scholarly journals Motor adaptation and generalization of reaching movements using motor primitives based on spatial coordinates

2015 ◽  
Vol 113 (4) ◽  
pp. 1217-1233 ◽  
Author(s):  
Hirokazu Tanaka ◽  
Terrence J. Sejnowski
Keyword(s):  
Force Field ◽  
Reference Frame ◽  
Equations Of Motion ◽  
Motor Adaptation ◽  
Cross Product ◽  
Visuomotor Rotation ◽  
Wide Range ◽  
Motor Information ◽  
Spatial Coordinates ◽  
The Cross

The brain processes sensory and motor information in a wide range of coordinate systems, ranging from retinal coordinates in vision to body-centered coordinates in areas that control musculature. Here we focus on the coordinate system used in the motor cortex to guide actions and examine physiological and psychophysical evidence for an allocentric reference frame based on spatial coordinates. When the equations of motion governing reaching dynamics are expressed as spatial vectors, each term is a vector cross product between a limb-segment position and a velocity or acceleration. We extend this computational framework to motor adaptation, in which the cross-product terms form adaptive bases for canceling imposed perturbations. Coefficients of the velocity- and acceleration-dependent cross products are assumed to undergo plastic changes to compensate the force-field or visuomotor perturbations. Consistent with experimental findings, each of the cross products had a distinct reference frame, which predicted how an acquired remapping generalized to untrained location in the workspace. In response to force field or visual rotation, mainly the coefficients of the velocity- or acceleration-dependent cross products adapted, leading to transfer in an intrinsic or extrinsic reference frame, respectively. The model further predicted that remapping of visuomotor rotation should under- or overgeneralize in a distal or proximal workspace. The cross-product bases can explain the distinct patterns of generalization in visuomotor and force-field adaptation in a unified way, showing that kinematic and dynamic motor adaptation need not arise through separate neural substrates.

scholarly journals No effects of cerebellar transcranial direct current stimulation on force field and visuomotor reach adaptation in young and healthy subjects

2019 ◽  
Vol 121 (6) ◽  
pp. 2112-2125 ◽  
Author(s):  
A. Mamlins ◽  
T. Hulst ◽  
O. Donchin ◽  
D. Timmann ◽  
J. Claassen
Keyword(s):  
Motor Learning ◽  
Force Field ◽  
Direct Current ◽  
Transcranial Direct Current Stimulation ◽  
Healthy Subjects ◽  
Motor Adaptation ◽  
Visuomotor Rotation ◽  
Direct Current Stimulation ◽  
Cerebellar Tdcs ◽  
Adaptation Task

Previous studies have shown that cerebellar transcranial direct current stimulation (tDCS) leads to faster adaptation of arm reaching movements to visuomotor rotation and force field perturbations in healthy subjects. The first aim of the present study was to confirm a stimulation-dependent effect on motor adaptation. Second, we investigated whether tDCS effects differ depending on onset, that is, before or at the beginning of the adaptation phase. A total of 120 healthy and right-handed subjects (60 women, mean age 23.2 ± SD 2.7 yr, range 18–31 yr) were tested. Subjects moved a cursor with a manipulandum to one of eight targets presented on a vertically orientated screen. Three baseline blocks were followed by one adaptation block and three washout blocks. Sixty subjects did a force field adaptation task (FF), and 60 subjects did a visuomotor adaptation task (VM). Equal numbers of subjects received anodal, cathodal, or sham cerebellar tDCS beginning either in the third baseline block or at the start of the adaptation block. In FF and VM, tDCS and the onset of tDCS did not show a significant effect on motor adaptation (all P values >0.05). We were unable to support previous findings of modulatory cerebellar tDCS effects in reaching adaptation tasks in healthy subjects. Prior to possible application in patients with cerebellar disease, future experiments are needed to determine which tDCS and task parameters lead to robust tDCS effects. NEW & NOTEWORTHY Transcranial direct current stimulation (tDCS) is a promising tool to improve motor learning. We investigated whether cerebellar tDCS improves motor learning in force field and visuomotor tasks in healthy subjects and what influence the onset of stimulation has. We did not find stimulation effects of tDCS or an effect of onset of stimulation. A reevaluation of cerebellar tDCS in healthy subjects and at the end of the clinical potential in cerebellar patients is demanded.

