Evolution of Motor Memory During the Seconds After Observation of Motor Error

2007 ◽  
Vol 97 (6) ◽  
pp. 3976-3985 ◽  
Author(s):  
Vincent S. Huang ◽  
Reza Shadmehr

When a movement results in error, the nervous system amends the motor commands that generate the subsequent movement. Here we show that this adaptation depends not just on error, but also on passage of time between the two movements. We observed that subjects learned a reaching task faster, i.e., with fewer trials, when the intertrial time intervals (ITIs) were lengthened. We hypothesized two computational mechanisms that could have accounted for this. First, learning could have been driven by a Bayesian process where the learner assumed that errors are the result of perturbations that have multiple timescales. In theory, longer ITIs can produce faster learning because passage of time might increase uncertainty, which in turn increases sensitivity to error. Second, error in a trial may result in a trace that decays with time. If the learner continued to sample from the trace during the ITI, then adaptation would increase with increased ITIs. The two models made separate predictions: The Bayesian model predicted that when movements are separated by random ITIs, the learner would learn most from a trial that followed a long time interval. In contrast, the trace model predicted that the learner would learn most from a trial that preceded a long time interval. We performed two experiments to test for these predictions and in both experiments found evidence for the trace model. We suggest that motor error produces an error memory trace that decays with a time constant of about 4 s, continuously promoting adaptation until the next movement.

Fluids ◽  
2018 ◽  
Vol 3 (3) ◽  
pp. 63 ◽  
Author(s):  
Thomas Meunier ◽  
Claire Ménesguen ◽  
Xavier Carton ◽  
Sylvie Le Gentil ◽  
Richard Schopp

The stability properties of a vortex lens are studied in the quasi geostrophic (QG) framework using the generalized stability theory. Optimal perturbations are obtained using a tangent linear QG model and its adjoint. Their fine-scale spatial structures are studied in details. Growth rates of optimal perturbations are shown to be extremely sensitive to the time interval of optimization: The most unstable perturbations are found for time intervals of about 3 days, while the growth rates continuously decrease towards the most unstable normal mode, which is reached after about 170 days. The horizontal structure of the optimal perturbations consists of an intense counter-shear spiralling. It is also extremely sensitive to time interval: for short time intervals, the optimal perturbations are made of a broad spectrum of high azimuthal wave numbers. As the time interval increases, only low azimuthal wave numbers are found. The vertical structures of optimal perturbations exhibit strong layering associated with high vertical wave numbers whatever the time interval. However, the latter parameter plays an important role in the width of the vertical spectrum of the perturbation: short time interval perturbations have a narrow vertical spectrum while long time interval perturbations show a broad range of vertical scales. Optimal perturbations were set as initial perturbations of the vortex lens in a fully non linear QG model. It appears that for short time intervals, the perturbations decay after an initial transient growth, while for longer time intervals, the optimal perturbation keeps on growing, quickly leading to a non-linear regime or exciting lower azimuthal modes, consistent with normal mode instability. Very long time intervals simply behave like the most unstable normal mode. The possible impact of optimal perturbations on layering is also discussed.


2013 ◽  
Vol 10 (88) ◽  
pp. 20130630 ◽  
Author(s):  
Lucie G. Bowden ◽  
Matthew J. Simpson ◽  
Ruth E. Baker

Cell trajectory data are often reported in the experimental cell biology literature to distinguish between different types of cell migration. Unfortunately, there is no accepted protocol for designing or interpreting such experiments and this makes it difficult to quantitatively compare different published datasets and to understand how changes in experimental design influence our ability to interpret different experiments. Here, we use an individual-based mathematical model to simulate the key features of a cell trajectory experiment. This shows that our ability to correctly interpret trajectory data is extremely sensitive to the geometry and timing of the experiment, the degree of motility bias and the number of experimental replicates. We show that cell trajectory experiments produce data that are most reliable when the experiment is performed in a quasi-one-dimensional geometry with a large number of identically prepared experiments conducted over a relatively short time-interval rather than a few trajectories recorded over particularly long time-intervals.


