Connectionists: preprints on movement duration and orientation models

[Ning Qian]

Dear Colleagues,

The pdf files for the following two preprints are available for download 
(see web address after each abstract below).

Best regards,

Ning Qian


    An Optimization Principle for Determining Movement Duration

Hirokazu Tanaka, John Krakauer, and Ning Qian, /J. Neurophysiol./, 2006, 
in press.


      Abstract

Movement duration is an integral component of motor control, but nearly 
all extant optimization models of motor planning pre-fix duration 
instead of explaining it. Here we propose a new optimization principle 
that predicts movement duration. The model assumes that the brain 
attempts to minimize movement duration under the constraint of meeting 
an accuracy criterion. The criterion is task and context dependent but 
is fixed for a given task and context. The model determines a unique 
duration as a tradeoff between speed (time optimality) and accuracy 
(acceptable end-point scatter). We analyzed the model for a linear motor 
plant, and obtained a closed-form equation for determining movement 
duration. By solving the equation numerically with specific 
plant-parameters for the eye and arm, we found that the model can 
reproduce saccade duration as a function of amplitude (the main 
sequence), and arm-movement duration as a function of the 
target-distance-to-size ratio (Fitts' law). In addition, it explains the 
dependence of peak saccadic speed on amplitude, and the dependence of 
saccadic duration on initial eye position. Furthermore, for arm 
movements, the model predicts a scaling relationship between peak 
velocity and distance, and a reduction in movement duration with a 
moderate increase in viscosity. Finally, for a linear plant, our model 
predicts a neural control signal identical to that of the 
minimum-variance model set to the same movement duration. This control 
signal is a smooth function of time (except at the end point), in 
contrast to the discontinuous bang-bang control found in the 
time-optimal-control literature. We suggest that one aspect of movement 
planning, as revealed by movement duration, may be to assign an 
end-point accuracy criterion for a given task and context.

http://brahms.cpmc.columbia.edu/publications/min-time.pdf



    A Comparison among some Models of V1 Orientation Selectivity

Andrew F. Teich and Ning Qian, /J. Neurophysiol./, 2006, in press.


      Abstract

Several models exist for explaining V1 orientation tuning. The modified 
feedforward model (MFM) and the recurrent model (RM) are major examples. 
We have implemented, at the same level of detail, these two models 
alongside a few newer variations, and thoroughly compared their 
receptive-field structures. We found that anti-phase inhibition in the 
MFM enhances both spatial phase information and orientation tuning, 
producing well-tuned simple cells. This remains true for a newer version 
of the MFM that incorporates un-tuned complex-cell inhibition. In 
contrast, when the recurrent connections in the RM are strong enough to 
produce typical V1 orientation tuning, they also eliminate spatial phase 
information, making the cells complex. Introducing phase-specificity 
into the connections of the RM (as done in an original version of the 
RM) can make the cells phase sensitive, but the cells show an incorrect 
90 deg peak-shift of orientation tuning under opposite contrast signs. 
An inhibition-dominant version of the RM can generate well-tuned cells 
across the simple/complex spectrum, but it predicts that the net effect 
of cortical interactions is to suppress feedforward excitation across 
all orientations in simple cells. Finally, adding anti-phase inhibition 
used in the MFM into the RM produces a most general model. We call this 
new model the modified recurrent model (MRM) and show that this model 
can also produce well-tuned cells throughout the simple/complex 
spectrum. Unlike the inhibition-dominant RM, the MRM is consistent with 
data from cat V1 suggesting that the net effect of cortical interactions 
is to boost simple cell responses at the preferred orientation. These 
results suggest that the MFM is well suited for explaining orientation 
tuning in simple cells, whereas the standard RM is for complex cells. 
The assignment of the RM to complex cells also avoids conflicts between 
the RM and the experiments of cortical inactivation (done on simple 
cells) and the spatial-frequency dependence of orientation tuning (found 
in simple cells). Since orientation-tuned V1 cells show a continuum of 
simple- to complex-cell behavior, the MRM provides the best description 
of V1 data.

http://brahms.cpmc.columbia.edu/publications/orient-models.pdf




-- 
Ning Qian, Ph. D.
Associate Professor
Ctr. Neurobiology & Behavior
Columbia University / NYSPI
Kolb Annex, Rm 519
1051 Riverside Drive, Box 87
New York, NY 10032, USA

http://brahms.cpmc.columbia.edu
nq6 at columbia.edu
212-543-6931 ext 600 (Office)
212-543-5816 (Fax)