Computational Neuroscience
My lab's interests focus on understanding the cerebral cortex. We
use theoretical and computational methods to unravel the circuitry of the cerebral cortex,
the rules by which this circuitry develops or "self-organizes", and the
computational functions of this circuitry.
One goal of the lab is to understand the role of
activity-dependent, "correlation-based" mechanisms of synaptic
plasticity in determining cortical structure and function (see lab
publications on Models of
Neural Development, below). Under these mechanisms, synaptic
change appears to follow a rule like that proposed by Hebb in 1949: a
synapse is strengthened when pre- and postsynaptic activations are
correlated. We have analyzed cortical development in the presence of
such plasticity. One prominent feature of visual cortical development
is the formation of ocular dominance columns. These are alternating
patches of cortical cells that receive input only from the left eye or
only from the right eye. The left- and right-eye inputs segregate,
beginning from an initially intermixed condition, through an
activity-dependent synaptic competition. We have predicted the
conditions under which input neural activity will lead to such
segregation, and the size of the resulting patches. Another feature
of visual cortex is the tuning of the cells to respond to light-dark
borders of a particular orientation. Our analysis revealed that the
development of such orientation selectivity can be explained by a
correlation-based competition between ON-center and OFF-center inputs
to the visual cortex, very much like the left-eye/right-eye
competition that leads to ocular dominance column formation but in a
different parameter regime. More recently we have addressed the
combined development of ocular dominance and orientation selectivity,
showing how the orientation preferences of the two eyes can become
matched despite the tendency of the two eyes to segregate from one
another. All of these models make strong, testable predictions as to
the pattern of correlations that must exist among the activities of
inputs to cortex during development, if the mature cortical structure
arises by correlation-based rules. In addition, our hypothesis as to
the mechanism of matching of the two eye's orientation preferences
leads to testable predictions for the relationship between the two
eye's receptive fields in mature visual cortical cells, and explains
existing observations of the distribution of best stimulus disparities
in these cells.
Another goal of the lab is to develop realistic and testable
models of mature cortical circuitry (see lab publications on Models of
Neuronal Integration and Circuitry, below). We have developed
improved simple models of cortical excitatory cells and shown how
these naturally account for the high variability of cortical
responses. We have developed a candidate circuit model to explain the
full response properties of cortical cells in layer 4 (the
input-recipient layer) of cat primary visual cortex, addressing the
invariance of orientation tuning under changes in stimulus contrast
and a variety of other response properties. The model makes a number
of predictions, notably as to the response properties of inhibitory
neurons in layer 4. This circuit model involves "correlation-based
intracortical circuitry", and thus closely connects with the studies
described above of cortical development. We are now working on a
number of other aspects of the V1 circuit and also on the
circuitry of other areas, such as monkey visual area LIP.
While I was at UCSF, I also developed an experimental component to my lab,
focused on the study of the simultaneous activity of many neurons in
visual cortex using the "tetrode"
method of recording (see lab publications on Experimental
Results, below). Experiments applied these methods in cat visual
cortex and LGN (the nucleus providing visual input to cortex).
Additional publications from that work are still in process.
I am not establishing
an experimental lab at Columbia. Instead, Michael Stryker has taken
over the operation of the lab at UCSF.
Publications:
(Here's info on on how to download and view these
publications, including info on postscript, gzipped (.gz) files,
pdf files, tar files, tiff files, and other related topics.)
Pubs are organized in 5 overlapping categories:
Most Recent Publications:
- Ganguli, S., J.W. Bisley, J.D. Roitman, M.N. Shadlen,
M.E. Goldberg, and K.D. Miller (2008).
One-dimensional dynamics of attention and decision making in LIP.
Neuron 58:15-25
[pdf file]
[supplemental materials, pdf]
- Sharpee, T.O., K.D. Miller KD and M.P. Stryker (2008).
