-
1
-
-
12044249591
-
The analysis of observed chaotic data in physical systems
-
Abarbanel, H. D. I., Brown, R., Sidorowich, J. & Tsimring, L. [1993] "The analysis of observed chaotic data in physical systems," Rev. Mod. Phys. 65, 1331-1392.
-
(1993)
Rev. Mod. Phys.
, vol.65
, pp. 1331-1392
-
-
Abarbanel, H.D.I.1
Brown, R.2
Sidorowich, J.3
Tsimring, L.4
-
2
-
-
0010893550
-
-
Plenum Press, New York
-
Abraham, N., Albano, A., Passamante, A. & Rapp, P. E. [1989] Measures of Complexity and Chaos (Plenum Press, New York).
-
(1989)
Measures of Complexity and Chaos
-
-
Abraham, N.1
Albano, A.2
Passamante, A.3
Rapp, P.E.4
-
3
-
-
0002635857
-
A nonlinear correlation function for selecting the delay time in dynamical reconstructions
-
Aguirre, L. A. [1995] "A nonlinear correlation function for selecting the delay time in dynamical reconstructions," Phys. Lett. A203, 88-94.
-
(1995)
Phys. Lett.
, vol.A203
, pp. 88-94
-
-
Aguirre, L.A.1
-
4
-
-
0042075109
-
Retrieving dynamical invariants from chaotic data using NARMAX models
-
Aguirre, L. A. & Billings, S. A. [1995] "Retrieving dynamical invariants from chaotic data using NARMAX models," Int. J. Bifurcation and Chaos 5, 449-474.
-
(1995)
Int. J. Bifurcation and Chaos
, vol.5
, pp. 449-474
-
-
Aguirre, L.A.1
Billings, S.A.2
-
5
-
-
0001612833
-
Kolmogorov-Smirnov test distinguishes attractors with similar dimensions
-
Albano, A. M., Rapp, P. E. & Passamante, A. [1995] "Kolmogorov-Smirnov test distinguishes attractors with similar dimensions," Phys. Rev. E52, 196-206.
-
(1995)
Phys. Rev.
, vol.E52
, pp. 196-206
-
-
Albano, A.M.1
Rapp, P.E.2
Passamante, A.3
-
6
-
-
0001979913
-
Sensory mechanism, the reduction of redundancy, and intelligence
-
Her Majesty's Stationery Office, London
-
Barlow, H. [1959] "Sensory mechanism, the reduction of redundancy, and intelligence," in National Physical Laboratory Symposium N. 10, The Mechanization of Thought Processes (Her Majesty's Stationery Office, London).
-
(1959)
National Physical Laboratory Symposium N. 10, The Mechanization of Thought Processes
-
-
Barlow, H.1
-
7
-
-
0001471775
-
Unsupervised learning
-
Barlow, H. [1989] "Unsupervised learning," Neural Comput. 1, 295-311.
-
(1989)
Neural Comput.
, vol.1
, pp. 295-311
-
-
Barlow, H.1
-
8
-
-
0004113976
-
-
Technical Report, Aston University, Birmingham, United Kingdom
-
Bishop, C. M. [1994] "Mixture density networks," Technical Report, Aston University, Birmingham, United Kingdom.
-
(1994)
Mixture Density Networks
-
-
Bishop, C.M.1
-
11
-
-
0000202504
-
Chaos and deterministic versus stochastic non-linear modelling
-
Casdagli, M. [1991] "Chaos and deterministic versus stochastic non-linear modelling," J. R. Stat. Soc. B54, 303-328.
-
(1991)
J. R. Stat. Soc.
, vol.B54
, pp. 303-328
-
-
Casdagli, M.1
-
15
-
-
48749145105
-
Symbolic dynamics of noisy chaos
-
Crutchfield, J. P. & Packard, N. H. [1983] "Symbolic dynamics of noisy chaos," Physica 7D, 201-223.
-
(1983)
Physica
, vol.7 D
, pp. 201-223
-
-
Crutchfield, J.P.1
Packard, N.H.2
-
16
-
-
0029013513
-
Nonlinear higher-order statistical decorrelation by volume-conserving neural architectures
-
Deco, G. & Brauer, W. [1995] "Nonlinear higher-order statistical decorrelation by volume-conserving neural architectures," Neural Networks 8, 525-535.
-
(1995)
Neural Networks
, vol.8
, pp. 525-535
-
-
Deco, G.1
Brauer, W.2
-
17
-
-
0001285642
-
Learning time series evolution by unsupervised extraction of correlations
-
Deco, G. & Schürmann, B. [1995a] "Learning time series evolution by unsupervised extraction of correlations," Phys. Rev. E51, 1780-1790.
