-
1
-
-
0039065101
-
-
L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998).
-
(1998)
Rev. Mod. Phys.
, vol.70
, pp. 223
-
-
Gammaitoni, L.1
Hänggi, P.2
Jung, P.3
Marchesoni, F.4
-
3
-
-
0037712665
-
-
G. Wenning and K. Obermayer, Phys. Rev. Lett. 90, 120602 (2003); S. Laughlin and T. Sejnowski, Science 301, 1870 (2003); T. Hoch, G. Wenning and C. Obermayer, Phys. Rev. E 68, 011911 (2003); B. Kosko and S. Mitaim, Neural Networks 16, 755 (2003); M. Chacron, A. Longtin, and L. Maler, Network Comput. Neural Syst. 14, 803 (2003); I. Goychuk and P. Hänggi, Phys. Rev. E 69, 021104 (2004).
-
(2003)
Phys. Rev. Lett.
, vol.90
, pp. 120602
-
-
Wenning, G.1
Obermayer, K.2
-
4
-
-
0141645490
-
-
G. Wenning and K. Obermayer, Phys. Rev. Lett. 90, 120602 (2003); S. Laughlin and T. Sejnowski, Science 301, 1870 (2003); T. Hoch, G. Wenning and C. Obermayer, Phys. Rev. E 68, 011911 (2003); B. Kosko and S. Mitaim, Neural Networks 16, 755 (2003); M. Chacron, A. Longtin, and L. Maler, Network Comput. Neural Syst. 14, 803 (2003); I. Goychuk and P. Hänggi, Phys. Rev. E 69, 021104 (2004).
-
(2003)
Science
, vol.301
, pp. 1870
-
-
Laughlin, S.1
Sejnowski, T.2
-
5
-
-
85035194143
-
-
G. Wenning and K. Obermayer, Phys. Rev. Lett. 90, 120602 (2003); S. Laughlin and T. Sejnowski, Science 301, 1870 (2003); T. Hoch, G. Wenning and C. Obermayer, Phys. Rev. E 68, 011911 (2003); B. Kosko and S. Mitaim, Neural Networks 16, 755 (2003); M. Chacron, A. Longtin, and L. Maler, Network Comput. Neural Syst. 14, 803 (2003); I. Goychuk and P. Hänggi, Phys. Rev. E 69, 021104 (2004).
-
(2003)
Phys. Rev. E
, vol.68
, pp. 011911
-
-
Hoch, T.1
Wenning, G.2
Obermayer, C.3
-
6
-
-
0038045067
-
-
G. Wenning and K. Obermayer, Phys. Rev. Lett. 90, 120602 (2003); S. Laughlin and T. Sejnowski, Science 301, 1870 (2003); T. Hoch, G. Wenning and C. Obermayer, Phys. Rev. E 68, 011911 (2003); B. Kosko and S. Mitaim, Neural Networks 16, 755 (2003); M. Chacron, A. Longtin, and L. Maler, Network Comput. Neural Syst. 14, 803 (2003); I. Goychuk and P. Hänggi, Phys. Rev. E 69, 021104 (2004).
-
(2003)
Neural Networks
, vol.16
, pp. 755
-
-
Kosko, B.1
Mitaim, S.2
-
7
-
-
0347625929
-
-
G. Wenning and K. Obermayer, Phys. Rev. Lett. 90, 120602 (2003); S. Laughlin and T. Sejnowski, Science 301, 1870 (2003); T. Hoch, G. Wenning and C. Obermayer, Phys. Rev. E 68, 011911 (2003); B. Kosko and S. Mitaim, Neural Networks 16, 755 (2003); M. Chacron, A. Longtin, and L. Maler, Network Comput. Neural Syst. 14, 803 (2003); I. Goychuk and P. Hänggi, Phys. Rev. E 69, 021104 (2004).
-
(2003)
Network Comput. Neural Syst.
