Recently developed methods for estimating directionality in the coupling between oscillators were tested on experimental time series data from electroreceptors of paddlefish, because each electroreceptor contains two distinct types of noisy oscillators. One type of oscillator is in the sensory epithelia, and another type is in the terminals of afferent neurons. Based on morphological organization and our previous work, we expected unidirectional coupling, whereby epithelial oscillations synaptically influence the spiking oscillators of afferent neurons. Using directionality analysis we confirmed unidirectional coupling of oscillators embedded in electroreceptors. We studied the performance of directionality algorithms for decreasing length of data. Also, we experimentally varied the strength of oscillator coupling, to test the effect of coupling strength on directionality algorithms.

2.
J. S.
Bendat
and
A. G.
Piersol
,
Random Data: Analysis and Measurement Procedures
, 3rd ed. (
Wiley
, New York,
2000
).
3.
H. D. I.
Abarbanel
,
Analysis of Observed Chaotic Data
(
Springer-Verlag
, New York,
1997
).
4.
H.
Kantz
and
T.
Schreiber
,
Nonlinear Time Series Analysis
(
Cambridge University Press
,
Cambridge
,
1997
).
5.
M. G.
Rosenblum
,
A. S.
Pikovsky
,
J.
Kurths
,
C.
Schäfer
, and
P.
Tass
, “
Phase synchronization: From theory to data analysis
,” in
Handbook of Biological Physics
, Neuro-Informatics and Neural Modeling, edited by
F.
Moss
and
S.
Gielen
(
Elsevier Science
,
Amsterdam
,
2001
), Vol.
4
, Chap. 9, pp.
279
321
.
6.
A.
Pikovsky
,
M.
Rosenblum
, and
J.
Kurths
,
Synchronization: A Universal Concept in Nonlinear Science
(
Cambridge University Press
, Cambridge,
2001
).
7.
8.
A.
Kaiser
and
T.
Schreiber
,
Physica D
166
,
43
(
2002
).
9.
N. F.
Rulkov
,
M. M.
Sushchik
, and
L. S.
Tsimring
,
Phys. Rev. E
51
,
980
(
1995
).
10.
S. J.
Schiff
,
P.
So
, and
T.
Chang
,
Phys. Rev. E
54
,
6708
(
1996
).
11.
M. L.
Van Quyen
,
J.
Martinerie
,
C.
Adam
, and
F. J.
Varela
,
Physica D
127
,
250
(
1999
).
12.
R.
Quian Quiroga
,
J.
Arnold
, and
P.
Grassberger
,
Phys. Rev. E
61
,
5142
(
2000
).
13.
C. W. J.
Granger
,
Econometrica
37
,
424
(
1969
).
14.
C. W. J.
Granger
,
J. Econ. Dyn. Control
2
,
329
(
1980
).
15.
F. C.
Hoppensteadt
and
E. M.
Izhikevich
,
Weakly Connected Neural Networks
(
Springer-Verlag
,
New York
,
1997
).
16.
M. G.
Rosenblum
and
A.
Pikovsky
,
Phys. Rev. E
64
,
045202
(
2001
).
17.
M. G.
Rosenblum
,
L.
Cimponeriu
,
A.
Bezerianos
,
A.
Patzak
, and
R.
Mrowka
,
Phys. Rev. E
65
,
041909
(
2002
).
18.
R.
Mrowka
,
L.
Cimponeriu
,
A.
Patzak
, and
M. G.
Rosenblum
,
Am. J. Physiol.
285
,
R1395
(
2003
).
19.
L.
Cimponeriu
,
M. G.
Rosenblum
,
T.
Fieseler
,
J.
Dammers
,
M.
Schiek
,
M.
Majtanik
,
P.
Morosan
,
A.
Bezerianos
, and
P.
Tass
,
Prog. Theor. Phys. Suppl.
150
,
22
(
2003
).
20.
M.
Palus
,
V.
Komárek
,
Z.
Hrnčíř
, and
K.
Štěrbovǎ
,
Phys. Rev. E
63
,
046211
(
2001
).
21.
D. A.
Smirnov
,
M. B.
Bodrov
,
J. L.
Perez Velazquez
,
R. A.
Wennberg
, and
B. P.
Bezruchko
,
Chaos
15
,
024102
(
2005
).
22.
D. A.
Smirnov
and
R. G.
Andrzejak
,
Phys. Rev. E
71
,
036207
(
2005
).
23.
B.
Bezruchko
,
V.
Ponomarenko
,
M. G.
Rosenblum
, and
A.
Pikovsky
,
Chaos
13
,
179
(
2003
).
24.
D. F.
Russell
,
L. A.
Wilkens
, and
F.
Moss
,
Nature
402
,
291
(
1999
).
25.
A. B.
Neiman
and
D. F.
Russell
,
Phys. Rev. Lett.
86
,
3443
(
2001
).
26.
A. B.
Neiman
and
D. F.
Russell
,
J. Neurophysiol.
92
,
492
(
2004
).
27.
A. B.
Neiman
and
D. F.
Russell
,
Phys. Rev. E
71
,
061915
(
2005
).
28.
A. B.
Neiman
,
X.
Pei
,
D. F.
Russell
,
W.
Wojtenek
,
L. A.
Wilkens
,
F.
Moss
,
H. A.
Braun
,
M.
Huber
, and
K.
Voigt
,
Phys. Rev. Lett.
82
,
660
(
1999
).
29.
A. B.
Neiman
and
D. F.
Russell
,
Phys. Rev. Lett.
88
,
138103
(
2002
).
30.
S.
Liepelt
,
J. A.
Freund
,
L.
Schimansky-Geier
,
A. B.
Neiman
, and
D. F.
Russell
,
J. Theor. Biol.
237
,
30
(
2005
).
31.
L. A.
Wilkens
,
D. F.
Russell
,
X.
Pei
, and
C.
Gurgens
,
Proc. R. Soc. London, Ser. B
264
,
1723
(
1997
).
32.
J. M.
Jørgensen
,
A.
Flock
, and
J.
Wersäll
,
Z. Zellforsch Mikrosk Anat.
130
,
362
(
1972
).
33.
F.
Gabbiani
and
C.
Koch
, in
Methods in Neural Modeling: from Ions to Networks
, edited by
C.
Koch
and
I.
Segev
(
MIT
,
Cambridge, MA
,
1998
), pp.
313
360
.
34.
M.
Paluš
and
A.
Stefanovska
,
Phys. Rev. E
67
,
055201
(
2003
).
35.
D. A.
Smirnov
and
B. P.
Bezruchko
,
Phys. Rev. E
68
,
046209
(
2003
).
37.
J.
Theiler
,
B.
Galdrikian
,
A.
Longtin
,
S.
Eubank
, and
J. D.
Farmer
,
Physica D
58
,
77
(
1992
).
38.
K.
Dolan
,
M. L.
Spano
, and
F.
Moss
, “
Detecting unstable periodic orbits in biological systems
,” in
Handbook of Biological Physics
, Neuro-Informatics and Neural Modeling, edited by
F.
Moss
and
S.
Gielen
(
Elsevier Science
Amsterdam
,
2001
), Vol.
4
, pp.
131
153
.
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