typically multipeaked and became more and more biphasic toward the end of the first year of life. Torques at the shoulder and elbow were correlated tightly for movements in the prereaching period as well as for reaches later in the year. Furthermore, slopes of a regression of shoulder dynamic torque on elbow dynamic torque were remarkably constant at a value approximately 2.5-3.0. If linear synergy is used by the nervous system to reduce the controlled degrees of freedom, it will act as a strong constraint on the complex of possible coordination patterns for arm movement early in life. Natural reaching movements can capitalize on this constraint because it simplifies the process of learning to reach.

Coordinating two degrees of freedom during human arm movement: load and speed invariance of relative joint torques.

1. Eight subjects performed three series of pointing tasks with the unconstrained arm. Series one and two required subjects to move between two fixed targets as quickly as possible with different weights attached to the wrist. By specifying initial and final positions of the finger tip, the first series was performed by flexion of both shoulder and elbow and the second by shoulder flexion and elbow extension. The third series required flexion at both joints, and subjects were instructed to vary movement speed. We examined how variations in load or intended speed were associated with changes in the amount and timing of the electromyographic (EMG) activity and the net muscle torque production. 2. EMG and torque patterns at the individual joints varied with load and speed according to most of the same rules we have described for single-joint movements. 1) Movements were produced by biphasic torque pulses and biphasic or triphasic EMG bursts at both joints. 2) The accelerating impulse was proportional to the load when the subject moved "as fast and accurately as possible" or to speed if that was intentionally varied. 3) The area of the EMG bursts of agonist muscles varied with the impulse. 4) The rates of rise of the net muscle torques and of the EMG bursts were proportional to intended speed and insensitive to inertial load. 5) The areas of the antagonist muscle EMG bursts were proportional to intended movement speed but showed less dependence on load, which is unlike what is observed during single-joint movements. 3. Comparisons across joints showed that the impulse produced at the shoulder was proportional to that produced at the elbow as both varied together with load and speed. The torques at the two joints varied in close synchrony, achieving maxima and going through zero almost simultaneously. 4. We hypothesize that "coordination" of the elbow and shoulder is by the planning and generation of synchronized, biphasic muscle torque pulses that remain in near linear proportionality to each other throughout most of the movement. This linear synergy produces movements with the commonly observed kinematic properties and that are preserved over changes in speed and load.