On the importance of the static nonlinearity in estimating
spatiotemporal neural filters with natural stimuli.
J Neurophysiol. 2008 Mar 19 (Epub ahead of print).
[pdf file]
- Palmer, S.E. and K.D. Miller (2007).
Effects of Inhibitory Gain and Conductance Fluctuations in a
Simple Model for Contrast-Invariant Orientation Tuning in
Cat V1. Journal of Neurophysiology 98: 63-78.
[pdf file]
- Sharpee, T.O., H. Sugihara, A.V. Kurgansky, S.P. Rebrik,
M.P. Stryker and K.D. Miller (2006).
Adaptive Filtering Enhances Information Transmission in Visual Cortex.
Nature 439, 936-942.
[pdf file]
[web supplement, pdf file]
(see also supplementary videos at Nature site).
Some Reviews/Overviews:
- Miller, K.D. (2003). Understanding Layer 4 of the Cortical
Circuit: A Model Based on Cat V1.
Cerebral Cortex 13, 73-82.
[pdf file]
A review of our modeling of the circuitry of layer 4 (the
input-recipient layer) of cat V1 and of related experiments, and of the
implications for understanding cortical layer 4 more generally. This
is an updated version of the portions of the Miller, Simons and Pinto
(2001) review dealing with V1, but without the discussion found in
that review of somatosensory cortex and the parallels between the two.
- Miller, K.D., D.J. Simons and D.J. Pinto (2001). Processing in
Layer 4 of the Neocortical Circuit: New Insights From Visual and
Somatosensory Cortex. Current Opinion in Neurobiology 11, 488-497.
[pdf file]
A review of common features of layer 4 (the input-recipient layer) of
visual and somatosensory cortex, focusing on the role of strong
feedforward inhibition.
Note: this is the pdf as it appeared in Current Opinion in
Neurobiology, copyright 2001 by Elsevier Science, provided here
with permission from Elsevier Science. Single copies of this article
may be downloaded and printed for the reader's personal research and
study.
- Ferster, D. and K.D. Miller (2000). Neural Mechanisms of
Orientation Selectivity in the Visual Cortex. Annual Reviews of
Neuroscience 23, 441-471.
[pdf file (0.3 MB)]
[compressed postscript (0.4 MB)]
[view on web (HTML)]
A review of experimental findings and modeling, including our own
modeling, characterizing the mature circuitry underlying orientation-tuned
responses. (See papers below on
Models of
Neuronal Integration and Circuitry).
- Miller, K.D., E. Erwin and A. Kayser (1999). Is the
Development of Orientation Selectivity Instructed by Activity?.
Journal of Neurobiology 41, 44-57.
[pdf file (0.4 MB)]
[compressed postscript (1.1 MB)]
An overview of our modeling of the development of orientation
selectivity and related experimental findings. (See papers below on
Models of
Neural Development).
- Miller, K.D. (1996a). Receptive Fields and Maps in the Visual Cortex:
Models of Ocular Dominance and Orientation Columns. In
Models of Neural Networks III, E. Domany, J.L. van Hemmen,
and K. Schulten, Eds. (Springer-Verlag, NY), pp. 55--78.
[compressed postscript]
[postscript]
An earlier review of our developmental modeling, presenting more
details of the models and covering ocular dominance as well as
orientation, but not covering our more recent results, e.g. those in
the Erwin and Miller and Kayser and Miller papers below (Models of
Neural Development).
Models of Neural Development:
If you're just getting started: here's a link to a guided tour
through the papers related to models of visual cortical development.
- Kayser, A.S. and K.D. Miller (2002). Opponent inhibition: A
developmental model of layer 4 of the neocortical circuit.
Neuron 33, 131-142.
[pdf file (3 MB)]
- Miller, K.D. and E. Erwin (2001). Effects of monocular
deprivation and reverse suture on orientation maps can be explained by
activity-instructed development of geniculocortical connections.