1999 ◽  
Vol 09 (07) ◽  
pp. 1089-1121 ◽  
Author(s):  
A. BABIN ◽  
A. MAHALOV ◽  
B. NICOLAENKO

The 3-D rotating Boussinesq equations (the "primitive" equations of geophysical fluid flows) are analyzed in the asymptotic limit of strong stable stratification. The resolution of resonances and a nonstandard small divisor problem are the basis for error estimates for such fast singular oscillating limits. Existence on infinite time intervals of regular solutions to the viscous 3-D "primitive" equations is proven for initial data in Hα, α≥ 3/4. Existence on a long-time interval T*of regular solutions to the 3-D inviscid equations is proven for initial data in Hα, α > 5/2 (T*→∞ as the frequency of gravity waves →∞).


The transformation operator of electrodynamics for a finite time interval with uncertain boundaries is represented by a continuous switching on and off of the charge. It is shown that its divergencies are the same as those appearing in the S matrix theory, and a covariant procedure is given for isolating their infinite parts. Provided Gupta’s renormalized Lagrangian is used as a starting point all the infinities may be removed. The coefficients of the counter terms are power series in the time-dependent charge with coefficients that are independent of the time interval being considered. The practice of approximating the matrix elements of the transformation operators for long time intervals by matrix elements of the S matrix is discussed and justified. In an appendix the extension of these results to the renormalizable meson theories is discussed.


2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Manish Gupta ◽  
Jyotsna Mishra ◽  
K. S. Pitre

A study has been made on the mechanism of corrosion of mild steel and the effect of nitrilo trimethylene phosphonic (NTMP) acid as a corrosion inhibitor in acidic medium, that is, 10% HC1 using the weight loss method and electrochemical techniques, that is, potentiodynamic and galvanostatic polarization measurements. Although corrosion is a long-time process, but it takes place at a faster rate in the beginning which goes on decreasing with due course of time. The above-mentioned methods of corrosion rate determination furnish an average value for a long-time interval. Looking at the versatility and minimum detection limit of the voltammetric method, the authors have developed a new voltammetric method for the determination of corrosion rate at short-time intervals. The results of corrosion of mild steel in 10% HC1 solution with and without NTMP inhibitor at short-time intervals have been reported. The corrosion inhibition efficiency of NTMP is 93% after 24 h.


1985 ◽  
Vol 18 (2) ◽  
pp. 165-225 ◽  
Author(s):  
Lars Folke Olsen ◽  
Hans Degn

Chaos is a widespread and easily recognizable phenomenon that hardly anybody took notice of until recently. The reason may be that chaos has something profoundly counterintuitive about it. It will not fit easily into any familiar cause–effect frame. The best introduction to chaos is by the way of an example. Consider a leaking faucet (Shaw, 1984). When the weight of the accumulating drop exceeds the surface tension the drop falls and a new drop begins to form. If the leak is small and the pressure in the faucet is constant, the time taken for the drop to reach the critical weight is constant. The dripping is perfectly periodic, the period depending on the leak rate. If the leak is slightly increased, the period of dripping will decrease slightly and vice versa. However, somewhere beyond this point the leaking faucet becomes a nuisance. When the leak is increased beyond a certain point the dripping looses its regularity. The time interval between the drops will first alternate periodically between a short and a long time interval. After a further increase of the leak this double periodic pattern will become unstable and change into a new pattern where four different time intervals between the drops alternate periodically. As the leak is further increased the period will double again and again and finally the dripping becomes completely irregular without any repeating pattern. When this occurs we are observing chaos. At the same time we are posed with the problem of understanding how such a ridiculously simple system can show random behaviour.


2008 ◽  
Vol 23 (6) ◽  
pp. 430-433 ◽  
Author(s):  
Richard Mahlberg ◽  
Thorsten Kienast ◽  
Tom Bschor ◽  
Mazda Adli

AbstractPatients with affective disorders have often been reported to experience subjective changes in how they perceive the flow of time. Time reproduction tasks provide information about the memory component of time perception and are thought to remain unaffected by pulse rate disturbances in the pacemaker of the internal clock.In our study, 30 patients with acute depression, 30 patients with acute mania, and 30 healthy subjects of all age groups were presented with a time reproduction task. Participants were asked to observe a stimulus presented on a computer screen for a certain length of time and, subsequently, to reproduce the stimulus for a similar length of time by pressing the space bar on the computer keyboard. Stimuli were presented to each subject for 1, 6, and 37 s.On average, the time intervals reproduced by manic patients were shorter than those reproduced by depressed patients. Manic patients reproduced the short time interval (6 s) correctly, but under-reproduced the long time interval (37 s, P < 0.001). Depressed patients correctly reproduced the long time interval, but over-reproduced the short time interval (P < 0.001).Remembering time intervals as having been longer than they actually were may lead to a slowed experience of time, as has been described in depressed patients; precisely the converse seems to apply to manic patients.