scholarly journals Combining experimental and simulation data of molecular processes via augmented Markov models

2017 ◽  
Vol 114 (31) ◽  
pp. 8265-8270 ◽  
Author(s):  
Simon Olsson ◽  
Hao Wu ◽  
Fabian Paul ◽  
Cecilia Clementi ◽  
Frank Noé
Keyword(s):  
Force Field ◽  
Structural Changes ◽  
Markov Models ◽  
Force Fields ◽  
Divide And Conquer ◽  
Simulation Data ◽  
Wide Range ◽  
Simulation And Experiment ◽  
Kinetics Of

Accurate mechanistic description of structural changes in biomolecules is an increasingly important topic in structural and chemical biology. Markov models have emerged as a powerful way to approximate the molecular kinetics of large biomolecules while keeping full structural resolution in a divide-and-conquer fashion. However, the accuracy of these models is limited by that of the force fields used to generate the underlying molecular dynamics (MD) simulation data. Whereas the quality of classical MD force fields has improved significantly in recent years, remaining errors in the Boltzmann weights are still on the order of a few kT, which may lead to significant discrepancies when comparing to experimentally measured rates or state populations. Here we take the view that simulations using a sufficiently good force-field sample conformations that are valid but have inaccurate weights, yet these weights may be made accurate by incorporating experimental data a posteriori. To do so, we propose augmented Markov models (AMMs), an approach that combines concepts from probability theory and information theory to consistently treat systematic force-field error and statistical errors in simulation and experiment. Our results demonstrate that AMMs can reconcile conflicting results for protein mechanisms obtained by different force fields and correct for a wide range of stationary and dynamical observables even when only equilibrium measurements are incorporated into the estimation process. This approach constitutes a unique avenue to combine experiment and computation into integrative models of biomolecular structure and dynamics.

scholarly journals Assessment of Linearization Approaches for Multibody Dynamics Formulations

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Francisco González ◽  
Pierangelo Masarati ◽  
Javier Cuadrado ◽  
Miguel A. Naya
Keyword(s):  
Mechanical System ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Practical Applications ◽  
Linearization Methods ◽  
Highly Nonlinear ◽  
Wide Range ◽  
The Way

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

Calculation of the primary trajectories of seeds and other particles in strong winds

1983 ◽  
Vol 219 (1215) ◽  
pp. 217-217
Keyword(s):  
Equations Of Motion ◽  
Aerodynamic Resistance ◽  
Reynolds Numbers ◽  
Spherical Particles ◽  
Spores And Pollen ◽  
General Terms ◽  
Wide Range ◽  
Strong Winds ◽  
Dispersal Distances ◽  
Enormous Number

The movement of variously dense spherical particles representing a variety of seeds, fruits, spores and pollen, and released from rest into arbitrary winds and a gravitational field is discussed in general terms that account in detail for changes in the quasi-static aerodynamic resistance to motion experienced by such particles during aerial flight. A hybrid analytical-empirical law is established which describes this resistance fairly accurately for particle Reynolds numbers in the range 0—60 000 and that allows for the numerical integration of the equations of motion so as to cover a very wide range of flight conditions. This makes possible the provision of a set of four-parameter universal range tables from which the dispersal distances for an enormous number of practical cases may be estimated. One particular case of particle movement in a region of pseudo-thermal convection is also discussed and this shows how a marked degree of deposition concentration may be induced in some circumstances by such a flow. Botanists and ecologists concerned with seed and particle dispersal in the environment may find the universal range tables of particular interest and use. This is because the tables obviate the need for the integration of the equations of motion when dealing with individual cases and permit an estimation of range purely on the basis of the specified quantities of particle size, density and altitude of release, atmospheric wind speed, density and viscosity, and the acceleration due to gravity.