-
(1995)
Phys. Rev.
, vol.E51
, pp. 1780-1790
-
-
Deco, G.1
Schürmann, B.2
-
18
-
-
4243248697
-
Statistical ensemble theory of redundancy reduction and the duality between unsupervised and supervised learning
-
Deco, G. & Schürmann, B. [1995b] "Statistical ensemble theory of redundancy reduction and the duality between unsupervised and supervised learning," Phys. Rev. E52, 6580-6587.
-
(1995)
Phys. Rev.
, vol.E52
, pp. 6580-6587
-
-
Deco, G.1
Schürmann, B.2
-
20
-
-
0030627424
-
Information flow in chaotic symbolic dynamics for finite and infinitesimal resolution
-
Deco, G., Schittenkopf, C. & Schürmann, B. [1997] "Information flow in chaotic symbolic dynamics for finite and infinitesimal resolution," Int. J. Bifurcation and Chaos 7(1), 97-105.
-
(1997)
Int. J. Bifurcation and Chaos
, vol.7
, Issue.1
, pp. 97-105
-
-
Deco, G.1
Schittenkopf, C.2
Schürmann, B.3
-
21
-
-
35949018382
-
Ergodic theory of chaos and strange attractors
-
Eckmann, J.-P. & Ruelle, D. [1985] "Ergodic theory of chaos and strange attractors," Rev. Mod. Phys. 57, 617-656.
-
(1985)
Rev. Mod. Phys.
, vol.57
, pp. 617-656
-
-
Eckmann, J.-P.1
Ruelle, D.2
-
22
-
-
0027294340
-
Improving generalization by nonconvergent model selection methods
-
Finnoff, W., Hergert, F. & Zimmermann, H. G. [1993] "Improving generalization by nonconvergent model selection methods," Neural Networks 6, 771-783.
-
(1993)
Neural Networks
, vol.6
, pp. 771-783
-
-
Finnoff, W.1
Hergert, F.2
Zimmermann, H.G.3
-
23
-
-
0040335709
-
Information dimension and the probabilistic structure of chaos
-
Farmer, J. D. [1982] "Information dimension and the probabilistic structure of chaos," Z. Naturforsch. A37, 1304-1325.
-
(1982)
Z. Naturforsch.
, vol.A37
, pp. 1304-1325
-
-
Farmer, J.D.1
-
24
-
-
34548696055
-
Independent coordinates for strange attractors from mutual information
-
Fraser, A. M. & Swinney, H. L. [1986] "Independent coordinates for strange attractors from mutual information," Phys. Rev. A33, 1134-1140.
-
(1986)
Phys. Rev.
, vol.A33
, pp. 1134-1140
-
-
Fraser, A.M.1
Swinney, H.L.2
-
25
-
-
0024627335
-
Information and entropy in strange attractors
-
Fraser, A. M. [1989] "Information and entropy in strange attractors," IEEE Trans. Inf. Th. 35, 245-262.
-
(1989)
IEEE Trans. Inf. Th.
, vol.35
, pp. 245-262
-
-
Fraser, A.M.1
-
27
-
-
33646981873
-
Characterization of strange attractors
-
Grassberger, P. & Procaccia, I. [1983] "Characterization of strange attractors," Phys. Rev. Lett. 50, 346-349.
-
(1983)
Phys. Rev. Lett.
, vol.50
, pp. 346-349
-
-
Grassberger, P.1
Procaccia, I.2
-
28
-
-
0000090102
-
Finite sample corrections to entropy and dimension estimates
-
Grassberger, P. [1990] "Finite sample corrections to entropy and dimension estimates," Phys. Lett. A128, 369-373.
-
(1990)
Phys. Lett.
, vol.A128
, pp. 369-373
-
-
Grassberger, P.1
-
29
-
-
0001346065
-
Calculation of the entropy in chaotic systems
-
Györgyi, G. & Szépfalusy, P. [1985] "Calculation of the entropy in chaotic systems," Phys. Rev. A31, 3477-3479.
-
(1985)
Phys. Rev.
, vol.A31
, pp. 3477-3479
-
-
Györgyi, G.1
Szépfalusy, P.2
-
30
-
-
0002591468
-
A two-dimensional mapping with a strange attractor
-
Hénon, M. [1976] "A two-dimensional mapping with a strange attractor," Commun. Math. Phys. 50, 69-77.
-
(1976)
Commun. Math. Phys.
