Abelian sandpile model: Difference between revisions

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A '''Poincaré plot''', named after [[Henri Poincaré]], is used to quantify [[self-similarity]] in processes, usually [[periodic function]]s. It is also known as a '''return map'''.<ref>[http://classes.yale.edu/fractals/chaos/ReturnMap/ReturnMap.html Yale Fractal Geometry Course Notes]</ref><ref>[http://www.cbi.dongnocchi.it/glossary/ReturnMap.html GLOSSARY OF TERMS USED IN TIME SERIES ANALYSIS OF CARDIOVASCULAR DATA]</ref>
 
Given a time series of the form
 
: <math>x_t, x_{t+1}, x_{t+2}, \ldots, \, </math>
 
a return map in its simplest form first plots (''x''<sub>1</sub>,&nbsp;''x''<sub>2</sub>), then plots (''x''<sub>2</sub>,&nbsp;''x''<sub>3</sub>), then (''x''<sub>3</sub>,&nbsp;''x''<sub>4</sub>), and so on.
 
Some quotes from the literature:
* "... is a plot of RR(''n'') on the ''x''-axis versus RR(''n''&nbsp;+&nbsp;1) on the ''y''-axis."<ref>[http://www.biopac.com/FAQ-Details.asp?ID=352 Biopac FAQ for tachograms].</ref>
* "... Poincaré plot, which takes a sequence of intervals and plots each interval against the following interval."<ref>[http://cat.inist.fr/?aModele=afficheN&cpsidt=14122427 Do existing measures of Poincaré plot geometry reflect nonlinear features of heart rate variability?] ISSN 0018-9294.</ref>
* "... a graph in which each RR interval is plotted as a function of the previous RR interval."<ref>
{{cite journal
| author = Heikki V. Huikuri, Timo H. Mäkikallio, Chung-Kang Peng, Ary L. Goldberger, Ulrik Hintze, and Mogens Møller
| date = January 4, 2000
| pages = 47&ndash;53
| volume = 101
| title = Fractal Correlation Properties of R-R Interval Dynamics and Mortality in Patients With Depressed Left Ventricular Function After an Acute Myocardial Infarction.
| journal = Circulation
| pmid = 10618303
| publisher = American Heart Association. 7272 Greenville Avenue, Dallas, TX
| url = http://circ.ahajournals.org/cgi/content/full/101/1/47
| format = online
| quote = Analysis of time and frequency domain measures of heart rate (HR) variability from 24-hour ambulatory ECG recordings provides prognostic information on patients after an acute myocardial infarction.1–4 A number of new methods based on nonlinear system theory (“chaos theory and fractals”) have been recently developed to quantify the complex HR dynamics and to complement the conventional measures of HR variability.5–12 New fractal analysis methods have already provided clinically useful information on patients with impaired left ventricular function,13–15 but their prognostic power has not been proved in large-scale studies. In the present investigation, we assessed the use of various fractal analysis methods of HR variability to predict death in a population of patients with acute myocardial infarction (MI) and depressed left ventricular function. The prediction of death was evaluated in survivors of acute MI included in the Danish Investigations of Arrhythmia and Mortality on Dofetilide (DIAMOND-MI) trial. We also sought to determine whether these new fractal measures of R-R interval dynamics predict specifically either arrhythmic or nonarrhythmic cardiac death.
| issn = 1524-4539
| issue = 1
| doi = 10.1161/01.CIR.101.1.47
}}
</ref>
 
==RR tachograph==
 
The [[Heart_rate_turbulence#History|RR]] tachograph is a picture of the RR-interval, which is the interval between R-waves of the tachogram, usually felt as heartbeats.
 
==See also==
* [[Recurrence plot]]
* [[Poincaré map]]
* [[Heart rate variability]] (HRV), a use of Poincaré plots to assess heart functionality.
 
==References==
<references/>
 
{{DEFAULTSORT:Poincare plot}}
[[Category:Scaling symmetries]]
[[Category:Dynamical systems]]
[[Category:Chaos theory]]
[[Category:Statistical charts and diagrams]]
 
 
{{mathapplied-stub}}

Revision as of 02:26, 17 September 2013

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A Poincaré plot, named after Henri Poincaré, is used to quantify self-similarity in processes, usually periodic functions. It is also known as a return map.[1][2]

Given a time series of the form

a return map in its simplest form first plots (x1, x2), then plots (x2, x3), then (x3, x4), and so on.

Some quotes from the literature:

  • "... is a plot of RR(n) on the x-axis versus RR(n + 1) on the y-axis."[3]
  • "... Poincaré plot, which takes a sequence of intervals and plots each interval against the following interval."[4]
  • "... a graph in which each RR interval is plotted as a function of the previous RR interval."[5]

RR tachograph

The RR tachograph is a picture of the RR-interval, which is the interval between R-waves of the tachogram, usually felt as heartbeats.

See also

References

  1. ↑ Yale Fractal Geometry Course Notes
  2. ↑ GLOSSARY OF TERMS USED IN TIME SERIES ANALYSIS OF CARDIOVASCULAR DATA
  3. ↑ Biopac FAQ for tachograms.
  4. ↑ Do existing measures of Poincaré plot geometry reflect nonlinear features of heart rate variability? ISSN 0018-9294.
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