Estimating the distribution of dynamic invariants: illustrated with an application to human photo-plethysmographic time series-6

<p><b>Copyright information:</b></p><p>Taken from "Estimating the distribution of dynamic invariants: illustrated with an application to human photo-plethysmographic time series"</p><p>http://www.nonlinearbiomedphys.com/content/1/1/8</p><p>Nonlinear Biomedical Physics 2007;1():8-8.</p><p>Published online 23 Jul 2007</p><p>PMCID:PMC1997126.</p><p></p>he four distinct physiological waveforms is shown. The four rhythms correspond to those in figure 4. These figures show that complexity with 2, 3, and 4, symbols (plots (a), (b), and (c), respectively) is sufficient to differentiate between at least three of these four physiological states. The lowest complexity corresponds to "post-operative" state, the next highest to "quasi-stable" followed by "healthy" and finally "unstable". As in figure 6 there is considerable overlap between the "normal" and "quasi-stable" samples. However, for complexity with a binary partition (panel (a)) the four rhythms do appear to be distinct

Estimating the distribution of dynamic invariants: illustrated with an application to human photo-plethysmographic time series-7

<p><b>Copyright information:</b></p><p>Taken from "Estimating the distribution of dynamic invariants: illustrated with an application to human photo-plethysmographic time series"</p><p>http://www.nonlinearbiomedphys.com/content/1/1/8</p><p>Nonlinear Biomedical Physics 2007;1():8-8.</p><p>Published online 23 Jul 2007</p><p>PMCID:PMC1997126.</p><p></p>vational noise (respectively). The remaining panels are representative ATS time series. Panels (b), (c), (d) and (e) are surrogates for panel (a), and Panels (g), (h), (i) and (j) are for panel (f). Each surrogate is computed with a different level of transition probability . In panels (b) and (g), = 0.2; in panels (c) and (h), = 0.4; in panels (d) and (i), = 0.6; and, in panels (e) and (j), = 0.8. In each case the attractors reconstructed from the surrogates have the same qualitative features as that of the data – with the possible exception of panel (e). The likely reason for this noted exception is the relatively high transition probability (= 0.8) and the relatively low noise level (1%). Of course, for smaller values of (i.e. = 0.1) the similarity is even more striking

Estimating the distribution of dynamic invariants: illustrated with an application to human photo-plethysmographic time series-0

<p><b>Copyright information:</b></p><p>Taken from "Estimating the distribution of dynamic invariants: illustrated with an application to human photo-plethysmographic time series"</p><p>http://www.nonlinearbiomedphys.com/content/1/1/8</p><p>Nonlinear Biomedical Physics 2007;1():8-8.</p><p>Published online 23 Jul 2007</p><p>PMCID:PMC1997126.</p><p></p>vational noise (respectively). The remaining panels are representative ATS time series. Panels (b), (c), (d) and (e) are surrogates for panel (a), and Panels (g), (h), (i) and (j) are for panel (f). Each surrogate is computed with a different level of transition probability . In panels (b) and (g), = 0.2; in panels (c) and (h), = 0.4; in panels (d) and (i), = 0.6; and, in panels (e) and (j), = 0.8. In each case the attractors reconstructed from the surrogates have the same qualitative features as that of the data – with the possible exception of panel (e). The likely reason for this noted exception is the relatively high transition probability (= 0.8) and the relatively low noise level (1%). Of course, for smaller values of (i.e. = 0.1) the similarity is even more striking

Simulations of high density instances () of the R2 model.

<p>Low and high initial speeds are considered. The simulation with high initial speed shows small groups dispersing in many directions. Plot (a) shows a snapshot after 100 s and (b) one after 500 s.</p

Homing flight 2: flock separation for models with different interaction structure.

<p>In (a), simulations consider initial conditions from the input data, while (b) averages over ten simulations of random initial conditions, and all time intervals. From the plots, a split occurs in the flock after (see (a)), while has the strongest collective component (see (b)).</p

Low density simulations of the modified Vicsek model and the “best” R1 model.

<p>The same initial conditions were used for both models. Qualitatively, the R1 model dynamics resemble the modified Visek model: individuals move away in groups. Plot (a) shows a snapshot at and (b) one at .</p

Comparison of between the modified Vicsek model data and the “best” R1 model.

<p>Statistics were averaged over 10 simulations, with both models using the same initial conditions. In (a) low density initial conditions (,) and in (b) high density initial conditions (,). The range of the simulations is delimited by the dashed lines.</p

Homing flight 4: Flock separation for models with different interaction structure.

<p>In (a), simulations consider initial conditions from the input data, while (b) averages over ten simulations of random initial conditions. From the plots, shows the best resemblance to the input data (see (a)) and the strongest collective component (see (b)).</p

Comparison of between the modified Vicsek model data and the “best” R1 model.

<p>Statistics were averaged over 10 simulations, with both models using the same initial conditions. In (a) low density initial conditions (,) and in (b) high density initial conditions (,). The range of the simulations is delimited by the dashed lines.</p

The “optimal” <i>M</i> value.

<p>Averaged mean absolute error (MAE) values between models and their source data for each homing flight. The MAEs from all the models of the same type (same <i>M</i>) were averaged in order to find which interaction followed best the separation dynamics. The models with show the least averaged MAE in all flights.)</p