, vol.50
, pp. 69-77
-
-
Hénon, M.1
-
31
-
-
0028346501
-
Finite sample effects in sequence analysis
-
Herzel, H., Schmitt, A. O. & Ebeling, W. [1994] "Finite sample effects in sequence analysis," Chaos, Solitons & Fractals 4, 97-113.
-
(1994)
Chaos, Solitons & Fractals
, vol.4
, pp. 97-113
-
-
Herzel, H.1
Schmitt, A.O.2
Ebeling, W.3
-
32
-
-
0001282028
-
Method to distinguish possible chaos from colored noise and to determine embedding parameters
-
Kennel, M. B. & Isabelle, S. [1992] "Method to distinguish possible chaos from colored noise and to determine embedding parameters," Phys. Rev. A46, 3111-3118.
-
(1992)
Phys. Rev.
, vol.A46
, pp. 3111-3118
-
-
Kennel, M.B.1
Isabelle, S.2
-
33
-
-
0001450585
-
A metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces
-
Kolmogorov, A. N. [1958] "A metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces," Dokl. Akad. Nauk SSSR 119, 861-864.
-
(1958)
Dokl. Akad. Nauk SSSR
, vol.119
, pp. 861-864
-
-
Kolmogorov, A.N.1
-
34
-
-
0001494176
-
Entropy per unit time as a metric invariant of automorphisms
-
Kolmogorov, A. N. [1959] "Entropy per unit time as a metric invariant of automorphisms,quot; Dokl. Akad. Nauk SSSR 124, 754-755.
-
(1959)
Dokl. Akad. Nauk SSSR
, vol.124
, pp. 754-755
-
-
Kolmogorov, A.N.1
-
35
-
-
84981969926
-
Über die möglichkeit der zustandsvoraussage chaotischer systeme
-
Leven, R. W. " Pompe, B. [1986] "Über die Möglichkeit der Zustandsvoraussage chaotischer Systeme," Ann. Phys. 43, 259-278.
-
(1986)
Ann. Phys.
, vol.43
, pp. 259-278
-
-
Leven, R.W.1
Pompe, B.2
-
37
-
-
0000241853
-
Deterministic non-periodic flow
-
Lorenz, E. N. [1963] "Deterministic non-periodic flow," J. Atmos. Sci. 20, 130-141.
-
(1963)
J. Atmos. Sci.
, vol.20
, pp. 130-141
-
-
Lorenz, E.N.1
-
38
-
-
36149048755
-
Information theoretical approach to noisy dynamics
-
Matsumoto, K. " Tsuda, I. [1985] "Information theoretical approach to noisy dynamics," J. Phys. A: Math. Gen. 18, 3561-3566.
-
(1985)
J. Phys. A: Math. Gen.
, vol.18
, pp. 3561-3566
-
-
Matsumoto, K.1
Tsuda, I.2
-
39
-
-
0000672424
-
Fast learning in networks of locally-tuned processing units
-
Moody, J. & Darken, C. [1989] "Fast learning in networks of locally-tuned processing units," Neural Comput. 1, 281-294.
-
(1989)
Neural Comput.
, vol.1
, pp. 281-294
-
-
Moody, J.1
Darken, C.2
-
40
-
-
0001259448
-
Estimation of mutual information using kernel density estimators
-
Moon, Y., Rajagopalan, B. & Lall, U. [1995] "Estimation of mutual information using kernel density estimators," Phys. Rev. E52, 2318-2321.
-
(1995)
Phys. Rev.
, vol.E52
, pp. 2318-2321
-
-
Moon, Y.1
Rajagopalan, B.2
Lall, U.3
-
41
-
-
0002245041
-
Estimation of conditional densities: A comparison of neural network approaches
-
Springer, Berlin
-
Neuneier, R., Finnoff, W., Hergert, F. & Ormoneit, D. [1994] "Estimation of conditional densities: A comparison of neural network approaches," in Int. Conf. Artificial Neural Networks, ICANN (Springer, Berlin), p. 689.
-
(1994)
Int. Conf. Artificial Neural Networks, ICANN
, pp. 689
-
-
Neuneier, R.1
Finnoff, W.2
Hergert, F.3
Ormoneit, D.4
-
43
-
-
5544310124
-
Finite correlation dimension for stochastic systems with power-law spectra
-
Osborne, A. R. & Provenzale, A. [1989] "Finite correlation dimension for stochastic systems with power-law spectra," Physica D35, 357-381.
-
(1989)
Physica
, vol.D35
, pp. 357-381
-
-
Osborne, A.R.1
Provenzale, A.2
-
44
-
-
0000938560
-
Information theoretic test for nonlinearity in time series
-
Paluš, M., Albrecht, V. & Dvořák, I. [1993] "Information theoretic test for nonlinearity in time series," Phys. Lett. A175, 203-209.
