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result sql = The electroencephalogram recordings from human scalp are analysed in the framework of recent methods of nonlinear dynamics. THREE STAGES OF BRAIN ACTIVITY ARE CONSIDERED: the alpha waves (eyes closed), the deep sleep (stage four) and the Creutzfeld-Jakob coma. Two dynamical parameters of the attractors are evaluated. These are the Lyapunov exponents, which measure the divergence or convergence of trajectories in phase space and the Kolmogorov or metric entropy, whose inverse gives the mean predicting time of a given EEG signal. In all the stages considered, the results reveal the presence of at least two positive Lyapunov exponents, which are the footprints of chaos. This number increases to three positive exponents in the case of alpha waves, indicating that although for very short episodes the alpha waves seem extremely coherent, the variability of the brain increases markedly over larger periods of activity. The degree of entropy/chaos increases from coma to deep sleep and then to alpha waves. The large predicting time observed for deep sleep suggests that these waves are related to a slow rate of information processing. The predicting time of the alpha waves is much smaller, indicating a rapid loss of information. Finally, with the help of the Lyapunov exponents, the attractor's dimensions are evaluated using two different conjectures and compared to values obtained previously by the Grassberger-Procaccia algorithm.
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result sql = Predictability of human EEG: a dynamical approach.
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char = J;code = 74
char = a;code = 97
char = k;code = 107
char = o;code = 111
char = b;code = 98
char = ;code = 32
char = c;code = 99
char = o;code = 111
char = m;code = 109
char = a;code = 97
char = .;code = 46
char = ;code = 32
char = T;code = 84
char = w;code = 119
char = o;code = 111
char = ;code = 32
char = d;code = 100
char = y;code = 121
char = n;code = 110
char = a;code = 97
char = m;code = 109
char = i;code = 105
char = c;code = 99
char = a;code = 97
char = l;code = 108
char = ;code = 32
char = p;code = 112
char = a;code = 97
char = r;code = 114
char = a;code = 97
char = m;code = 109
char = e;code = 101
char = t;code = 116
char = e;code = 101
char = r;code = 114
char = s;code = 115
char = ;code = 32
char = o;code = 111
char = f;code = 102
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = a;code = 97
char = t;code = 116
char = t;code = 116
char = r;code = 114
char = a;code = 97
char = c;code = 99
char = t;code = 116
char = o;code = 111
char = r;code = 114
char = s;code = 115
char = ;code = 32
char = a;code = 97
char = r;code = 114
char = e;code = 101
char = ;code = 32
char = e;code = 101
char = v;code = 118
char = a;code = 97
char = l;code = 108
char = u;code = 117
char = a;code = 97
char = t;code = 116
char = e;code = 101
char = d;code = 100
char = .;code = 46
char = ;code = 32
char = T;code = 84
char = h;code = 104
char = e;code = 101
char = s;code = 115
char = e;code = 101
char = ;code = 32
char = a;code = 97
char = r;code = 114
char = e;code = 101
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = L;code = 76
char = y;code = 121
char = a;code = 97
char = p;code = 112
char = u;code = 117
char = n;code = 110
char = o;code = 111
char = v;code = 118
char = ;code = 32
char = e;code = 101
char = x;code = 120
char = p;code = 112
char = o;code = 111
char = n;code = 110
char = e;code = 101
char = n;code = 110
char = t;code = 116
char = s;code = 115
char = ,;code = 44
char = ;code = 32
char = w;code = 119
char = h;code = 104
char = i;code = 105
char = c;code = 99
char = h;code = 104
char = ;code = 32
char = m;code = 109
char = e;code = 101
char = a;code = 97
char = s;code = 115
char = u;code = 117
char = r;code = 114
char = e;code = 101
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = d;code = 100
char = i;code = 105
char = v;code = 118
char = e;code = 101
char = r;code = 114
char = g;code = 103
char = e;code = 101
char = n;code = 110
char = c;code = 99
char = e;code = 101
char = ;code = 32
char = o;code = 111
char = r;code = 114
char = ;code = 32
char = c;code = 99
char = o;code = 111
char = n;code = 110
char = v;code = 118
char = e;code = 101
char = r;code = 114
char = g;code = 103
char = e;code = 101
char = n;code = 110
char = c;code = 99
char = e;code = 101
char = ;code = 32
char = o;code = 111
char = f;code = 102