2018 ◽  
pp. 124-130
Author(s):  
Yu. V. Petrov ◽  
S. I. Bakaras ◽  
S. A. Yukhno

This article presents the expressions which allow evaluating the potential accuracy of radio source location by the method of «imaginary base» when using the linear model of changing the bearing on it. The concept of the method of «imaginary base» is to be used in solving the triangulation problem not only of measuring bearing, but also their extrapolated values at a certain time interval. Potential characteristics is determined by accuracy, dynamic and geometrical factors, bearing measurement and extrapolation times. The article shows that when using a linear model, there are limitations both on the time of measuring bearing and on the time of extrapolation. It will be because of the increase in the variance of the error of estimating the distance. Limiting of series decomposition members number of non-linear bearing change dependence from time there are. It depends on the speed of changing bearing (depends on the range and speed) and the initial bearing (depends on the track angle). Extrapolation over long time intervals is possible only at long distances and at relatively low speeds.


1976 ◽  
Vol 66 (1) ◽  
pp. 45-60 ◽  
Author(s):  
Lewis J. Katz

abstract The application of microtremor spectra in predicting frequency-dependent amplification effects of local site geology was investigated. Long time-interval (&gt; 45 min) microtremor data were used to estimate Power Spectral Density (PSD) plots. Peaks occurring in these PSD plots were correlated with peaks of transfer functions (Haskell, 1960 and 1962) calculated from known geological models. The resulting apparent positive correlations indicate that a procedure of estimating PSD plots from long time intervals of microtremor data would be useful in predicting response spectra for earthquake risk evaluation.


2011 ◽  
Vol 46 (2) ◽  
pp. 63-73
Author(s):  
V. Pashkevich ◽  
G. Eroshkin

Construction of the New High-Precision Moon Rotation Series at a Long Time Intervals The main purposes of this research are the construction of the new high-precision Moon Rotation Series (MRS2011), dynamically adequate to the DE404/LE404 and the DE406/LE406 ephemeris, over long time intervals. The comparison of the new highprecision Moon Rotation solutions of MRS2011 with the solution of MRS2010 (Pashkevich and Eroshkin, 2010), which is dynamically adequate to the DE200/LE200 ephemeris over 418.9 year time interval, is performed. The dynamics of the rotational motion of the Moon is studied numerically by using Rodrigues-Hamilton parameters over 418.9, 2000 and 6000 years. The numerical solution of the Moon rotation is implemented with the quadruple precision of the calculations. The results of the numerical solution of the problem are compared with the composite semi-analytical theory of the Moon rotation (SMR) (Pashkevich and Eroshkin, 2010) with respect to the fixed ecliptic of epoch J2000. The initial conditions of the numerical integration are taken from SMR. The investigation of the discrepancies is carried out by the least squares and spectral analysis methods for the Newtonian case. All the secular, periodic and Poisson terms, representing the behavior of the residuals, are interpreted as corrections to SMR semi-analytical theory. As a result, the Moon Rotation Series (MRS2011) is constructed, which is dynamically adequate to the DE404/LE404 and the DE406/LE406 ephemeris over 418.9, 2000 and 6000 years. A numerical solution for the Moon rotation is obtained anew with the new initial conditions calculated by means of MRS2011. The discrepancies between the new numerical solution and the semi-analytical solution of MRS2011 do not surpass 20 mas over 418.9 year time interval, 64 mas over 2000 year time interval and 8 arc seconds over 6000 year time interval. Thus, the result of the comparison demonstrates a good consistency of MRS2011 series with the DE/LE ephemeris.


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