Visual Neuroscience 18, 821-834.
[postscript file (4 MB)]
[compressed postscript (1.2 MB)]
- Song, S., K.D. Miller and L.F. Abbott (2000). Competitive
Hebbian Learning Through Spike-Timing-Dependent Synaptic Plasticity.
Nature Neuroscience 3, 919-926.
[postscript file (0.9 MB)]
[compressed postscript (0.2 MB)]
- Miller, K.D., E. Erwin and A. Kayser (1999). Is the
Development of Orientation Selectivity Instructed by Activity?.
Journal of Neurobiology 41, 44-57.
[pdf file (0.4 MB)]
[compressed postscript (1.1 MB)]
- Erwin, E. and K.D. Miller (1999). The subregion
correspondence model of binocular simple cells.
Journal of Neuroscience 19, 7212-7229.
[compressed postscript (0.9 MB)]
[postscript (8.4 MB)]
- Erwin, E. and K.D. Miller (1998).
Correlation-Based Development of Ocularly-Matched Orientation
and Ocular Dominance Maps: Determination of Required Input
Activities.
Journal of Neuroscience 18, 9870-9895.
[compressed postscript (0.8 MB)]
[postscript (3 MB)]
- Miller, K.D. (1998).
Equivalence of a Sprouting-and-Retraction
Model of Neural Development and Correlation-Based Rules with
Subtractive Constraints. Neural Computation 10,
528-547.
[compressed postscript]
[postscript]
- Wimbauer, S., O.G. Wenisch, K.D. Miller and J.L. van Hemmen
(1997a). Development of spatiotemporal receptive fields of simple
cells: I. Model Formulation. Biological Cybernetics 77,
453-461.
[Biological Cybernetics Web site: abstract and pdf file]
[compressed postscript]
[postscript]
- Wimbauer, S., O.G. Wenisch, J.L. van Hemmen and K.D. Miller
(1997b). Development of spatiotemporal receptive fields of simple
cells: II. Simulation and Analysis. Biological Cybernetics
77, 463-477.
[Biological Cybernetics Web site: abstract and pdf file]
[compressed postscript (0.4 MB)]
[postscript (2.7 MB)]
- Miller,
K.D. (1996b). Synaptic Economics: Competition and Cooperation in
Synaptic Plasticity. Neuron 17, 367-370.
[compressed postscript]
[postscript]
Warning: corrections
in proof were not made by the printer, so there are an obvious error
and some funky sentences in the published version; these are corrected
in above net version, which also has some additional material. See also Neuron online
version of corrected manuscript.
- Troyer, T.W., A.J. Doupe and K.D. Miller (1996). An Associational
Hypothesis for Sensorimotor Learning of Birdsong. In
Computational Neuroscience: Trends in Research 1995, J.M. Bower,
Ed. (Academic Press), pp. 409-414.
[compressed postscript]
[postscript]
- Erwin,
E. and K.D. Miller (1996). Modeling Joint Development of Ocular
Dominance and Orientation Maps in Primary Visual Cortex. In
Computational Neuroscience: Trends in Research 1995,
J.M. Bower, Ed. (Academic Press), pp. 179-184.
[compressed postscript]
[postscript]
- Miller, K.D. (1996a). Receptive Fields and Maps in the Visual Cortex:
Models of Ocular Dominance and Orientation Columns. In
Models of Neural Networks III, E. Domany, J.L. van Hemmen,
and K. Schulten, Eds. (Springer-Verlag, NY), pp. 55--78.
[compressed postscript]
[postscript]
A shorter version of this was published as Miller,
K.D. (1995). Ocular Dominance and Orientation Columns. in
The Handbook of Brain Theory and Neural Networks, M.A. Arbib,
Ed. (MIT Press, Cambridge MA), pp. 660-665.