char = ;code = 32
char = t;code = 116
char = r;code = 114
char = a;code = 97
char = j;code = 106
char = e;code = 101
char = c;code = 99
char = t;code = 116
char = o;code = 111
char = r;code = 114
char = i;code = 105
char = e;code = 101
char = s;code = 115
char = ;code = 32
char = i;code = 105
char = n;code = 110
char = ;code = 32
char = p;code = 112
char = h;code = 104
char = a;code = 97
char = s;code = 115
char = e;code = 101
char = ;code = 32
char = s;code = 115
char = p;code = 112
char = a;code = 97
char = c;code = 99
char = e;code = 101
char = ;code = 32
char = a;code = 97
char = n;code = 110
char = d;code = 100
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = K;code = 75
char = o;code = 111
char = l;code = 108
char = m;code = 109
char = o;code = 111
char = g;code = 103
char = o;code = 111
char = r;code = 114
char = o;code = 111
char = v;code = 118
char = ;code = 32
char = o;code = 111
char = r;code = 114
char = ;code = 32
char = m;code = 109
char = e;code = 101
char = t;code = 116
char = r;code = 114
char = i;code = 105
char = c;code = 99
char = ;code = 32
char = e;code = 101
char = n;code = 110
char = t;code = 116
char = r;code = 114
char = o;code = 111
char = p;code = 112
char = y;code = 121
char = ,;code = 44
char = ;code = 32
char = w;code = 119
char = h;code = 104
char = o;code = 111
char = s;code = 115
char = e;code = 101
char = ;code = 32
char = i;code = 105
char = n;code = 110
char = v;code = 118
char = e;code = 101
char = r;code = 114
char = s;code = 115
char = e;code = 101
char = ;code = 32
char = g;code = 103
char = i;code = 105
char = v;code = 118
char = e;code = 101
char = s;code = 115
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = m;code = 109
char = e;code = 101
char = a;code = 97
char = n;code = 110
char = ;code = 32
char = p;code = 112
char = r;code = 114
char = e;code = 101
char = d;code = 100
char = i;code = 105
char = c;code = 99
char = t;code = 116
char = i;code = 105
char = n;code = 110
char = g;code = 103
char = ;code = 32
char = t;code = 116
char = i;code = 105
char = m;code = 109
char = e;code = 101
char = ;code = 32
char = o;code = 111
char = f;code = 102
char = ;code = 32
char = a;code = 97
char = ;code = 32
char = g;code = 103
char = i;code = 105
char = v;code = 118
char = e;code = 101
char = n;code = 110
char = ;code = 32
char = E;code = 69
char = E;code = 69
char = G;code = 71
char = ;code = 32
char = s;code = 115
char = i;code = 105
char = g;code = 103
char = n;code = 110
char = a;code = 97
char = l;code = 108
char = .;code = 46
char = ;code = 32
char = I;code = 73
char = n;code = 110
char = ;code = 32
char = a;code = 97
char = l;code = 108
char = l;code = 108
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = s;code = 115
char = t;code = 116
char = a;code = 97
char = g;code = 103
char = e;code = 101
char = s;code = 115
char = ;code = 32
char = c;code = 99
char = o;code = 111
char = n;code = 110
char = s;code = 115
char = i;code = 105
char = d;code = 100
char = e;code = 101
char = r;code = 114
char = e;code = 101
char = d;code = 100
char = ,;code = 44
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = r;code = 114
char = e;code = 101
char = s;code = 115
char = u;code = 117
char = l;code = 108
char = t;code = 116
char = s;code = 115
char = ;code = 32
char = r;code = 114
char = e;code = 101
char = v;code = 118
char = e;code = 101
char = a;code = 97
char = l;code = 108
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = p;code = 112
char = r;code = 114
char = e;code = 101
char = s;code = 115
char = e;code = 101
char = n;code = 110
char = c;code = 99
char = e;code = 101
char = ;code = 32
char = o;code = 111
char = f;code = 102
char = ;code = 32
char = a;code = 97
char = t;code = 116
char = ;code = 32
char = l;code = 108
char = e;code = 101
char = a;code = 97
char = s;code = 115
char = t;code = 116
char = ;code = 32
char = t;code = 116
char = w;code = 119
char = o;code = 111
char = ;code = 32
char = p;code = 112
char = o;code = 111
char = s;code = 115
char = i;code = 105
char = t;code = 116
char = i;code = 105
char = v;code = 118
char = e;code = 101
char = ;code = 32
char = L;code = 76
char = y;code = 121
char = a;code = 97
char = p;code = 112
char = u;code = 117
char = n;code = 110
char = o;code = 111
char = v;code = 118
char = ;code = 32
char = e;code = 101
char = x;code = 120
char = p;code = 112
char = o;code = 111
char = n;code = 110
char = e;code = 101
char = n;code = 110
char = t;code = 116
char = s;code = 115
char = ,;code = 44