-
(1993)
Phys. Lett.
, vol.A175
, pp. 203-209
-
-
Paluš, M.1
Albrecht, V.2
Dvořák, I.3
-
45
-
-
4243440738
-
Testing for nonlinearity using redundancies: Quantitative and qualitative aspects
-
Paluš, M. [1995] "Testing for nonlinearity using redundancies: Quantitative and qualitative aspects," Physica D80, 186-205.
-
(1995)
Physica
, vol.D80
, pp. 186-205
-
-
Paluš, M.1
-
47
-
-
0001473437
-
On estimation of a probability density function and mode
-
Parzen, E. [1962] "On estimation of a probability density function and mode," Ann. Math. Stat. 33, 1065-1076.
-
(1962)
Ann. Math. Stat.
, vol.33
, pp. 1065-1076
-
-
Parzen, E.1
-
49
-
-
5344241276
-
State predictability and information flow in simple chaotic systems
-
Pompe, B., Kruscha, J. & Leven, R. W. [1986] "State predictability and information flow in simple chaotic systems," Z. Naturforsch. A41, 801-818.
-
(1986)
Z. Naturforsch.
, vol.A41
, pp. 801-818
-
-
Pompe, B.1
Kruscha, J.2
Leven, R.W.3
-
50
-
-
0003207190
-
Measuring statistical dependences in a time series
-
Pompe, B. [1993] "Measuring statistical dependences in a time series," J. Stat. Phys. 73, 587-610.
-
(1993)
J. Stat. Phys.
, vol.73
, pp. 587-610
-
-
Pompe, B.1
-
51
-
-
0001450027
-
Generalized redundancies for time series analysis
-
Prichard, D. & Theiler, J. [1995] "Generalized redundancies for time series analysis," Physica D84, 476-493.
-
(1995)
Physica
, vol.D84
, pp. 476-493
-
-
Prichard, D.1
Theiler, J.2
-
53
-
-
0003046317
-
Experimental studies of chaotic neural behavior: Cellular activity and electroencephalographic signals
-
ed. Othmer, H. G. (Springer, Berlin)
-
Rapp, P. E., Zimmerman, I. D., Albano, A. M., deGuzman, G. C., Greenbaun, N. N. & Bashore, T. R. [1986] "Experimental studies of chaotic neural behavior: Cellular activity and electroencephalographic signals," Nonlinear Oscillations in Biology and Chemistry, ed. Othmer, H. G. (Springer, Berlin), p. 175.
-
(1986)
Nonlinear Oscillations in Biology and Chemistry
, pp. 175
-
-
Rapp, P.E.1
Zimmerman, I.D.2
Albano, A.M.3
DeGuzman, G.C.4
Greenbaun, N.N.5
Bashore, T.R.6
-
56
-
-
0001529784
-
Remarks on some nonparametric estimates of a density function
-
Rosenblatt, M. [1956] "Remarks on some nonparametric estimates of a density function," Ann. Math. Stat. 27, 832-837.
-
(1956)
Ann. Math. Stat.
, vol.27
, pp. 832-837
-
-
Rosenblatt, M.1
-
57
-
-
49549126801
-
An equation for continuous chaos
-
Rössler, O. E. [1976] "An equation for continuous chaos," Phys. Lett. A57, 397-398.
-
(1976)
Phys. Lett.
, vol.A57
, pp. 397-398
-
-
Rössler, O.E.1
-
58
-
-
0001235864
-
Observation of a strange attractor
-
Roux, J., Simonyi, R. & Swinney, H. L. [1983] "Observation of a strange attractor," Physica D8, 257-266.
-
(1983)
Physica
, vol.D8
, pp. 257-266
-
-
Roux, J.1
Simonyi, R.2
Swinney, H.L.3
-
59
-
-
0002867385
-
Exploring the intrinsic information loss in single-humped maps by refining multi-symbol partitions
-
Schittenkopf, C. & Deco, G. [1996] "Exploring the intrinsic information loss in single-humped maps by refining multi-symbol partitions," Physica D94, 57-64.
-
(1996)
Physica
, vol.D94
, pp. 57-64
-
-
Schittenkopf, C.1
Deco, G.2
-
60
-
-
0031143561
-
Testing nonlinear Markovian hypotheses in dynamical systems
-
Schittenkopf, C. & Deco, G. [1997] "Testing nonlinear Markovian hypotheses in dynamical systems," Physica D104, 61-74.