- Miller, K.D (1994). A Model for the Development of Simple Cell
Receptive Fields and Orientation Columns Through Activity-Dependent
Competition Between ON- and OFF-Center Inputs. Journal of
Neuroscience 14, 409-441.
[pdf (12.3 Mbytes)]
Here is a text-only version:
[compressed postscript (176 Kbytes)]
[postscript (488 Kbyes)]
Here are
most of the figures (tar file of gzip-ed (compressed) postscript
files: 900 Kbytes, files gunzip to 17 Mbytes). Here are the remaining
figures (tar file of gzipped scanned versions of three figures --
1.6 Mbytes, files gunzip to 2.8 Mbytes).
- Miller, K.D. and D.J.C. MacKay (1994). The Role of Constraints in
Hebbian Learning, Neural Computation 6, 100-126.
[pdf (scanned, 0.8 MB)]
[compressed postscript]
[postscript]
Here's a 1992 Caltech Tech Report version of this paper:
[compressed postscript]
[postscript]
The 1992 version is
longer, not as well written, but includes some extra topics.
- Miller, K.D., Editor (1992). Seminars in the Neurosciences, Vol. 4,
No. 1: Special Issue on The Use of Models in the Neurosciences.
- Miller, K.D. (1992). Development of Orientation Columns Via
Competition Between ON- and OFF-Center Inputs. NeuroReport
3, 73-76.
[pdf (scanned, 4.3 MB)]
- MacKay, D.J.C. and K.D. Miller (1990a). Analysis of Linsker's
applications of Hebbian rules to linear networks, Network 1,
257-298.
[pdf (scanned, 9 MB)]
Here is a text-only version:
[compressed postscript]
[postscript]
Here are the
figures (tar file of gzip-ed tiff
or postscript files).
- MacKay, D.J.C. and K.D. Miller (1990b). Analysis of Linsker's
simulations of Hebbian rules, Neural Computation 2, 169-182 (this
is a short preliminary version, the full paper is the above Network paper).
[pdf (scanned, 1 MB)]
- Miller, K.D. (1990a). Correlation-based models of neural
development, in Neuroscience and Connectionist Theory, M.A. Gluck
and D.E. Rumelhart, Eds. (Lawrence Erlbaum Associates, Hillsdale NJ),
pp. 267-353.
[pdf (scanned, 14 MB)]
Here is a
text-only version (tar file of gzipped
postscript files). Figures may be available here in the future.
- Miller, K.D. (1990b). Derivation of Hebbian equations from a
nonlinear model, Neural Computation 2, 319-331.
[compressed postscript]
[postscript]
- Miller, K.D. and M.P. Stryker (1990). Ocular dominance column
formation: Mechanisms and models, in Connectionist Modeling and Brain
Function: The Developing Interface, S.J. Hanson and C.R. Olson, Eds.
(MIT Press/Bradford), pp. 255-350.
[pdf (scanned, 10.5 MB)]
- Miller, K.D. (1989). Correlation-Based Mechanisms in Visual
Cortex: Theoretical and Experimental Studies. Ph.D. Thesis,
Stanford University, Program in Neurosciences (available from
University Microfilms, Ann Arbor).
Here is a text-only
version (tar file of gzipped postscript files).
Figures may be available here in the future.
- Miller, K.D., J.B. Keller and M.P. Stryker (1989). Ocular dominance
column development: Analysis and simulation. Science 245, 605-615.
[pdf (scanned, 6 MB)]
Models of Neuronal Integration and Circuitry:
- Ganguli, S., J.W. Bisley, J.D. Roitman, M.N. Shadlen,
M.E. Goldberg, and K.D. Miller (2008).
One-dimensional dynamics of attention and decision making in LIP.
Neuron 58:15-25
[pdf file]
[supplemental materials, pdf]
- Palmer, S.E. and K.D. Miller (2007).
Effects of Inhibitory Gain and Conductance Fluctuations in a
Simple Model for Contrast-Invariant Orientation Tuning in
Cat V1. Journal of Neurophysiology 98: 63-78.