char = ;code = 32
char = w;code = 119
char = h;code = 104
char = i;code = 105
char = c;code = 99
char = h;code = 104
char = ;code = 32
char = a;code = 97
char = r;code = 114
char = e;code = 101
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = f;code = 102
char = o;code = 111
char = o;code = 111
char = t;code = 116
char = p;code = 112
char = r;code = 114
char = i;code = 105
char = n;code = 110
char = t;code = 116
char = s;code = 115
char = ;code = 32
char = o;code = 111
char = f;code = 102
char = ;code = 32
char = c;code = 99
char = h;code = 104
char = a;code = 97
char = o;code = 111
char = s;code = 115
char = .;code = 46
char = ;code = 32
char = T;code = 84
char = h;code = 104
char = i;code = 105
char = s;code = 115
char = ;code = 32
char = n;code = 110
char = u;code = 117
char = m;code = 109
char = b;code = 98
char = e;code = 101
char = r;code = 114
char = ;code = 32
char = i;code = 105
char = n;code = 110
char = c;code = 99
char = r;code = 114
char = e;code = 101
char = a;code = 97
char = s;code = 115
char = e;code = 101
char = s;code = 115
char = ;code = 32
char = t;code = 116
char = o;code = 111
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = r;code = 114
char = e;code = 101
char = e;code = 101
char = ;code = 32
char = p;code = 112
char = o;code = 111
char = s;code = 115
char = i;code = 105
char = t;code = 116
char = i;code = 105
char = v;code = 118
char = e;code = 101
char = ;code = 32
char = e;code = 101
char = x;code = 120
char = p;code = 112
char = o;code = 111
char = n;code = 110
char = e;code = 101
char = n;code = 110
char = t;code = 116
char = s;code = 115
char = ;code = 32
char = i;code = 105
char = n;code = 110
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = c;code = 99
char = a;code = 97
char = s;code = 115
char = e;code = 101
char = ;code = 32
char = o;code = 111
char = f;code = 102
char = ;code = 32
char = a;code = 97
char = l;code = 108
char = p;code = 112
char = h;code = 104
char = a;code = 97
char = ;code = 32
char = w;code = 119
char = a;code = 97
char = v;code = 118
char = e;code = 101
char = s;code = 115
char = ,;code = 44
char = ;code = 32
char = i;code = 105
char = n;code = 110
char = d;code = 100
char = i;code = 105
char = c;code = 99
char = a;code = 97
char = t;code = 116
char = i;code = 105
char = n;code = 110
char = g;code = 103
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = a;code = 97
char = t;code = 116
char = ;code = 32
char = a;code = 97
char = l;code = 108
char = t;code = 116
char = h;code = 104
char = o;code = 111
char = u;code = 117
char = g;code = 103
char = h;code = 104
char = ;code = 32
char = f;code = 102
char = o;code = 111
char = r;code = 114
char = ;code = 32
char = v;code = 118
char = e;code = 101
char = r;code = 114
char = y;code = 121
char = ;code = 32
char = s;code = 115
char = h;code = 104
char = o;code = 111
char = r;code = 114
char = t;code = 116
char = ;code = 32
char = e;code = 101
char = p;code = 112
char = i;code = 105
char = s;code = 115
char = o;code = 111
char = d;code = 100
char = e;code = 101
char = s;code = 115
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = a;code = 97
char = l;code = 108
char = p;code = 112
char = h;code = 104
char = a;code = 97
char = ;code = 32
char = w;code = 119
char = a;code = 97
char = v;code = 118
char = e;code = 101
char = s;code = 115
char = ;code = 32
char = s;code = 115
char = e;code = 101
char = e;code = 101
char = m;code = 109
char = ;code = 32
char = e;code = 101
char = x;code = 120
char = t;code = 116
char = r;code = 114
char = e;code = 101
char = m;code = 109
char = e;code = 101
char = l;code = 108
char = y;code = 121
char = ;code = 32
char = c;code = 99
char = o;code = 111
char = h;code = 104
char = e;code = 101
char = r;code = 114
char = e;code = 101
char = n;code = 110
char = t;code = 116
char = ,;code = 44
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = v;code = 118
char = a;code = 97
char = r;code = 114
char = i;code = 105
char = a;code = 97
char = b;code = 98
char = i;code = 105
char = l;code = 108
char = i;code = 105
char = t;code = 116
char = y;code = 121
char = ;code = 32
char = o;code = 111
char = f;code = 102
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = b;code = 98
char = r;code = 114
char = a;code = 97
char = i;code = 105
char = n;code = 110
char = ;code = 32
char = i;code = 105
char = n;code = 110
char = c;code = 99
char = r;code = 114
char = e;code = 101
char = a;code = 97
char = s;code = 115
char = e;code = 101