Confidence Estimation of the Cross-Product Ratio of Binomial Proportions under Different Sampling Schemes

2021 ◽  
Vol 42 (2) ◽  
pp. 435-450
Author(s):  
Chanakan Sungboonchoo ◽  
Thuntida Ngamkham ◽  
Wararit Panichkitkosolkul ◽  
Andrei Volodin
Keyword(s):  
Cross Product ◽  
Confidence Estimation ◽  
Sampling Schemes ◽  
Product Ratio ◽  
Binomial Proportions ◽  
The Cross

Adaptation to Visuomotor Rotation and Force Field Perturbation Is Correlated to Different Brain Areas in Patients With Cerebellar Degeneration

2009 ◽  
Vol 101 (4) ◽  
pp. 1961-1971 ◽  
Author(s):  
K. Rabe ◽  
O. Livne ◽  
E. R. Gizewski ◽  
V. Aurich ◽  
A. Beck ◽  
...  
Keyword(s):  
Force Field ◽  
Decisive Role ◽  
Anterior Lobe ◽  
Magnetic Resonance Images ◽  
Cerebellar Degeneration ◽  
The Other ◽  
Posterior Lobe ◽  
Visuomotor Rotation ◽  
Dynamic Errors ◽  
And Gender

Although it is widely agreed that the cerebellum is necessary for learning and consolidation of new motor tasks, it is not known whether adaptation to kinematic and dynamic errors is processed by the same cerebellar areas or whether different parts play a decisive role. We investigated arm movements in a visuomotor (VM) rotation and a force field (FF) perturbation task in 14 participants with cerebellar degeneration and 14 age- and gender-matched controls. Magnetic resonance images were used to calculate the volume of cerebellar areas (medial, intermediate, and lateral zones of the anterior and posterior lobes) and to identify cerebellar structure important for the two tasks. Corroborating previous studies, cerebellar participants showed deficits in adaptation to both tasks compared with controls ( P < 0.001). However, it was not possible to draw conclusions from the performance in one task on the performance in the other task because an individual participant could show severe impairment in one task and perform relatively well in the other (ρ = 0.1; P = 0.73). We found that atrophy of distinct cerebellar areas correlated with impairment in different tasks. Whereas atrophy of the intermediate and lateral zone of the anterior lobe correlated with impairment in the FF task (ρ = 0.72, 0.70; P = 0.003, 0.005, respectively), atrophy of the intermediate zone of the posterior lobe correlated with adaptation deficits in the VM task (ρ = 0.64; P = 0.015). Our results suggest that adaptation to the different tasks is processed independently and relies on different cerebellar structures.

scholarly journals The Baum-Connes conjecture, noncommutative Poincaré duality, and the boundary of the free group

2003 ◽  
Vol 2003 (38) ◽  
pp. 2425-2445 ◽  
Author(s):  
Heath Emerson
Keyword(s):  
Free Group ◽  
Homology Class ◽  
Hyperbolic Group ◽  
Cross Product ◽  
Direct Connection ◽  
Poincaré Duality ◽  
Poincare Duality ◽  
Duality Map ◽  
The Cross ◽  
Gromov Boundary

For every hyperbolic groupΓwith Gromov boundary∂Γ, one can form the cross productC∗-algebraC(∂Γ)⋊Γ. For each such algebra, we construct a canonicalK-homology class. This class induces a Poincaré duality mapK∗(C(∂Γ)⋊Γ)→K∗+1(C(∂Γ)⋊Γ). We show that this map is an isomorphism in the case ofΓ=𝔽2, the free group on two generators. We point out a direct connection between our constructions and the Baum-Connes conjecture and eventually use the latter to deduce our result.

scholarly journals Angular Vectors in the Theory of Vectors

2017 ◽  
Vol 9 (5) ◽  
pp. 71
Author(s):  
Yevhen Mykolayovych Kharchenko
Keyword(s):  
Angular Velocity ◽  
Cross Product ◽  
Vector Form ◽  
Coordinate Vector ◽  
The Cross ◽  
Definition Of ◽  
Physical Quantities

The theory of angular vectors, which allows modelling of the properties of angular physical quantities, is considered. The meaning of the cross product of vectors was radically revised and changed. Formulas for finding torque and angular velocity in a coordinate-vector form with a correct mapping of their directions were deduced. Described definition of the inverse vector and its properties. The inversed vector allows us to perform vector division operations.

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