[pdf file (.76 MB)]
- Lauritzen, T.Z. and K.D. Miller (2003). Different roles for
simple- and complex-cell inhibition in V1.
Journal of Neuroscience 23, 10201-10213.
[pdf file (.43 MB)]
- Murphy, B.K. and K.D. Miller (2003). Multiplicative gain
changes are induced by excitation or inhibition alone. Journal
of Neuroscience 23, 10040-10051.
[pdf file (.26 MB)]
- Troyer, T.W., A.E. Krukowski and K.D. Miller (2002). LGN
input to simple cells and contrast-invariant orientation tuning: An
analysis. J Neurophysiol. 87, 2741-2752.
[pdf file (.37 MB)]
- Miller, K.D. and T.W. Troyer (2002). Neural Noise Can Explain
Expansive, Power-Law Nonlinearities in Neural Response Functions.
J Neurophysiol. 87, 653-659.
[pdf file (.25 MB)]
- Kayser, A.S. and K.D. Miller (2002). Opponent inhibition: A
developmental model of layer 4 of the neocortical circuit.
Neuron 33, 131-142.
[pdf file (3 MB)]
- Lauritzen, T.Z., A.E. Krukowski and K.D. Miller (2001).
Local correlation-based circuitry can account for responses to
multi-grating stimuli in a model of cat V1.
Journal of Neurophysiology 86, 1803-1815.
[pdf file (1.1 MB)]
[compressed postscript (1.3 MB)]
- Kayser, A., N.J. Priebe and K.D. Miller
(2001). Contrast-dependent nonlinearities arise locally in a model
of contrast-invariant orientation tuning.
Journal of Neurophysiology 85, 2130-2149.
[pdf file (0.75 MB)]
[compressed postscript (1.26 MB)]
- Krukowski, A.E. and K.D. Miller (2001). Thalamocortical NMDA
conductances and intracortical inhibition can explain cortical
temporal tuning. Nature Neuroscience 4, 424-430.
[pdf file (0.33 MB)]
[web supplement to this paper (pdf, 0.2 MB)]
- Ferster, D. and K.D. Miller (2000). Neural Mechanisms of
Orientation Selectivity in the Visual Cortex. Annual Reviews of
Neuroscience, 23:441-471.
[pdf file (0.3 MB)]
[compressed postscript (0.4 MB)]
[view on web (HTML)]
- Erwin, E. and K.D. Miller (1999). The subregion
correspondence model of binocular simple cells.
Journal of Neuroscience 19, 7212-7229.
[compressed postscript (0.9 MB)]
[postscript (8.4 MB)]
- Bush, P.C., D.A. Prince and K.D. Miller (1999).
Increased pyramidal neuronal excitability and enhanced
NMDA conductance can account for post-traumatic epileptogenesis
without disinhibition: a computational model.
Journal of Neurophysiology 82:1748-1758.
[compressed postscript (0.3 MB)]
[postscript (2.7 MB)]
- Troyer, T.W., A.E. Krukowski, N.J. Priebe and K.D. Miller (1998).
Contrast-Invariant Orientation Tuning in Visual Cortex:
Thalamocortical Input Tuning and Correlation-Based Intracortical
Connectivity.
Journal of Neuroscience, 18, 5908-5927.
[compressed postscript]
[postscript]
Warning: The last two pages of this paper contain dense figures that
can take many minutes to load in a postscript viewer or to print. You
can also get these separately:
All but last two pages:
[compressed postscript]
[postscript]
Last two pages:
[compressed postscript]
[postscript]
The paper has only one color page (P. 26). Here it is separately, in
case that helps you with printing:
[P. 26, compressed postscript]
[P. 26, postscript]
- Troyer, T. and K.D. Miller (1997).
