The name is absent



To show that place fields can be derived from grid-cells by Sparsification we
simulated a linear two-layer network. The input units were IOO simulated grid-
cells of a virtual rat with activity patterns synthesized by Gaussians arranged
on a hexagonal grid (Fig. 1 A). Some positional jitter, random anisotropy, and
amplitude variation of the Gaussians was introduced, and white noise was added
to qualitatively match the slightly irregular experimental data.

Let gi (r) denote the activity of grid-cell gi as a function of location r. Given
a virtual path
r(t) of a rat within the enclosure, the input into the hippocampus
coming from the grid-cells is
xi(t) := gi(~(t')'). To achieve sparseness we applied
independent component analysis (ICA) Hyvarinen (1999b) on a set of 200.000
time points from this input by subtracting the mean and using the CuBICA
algorithm, which attempts to diagonalize the tensors of third and fourth order
cumulants (Blaschke and Wiskott, 2004), but we have obtained similar results
with other Sparsification algorithms, such as FastICA (Hyvarinen, 1999a) or sim-
ply maximizing peak activity under a unit variance, zero mean and decorrelation
constraint. The sign of each output unit, which is arbitrary for ICA, was chosen
such that the value with the largest magnitude is positive, and then constants
Cj
were added to ensure nonnegative values. This yielded an affine transformation
with matrix
T producing 100 output signals yj∙(t) := Pi Tjixi(t) + cj∙ that are
maximally independent and significantly sparser than the input signals (kurtosis
increased on average from 2.9 for the input units to 28.6 for the output units).
The output-unit activities as a function of location are
pj(r) := Pi Tjigi(r) + Cj
and show localized place fields (Fig. 1, B). We measured the number of peaks in
a unit’s output by counting the number of distinct contiguous areas containing
pixels with at least 50% of the unit’s maximum activity. A large proportion of
output units (76%) show a single spot of activity (Fig. 1 B, units 1, 25, 50, 75),
some units (5%) show few spots (Fig. 1 B, unit 87), both being consistent with



More intriguing information

1. The name is absent
2. Database Search Strategies for Proteomic Data Sets Generated by Electron Capture Dissociation Mass Spectrometry
3. Structural Breakpoints in Volatility in International Markets
4. Problems of operationalizing the concept of a cost-of-living index
5. Keystone sector methodology:network analysis comparative study
6. Innovation Trajectories in Honduras’ Coffee Value Chain. Public and Private Influence on the Use of New Knowledge and Technology among Coffee Growers
7. The name is absent
8. The role of statin drugs in combating cardiovascular diseases
9. Running head: CHILDREN'S ATTRIBUTIONS OF BELIEFS
10. The name is absent
11. The economic doctrines in the wine trade and wine production sectors: the case of Bastiat and the Port wine sector: 1850-1908
12. Announcement effects of convertible bond loans versus warrant-bond loans: An empirical analysis for the Dutch market
13. Skills, Partnerships and Tenancy in Sri Lankan Rice Farms
14. The name is absent
15. Menarchial Age of Secondary School Girls in Urban and Rural Areas of Rivers State, Nigeria
16. The bank lending channel of monetary policy: identification and estimation using Portuguese micro bank data
17. The Challenge of Urban Regeneration in Deprived European Neighbourhoods - a Partnership Approach
18. THE CO-EVOLUTION OF MATTER AND CONSCIOUSNESS1
19. The name is absent
20. The name is absent