char = s;code = 115
char = ;code = 32
char = m;code = 109
char = a;code = 97
char = r;code = 114
char = k;code = 107
char = e;code = 101
char = d;code = 100
char = l;code = 108
char = y;code = 121
char = ;code = 32
char = o;code = 111
char = v;code = 118
char = e;code = 101
char = r;code = 114
char = ;code = 32
char = l;code = 108
char = a;code = 97
char = r;code = 114
char = g;code = 103
char = e;code = 101
char = r;code = 114
char = ;code = 32
char = p;code = 112
char = e;code = 101
char = r;code = 114
char = i;code = 105
char = o;code = 111
char = d;code = 100
char = s;code = 115
char = ;code = 32
char = o;code = 111
char = f;code = 102
char = ;code = 32
char = a;code = 97
char = c;code = 99
char = t;code = 116
char = i;code = 105
char = v;code = 118
char = i;code = 105
char = t;code = 116
char = y;code = 121
char = .;code = 46
char = ;code = 32
char = T;code = 84
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = d;code = 100
char = e;code = 101
char = g;code = 103
char = r;code = 114
char = e;code = 101
char = e;code = 101
char = ;code = 32
char = o;code = 111
char = f;code = 102
char = ;code = 32
char = e;code = 101
char = n;code = 110
char = t;code = 116
char = r;code = 114
char = o;code = 111
char = p;code = 112
char = y;code = 121
char = /;code = 47
char = c;code = 99
char = h;code = 104
char = a;code = 97
char = o;code = 111
char = s;code = 115
char = ;code = 32
char = i;code = 105
char = n;code = 110
char = c;code = 99
char = r;code = 114
char = e;code = 101
char = a;code = 97
char = s;code = 115
char = e;code = 101
char = s;code = 115
char = ;code = 32
char = f;code = 102
char = r;code = 114
char = o;code = 111
char = m;code = 109
char = ;code = 32
char = c;code = 99
char = o;code = 111
char = m;code = 109
char = a;code = 97
char = ;code = 32
char = t;code = 116
char = o;code = 111
char = ;code = 32
char = d;code = 100
char = e;code = 101
char = e;code = 101
char = p;code = 112
char = ;code = 32
char = s;code = 115
char = l;code = 108
char = e;code = 101
char = e;code = 101
char = p;code = 112
char = ;code = 32
char = a;code = 97
char = n;code = 110
char = d;code = 100
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = n;code = 110
char = ;code = 32
char = t;code = 116
char = o;code = 111
char = ;code = 32
char = a;code = 97
char = l;code = 108
char = p;code = 112
char = h;code = 104
char = a;code = 97
char = ;code = 32
char = w;code = 119
char = a;code = 97
char = v;code = 118
char = e;code = 101
char = s;code = 115
char = .;code = 46
char = ;code = 32
char = T;code = 84
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = l;code = 108
char = a;code = 97
char = r;code = 114
char = g;code = 103
char = e;code = 101
char = ;code = 32
char = p;code = 112
char = r;code = 114
char = e;code = 101
char = d;code = 100
char = i;code = 105
char = c;code = 99
char = t;code = 116
char = i;code = 105
char = n;code = 110
char = g;code = 103
char = ;code = 32
char = t;code = 116
char = i;code = 105
char = m;code = 109
char = e;code = 101
char = ;code = 32
char = o;code = 111
char = b;code = 98
char = s;code = 115
char = e;code = 101
char = r;code = 114
char = v;code = 118
char = e;code = 101
char = d;code = 100
char = ;code = 32
char = f;code = 102
char = o;code = 111
char = r;code = 114
char = ;code = 32
char = d;code = 100
char = e;code = 101
char = e;code = 101
char = p;code = 112
char = ;code = 32
char = s;code = 115
char = l;code = 108
char = e;code = 101
char = e;code = 101
char = p;code = 112
char = ;code = 32
char = s;code = 115
char = u;code = 117
char = g;code = 103
char = g;code = 103
char = e;code = 101
char = s;code = 115
char = t;code = 116
char = s;code = 115
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = a;code = 97
char = t;code = 116
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = s;code = 115
char = e;code = 101
char = ;code = 32
char = w;code = 119
char = a;code = 97
char = v;code = 118
char = e;code = 101
char = s;code = 115
char = ;code = 32
char = a;code = 97
char = r;code = 114
char = e;code = 101
char = ;code = 32
char = r;code = 114
char = e;code = 101
char = l;code = 108
char = a;code = 97
char = t;code = 116
char = e;code = 101
char = d;code = 100
char = ;code = 32
char = t;code = 116
char = o;code = 111
char = ;code = 32
char = a;code = 97
char = ;code = 32
char = s;code = 115
char = l;code = 108
char = o;code = 111
char = w;code = 119
char = ;code = 32
char = r;code = 114
char = a;code = 97
char = t;code = 116
char = e;code = 101