-
(1997)
Physica
, vol.D104
, pp. 61-74
-
-
Schittenkopf, C.1
Deco, G.2
-
62
-
-
0009520409
-
Strange attractors, chaotic behaviour, and information flow
-
Shaw, R. [1981] "Strange attractors, chaotic behaviour, and information flow," Z. Naturforsch. A36, 80-112.
-
(1981)
Z. Naturforsch.
, vol.A36
, pp. 80-112
-
-
Shaw, R.1
-
64
-
-
0000419815
-
On the concept of entropy for a dynamic system
-
Sinai, Y. G. [1959] "On the concept of entropy for a dynamic system," Dokl. Akad. Nauk SSSR 124, 768-771.
-
(1959)
Dokl. Akad. Nauk SSSR
, vol.124
, pp. 768-771
-
-
Sinai, Y.G.1
-
65
-
-
0001743342
-
Entropy decay as a measure of stochasticity in chaotic systems
-
Szépfalusy, P. & Györgyi, G. [1986] "Entropy decay as a measure of stochasticity in chaotic systems," Phys. Rev. A33, 2852-2855.
-
(1986)
Phys. Rev.
, vol.A33
, pp. 2852-2855
-
-
Szépfalusy, P.1
Györgyi, G.2
-
66
-
-
0021892282
-
Fuzzy identification of systems and its applications to modelling and control
-
Takagi, T. & Sugeno, M. [1985] "Fuzzy identification of systems and its applications to modelling and control," IEEE Trans. Syst. Man Cybern. 1, 116-132.
-
(1985)
IEEE Trans. Syst. Man Cybern.
, vol.1
, pp. 116-132
-
-
Takagi, T.1
Sugeno, M.2
-
67
-
-
0000779360
-
Detecting strange attractors in turbulence
-
Lecture Notes in Mathematics 898 (Springer, Berlin)
-
Takens, F. [1981] "Detecting strange attractors in turbulence," in Dynamical Systems and Turbulence, Lecture Notes in Mathematics 898 (Springer, Berlin), p. 366.
-
(1981)
Dynamical Systems and Turbulence
, pp. 366
-
-
Takens, F.1
-
68
-
-
44049111332
-
Testing for nonlinearity in time series: The method of surrogate data
-
Theiler, J., Eubank, S., Longtin, A., Galdrikian, B. & Farmer, J. D. [1992] "Testing for nonlinearity in time series: The method of surrogate data," Physica D58, 77-94.
-
(1992)
Physica
, vol.D58
, pp. 77-94
-
-
Theiler, J.1
Eubank, S.2
Longtin, A.3
Galdrikian, B.4
Farmer, J.D.5
-
69
-
-
43949156836
-
On the evidence for low-dimensional chaos in an epileptic electroencephalogram
-
Theiler, J. [1995] "On the evidence for low-dimensional chaos in an epileptic electroencephalogram," Phys. Lett. A196, 335-341.
-
(1995)
Phys. Lett.
, vol.A196
, pp. 335-341
-
-
Theiler, J.1
-
71
-
-
0002475925
-
Network structuring and training using rule-based knowledge
-
eds. Hanson, S. J., Cowan, J. D. & Giles, C. L. (Morgan Kaufmann, San Mateo)
-
Tresp, V., Hollatz, J. & Ahmad, S. [1993] "Network structuring and training using rule-based knowledge," Advances in Neural Information Processing Systems 5, eds. Hanson, S. J., Cowan, J. D. & Giles, C. L. (Morgan Kaufmann, San Mateo), p. 871.
-
(1993)
Advances in Neural Information Processing Systems 5
, pp. 871
-
-
Tresp, V.1
Hollatz, J.2
Ahmad, S.3
-
72
-
-
0003684846
-
Generating fuzzy rules from numerical Data, with applications
-
University of Southern California
-
Wang, L. X. & Mendel, J. M. [1991] "Generating fuzzy rules from numerical data, with applications," Technical report USC-SIPI REPORT 169, University of Southern California.
-
(1991)
Technical Report USC-SIPI REPORT 169
-
-
Wang, L.X.1
Mendel, J.M.2
-
73
-
-
0008494528
-
Determining Lyapunov exponents from a time series
-
Wolf, A., Swift, J. B., Swinney, H. L. & Vastano, J. A. [1985] "Determining Lyapunov exponents from a time series," Physica D16, 285-317.
-
(1985)
Physica
, vol.D16
, pp. 285-317
-
-
Wolf, A.1
Swift, J.B.2
Swinney, H.L.3
Vastano, J.A.4
|