Integrate-and-Fire Neurons Matched to Physiological F-I Curves Yield
High Input Sensitivity and Wide Dynamic Range. In
Computational Neuroscience: Trends in Research 1997, J.M. Bower,
Ed. (Plenum Press, NY), pp. 197-201.
[compressed postscript]
[postscript]
- Troyer, T.W. and K.D. Miller (1997). Physiological Gain Leads to
High ISI Variability in a Simple Model of a Cortical Regular Spiking
Cell. Neural Computation 9, 971-983.
[compressed postscript]
[postscript]
- Troyer, T.W., A.J. Doupe and K.D. Miller (1996). An Associational
Hypothesis for Sensorimotor Learning of Birdsong. In
Computational Neuroscience: Trends in Research 1995, J.M. Bower,
Ed. (Academic Press), pp. 409-414.
[compressed postscript]
[postscript]
Experimental Results:
- Sharpee, T.O., K.D. Miller KD and M.P. Stryker (2008).
On the importance of the static nonlinearity in estimating
spatiotemporal neural filters with natural stimuli.
J Neurophysiol. 2008 Mar 19 (Epub ahead of print).
[pdf file]
- Sharpee, T.O., H. Sugihara, A.V. Kurgansky, S.P. Rebrik,
M.P. Stryker and K.D. Miller (2006).
Adaptive Filtering Enhances Information Transmission in Visual Cortex.
Nature 439, 936-942.
[pdf file (0.4 MB)]
[web supplement, pdf file (0.4 MB)]
(see also supplementary videos at Nature site).
- Emondi, A.A., S.P. Rebrik, A.V. Kurgansky and K.D. Miller (2004).
Tracking neurons recorded from tetrodes across time.
Journal of Neuroscience Methods 135, 95-105.
[pdf file (0.3 MB)]
- Liu, R.C., S. Tzonev, S. Rebrik and K.D. Miller (2001).
Variability and information in a neural code of the cat lateral
geniculate nucleus. Journal of Neurophysiology 86, 2789-2806.
[pdf file (0.5 MB)]
- Wright, B.D., S. Rebrik, A.A. Emondi and K.D. Miller (1999). Cross
Channel Correlations In Tetrode Recordings: Implications For
Spike-Sorting. Neurocomputing 26-27:1033-1038 (in special
2-volume issue containing proceedings of CNS98, the 1998 Computation
and Neural Systems meeting).
[HTML]
[postscript]
- Wright, B.D., S. Rebrik and K.D. Miller (1998).
Spike-Sorting of Tetrode Recordings in Cat LGN and Visual Cortex:
Cross-Channel Correlations, Thresholds, and Automatic Methods.
Society for Neuroscience Abstracts, 24:895. (354.6)
[HTML of full poster]
- Rebrik, S., S. Tzonev and K.D. Miller (1998).
Analysis of Tetrode Recordings in Cat Visual System.
In Proceedings of CNS97 (Computation and Neural Systems
Meeting, Big Sky Montana, July 1997), J.M Bower, Ed. (Plenum Press).
[HTML]
- Tzonev, S., S. Rebrik, and K.D. Miller (1997).
Response Specificity of Lateral Geniculate Nucleus Neurons.
Society for Neuroscience Abstracts, 23:450. (177.1)
[HTML of full poster]
- Miller, K.D., B. Chapman and M.P. Stryker (1989). Responses of
cells in cat visual cortex depend on NMDA receptors, Proc. Nat.
Acad. Sci. USA 86, 5183-5187.
Publications: How to download and view
To download a paper: click on 'compressed postscript' (for a
version compressed with gzip; file ends in .gz; uncompress with
'gunzip') or 'uncompressed postscript' (for a plain postscript
version; takes longer to download, so use 'compressed' if your browser
understands .gz).
Recent papers have 'pdf' (portable document format)
option rather than uncompressed postscript. Most browsers know what
to do to display pdf files; if yours doesn't, you can read pdf files
with
Acrobat Reader (freely downloadable) or various public domain programs.