, vol.14
, pp. 803
-
-
Chacron, M.1
Longtin, A.2
Maler, L.3
-
8
-
-
45849155671
-
-
G. Wenning and K. Obermayer, Phys. Rev. Lett. 90, 120602 (2003); S. Laughlin and T. Sejnowski, Science 301, 1870 (2003); T. Hoch, G. Wenning and C. Obermayer, Phys. Rev. E 68, 011911 (2003); B. Kosko and S. Mitaim, Neural Networks 16, 755 (2003); M. Chacron, A. Longtin, and L. Maler, Network Comput. Neural Syst. 14, 803 (2003); I. Goychuk and P. Hänggi, Phys. Rev. E 69, 021104 (2004).
-
(2004)
Phys. Rev. E
, vol.69
, pp. 021104
-
-
Goychuk, I.1
Hänggi, P.2
-
10
-
-
0001472933
-
-
S. K. Han, W. S. Kim, and H. Kook, Phys. Rev. E 58, 2325 (1998); T. Kanamaru and Y. Okabe, ibid. 62, 2629 (2000).
-
(1998)
Phys. Rev. E
, vol.58
, pp. 2325
-
-
Han, S.K.1
Kim, W.S.2
Kook, H.3
-
11
-
-
0034238012
-
-
S. K. Han, W. S. Kim, and H. Kook, Phys. Rev. E 58, 2325 (1998); T. Kanamaru and Y. Okabe, ibid. 62, 2629 (2000).
-
(2000)
Phys. Rev. E
, vol.62
, pp. 2629
-
-
Kanamaru, T.1
Okabe, Y.2
-
14
-
-
33646974623
-
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note
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1/2N [9]. The capacity per neuron, C/N(J+1), reaches the maximum value of 3.8 N between J=2 and J=3.)
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16
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84856122815
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H=1/[1 +exp(-x)] are given at http://www.mpipks-dresden.mpg.de/~chris. In this case, the period-two limit cycle of the RNN (Sec. III A.) is replaced by a fixed point x -0.
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18
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33646977958
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note
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2 where 〉 ···〉 designates averaging over the state (note that F=2Q-C) [13].
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20
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84856127462
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jk} is listed at http://www.mpipks-dresden.mpg.de/~chris.
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33646975802
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note
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t at the previous time step was uniform. This is a property of the evolved weights.
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22
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33646984958
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note
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6000) taken from the GNU scientific library with seed randomized by the CPU clock. Results analogous to those reported for UWN noise were also obtained for Gaussian-distributed noise.
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23
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33646973385
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note
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The behavior described in the main text was obtained in 93% of our runs for weak noise [α<0.16 (Δα=0.01)], 81% of runs for moderate noise [0.16≤α<0.29 (Δα=0.01)], and 87% of runs for strong noise [0.29 ≤α≤1.0 (Δα=0.05)]. Ten runs were performed at each noise strength.
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24
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k and the corresponding eigenvectors (in a Mathematica 5.0 notepad) can be viewed at http://www.mpipks-dresden.mpg.de~chris.
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26
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33646970073
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note
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25 have settled to fixed points other than the states listed above.
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note
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This will also be the case when the sensory stimulus is extended in time and the sensory neurons rapidly adapt.
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note
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While we evaluated the success rate of recovery of weak signals in Fig. 4(b) after 1000 iterations, in most cases fewer than 20 iterations are required to converge to the correct memory state.
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34
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0003979924
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Addison-Wesley, Cambridge, MA
-
J. Hertz, A. Krogh, and R. Palmer, Introduction to the Theory of Neural Computation (Addison-Wesley, Cambridge, MA, 1991).
-
(1991)
Introduction to the Theory of Neural Computation
-
-
Hertz, J.1
Krogh, A.2
Palmer, R.3
-
35
-
-
0001518167
-
-
Z. Lou, Neural Comput. 3, 226 (1991); C. Monterola et al., J. Forecast 21, 435 (2002).
-
(1991)
Neural Comput.
, vol.3
, pp. 226
-
-
Lou, Z.1
-
36
-
-
0036735445
-
-
Z. Lou, Neural Comput. 3, 226 (1991); C. Monterola et al., J. Forecast 21, 435 (2002).
-
(2002)
J. Forecast
, vol.21
, pp. 435
-
-
Monterola, C.1
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