char = ;code = 32
char = o;code = 111
char = f;code = 102
char = ;code = 32
char = i;code = 105
char = n;code = 110
char = f;code = 102
char = o;code = 111
char = r;code = 114
char = m;code = 109
char = a;code = 97
char = t;code = 116
char = i;code = 105
char = o;code = 111
char = n;code = 110
char = ;code = 32
char = p;code = 112
char = r;code = 114
char = o;code = 111
char = c;code = 99
char = e;code = 101
char = s;code = 115
char = s;code = 115
char = i;code = 105
char = n;code = 110
char = g;code = 103
char = .;code = 46
char = ;code = 32
char = T;code = 84
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = p;code = 112
char = r;code = 114
char = e;code = 101
char = d;code = 100
char = i;code = 105
char = c;code = 99
char = t;code = 116
char = i;code = 105
char = n;code = 110
char = g;code = 103
char = ;code = 32
char = t;code = 116
char = i;code = 105
char = m;code = 109
char = e;code = 101
char = ;code = 32
char = o;code = 111
char = f;code = 102
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = a;code = 97
char = l;code = 108
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result sql = The electroencephalogram recordings from human scalp are analysed in the framework of recent methods of nonlinear dynamics. THREE STAGES OF BRAIN ACTIVITY ARE CONSIDERED: the alpha waves (eyes closed), the deep sleep (stage four) and the Creutzfeld-Jakob coma. Two dynamical parameters of the attractors are evaluated. These are the Lyapunov exponents, which measure the divergence or convergence of trajectories in phase space and the Kolmogorov or metric entropy, whose inverse gives the mean predicting time of a given EEG signal. In all the stages considered, the results reveal the presence of at least two positive Lyapunov exponents, which are the footprints of chaos. This number increases to three positive exponents in the case of alpha waves, indicating that although for very short episodes the alpha waves seem extremely coherent, the variability of the brain increases markedly over larger periods of activity. The degree of entropy/chaos increases from coma to deep sleep and then to alpha waves. The large predicting time observed for deep sleep suggests that these waves are related to a slow rate of information processing. The predicting time of the alpha waves is much smaller, indicating a rapid loss of information. Finally, with the help of the Lyapunov exponents, the attractor's dimensions are evaluated using two different conjectures and compared to values obtained previously by the Grassberger-Procaccia algorithm.
Publication: Biol Cybern 1991 ;64(5)::381-91.
Publication Date: 1991
Study Author(s): Gallez, D;Babloyantz, A;
Institution: Université Libre de Bruxelles, Service de Chimie Physique, Belgium.
Shortcut link to this study:
Publication Date: 1991
Study Author(s): Gallez, D;Babloyantz, A;
Institution: Université Libre de Bruxelles, Service de Chimie Physique, Belgium.
Shortcut link to this study:
The electroencephalogram recordings from human scalp are analysed in the framework of recent methods of nonlinear dynamics. THREE STAGES OF BRAIN ACTIVITY ARE CONSIDERED: the alpha waves (eyes closed), the deep sleep (stage four) and the Creutzfeld-Jakob coma. Two dynamical parameters of the attractors are evaluated. These are the Lyapunov exponents, which measure the divergence or convergence of trajectories in phase space and the Kolmogorov or metric entropy, whose inverse gives the mean predicting time of a given EEG signal. In all the stages considered, the results reveal the presence of at least two positive Lyapunov exponents, which are the footprints of chaos. This number increases to three positive exponents in the case of alpha waves, indicating that although for very short episodes the alpha waves seem extremely coherent, the variability of the brain increases markedly over larger periods of activity. The degree of entropy/chaos increases from coma to deep sleep and then to alpha waves. The large predicting time observed for deep sleep suggests that these waves are related to a slow rate of information processing. The predicting time of the alpha waves is much smaller, indicating a rapid loss of information. Finally, with the help of the Lyapunov exponents, the attractor's dimensions are evaluated using two different conjectures and compared to values obtained previously by the Grassberger-Procaccia algorithm.
PMID: 2049414
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