Postscript and gzip
Can't read postscript? Pick up ghostscript/ghostview; this
link includes pointers to Mac and PC as well as Unix versions.
To read compressed files: It's easy to install gzip/gunzip on
your system: Click here
to find Mac and Dos executables for gzip/gunzip, as well as
source code that should compile on any Unix machine. Web browsers can
be easily configured to automatically gunzip .gz files; talk to your
system manager, or see Los Alamos
faq, described below. Windows users: compressed (gzipped) files
can also be unpacked with
winzip.
Terrific general information about getting started with
postscript and gzip, including how to get your browser to
automatically uncompress and display gzipped postscript, is here at
the faq of the Los
Alamos physics
e-print archives.
Tar and tiff
Parts of a few papers, where indicated, are available only as tar
files of compressed postscript and/or tiff files.
A tar file is a Unix file that packs together a whole set of files.
Save the file to some filename.tar; then, to unpack the file on a Unix
system, say "tar xvf filename.tar". Windows users can unpack tar
files with winzip. After
unpacking, most of the resulting files will end with ".gz", meaning
they've been compressed with gzip.
If you can't view tiff files, and run X-windows,
pick up xv, a nice
image manipulation and viewing shareware program for X-windows.
Guided tour of cortical development papers:
If you wish to get started reading the papers on models of cortical
development, I recommend the following path (for postscript files, I
link here to the compressed versions; links to the uncompressed
versions are also available, above):
- (1) Read
Miller et al., 1999 for a biologically- rather than
theoretically-oriented review of the models of
orientation selectivity, including 1998 work on combined development
of orientation and ocular dominance and a preview of 2002 Kayser and Miller
work on development of a complete
intracortical circuit (vs. just feedforward connections).
Read
Miller, 1996a for a more theoretically-oriented overview, but only
through the separate models of orientation and of ocular dominance.
Also, you might read the very short Miller,
1996b, which is a minireview focusing on the biological nature of
synaptic competition. The existence of this competition is assumed in
our modeling, but we do not model its mechanism.
UPDATE: see
- (2) Read Miller, 1990a (text-only
version) for a detailed introduction to the ocular dominance model
and the mathematics underlying the models. While this focuses only on
the ocular dominance model, the mathematics of the orientation model
is identical. Miller, Keller and Stryker, 1989 is the original
reference, but Miller, 1990a is a better introduction.
- (3) Read Miller, 1994 (text,
most
figures, other
figures) for details of the orientation model.
- (4) Read Erwin and Miller,
1996 (short conference version) or
1998 (full paper) to see how the orientation and ocular
dominance models are merged into one model.
Also read
Erwin and Miller, 1999 to see the implications of this
combined orientation/ocular dominance model for the binocular
organization and disparity selectivity of mature simple cells, and
how this compares with experimental data.
See also Wimbauer et al.,
1997a and
1997b, in which this same formal model is used to study the
development of direction selectivity in oriented simple cells through
competition of lagged and non-lagged inputs.
- (5) Read Miller
and MacKay, 1994 and MacKay and Miller, 1990a (text, figures)
for a full understanding of the mathematics of a single-output-cell
model.
- (6) Further excursions:
(i) Read Miller,
1990b to see how the framework can be derived from a more fully
nonlinear starting point.
(ii) Read Miller,
1998 to see how the framework can be used to analyze models based
on synaptic sprouting and retraction as well as on modification of
the strengths of anatomically fixed synapses.
(iii) Read the Ph.D. thesis (Miller, 1989) (text-only),
chapters 5 and 6, for the fullest available mathematical analysis of
the full (many-output-cell) model. Alternatively, Miller and Stryker,
1990 has somewhat more mathematical detail than Miller, 1990a, but
less than the thesis. The full thesis includes all the material in
both Miller, 1990a and Miller and Stryker, 1990.
See Also: