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>
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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}}

Latest revision as of 20:58, 17 August 2014

Today, there are several other types of web development and blogging software available to design and host your website blogs online and that too in minutes, if not hours. You can either install Word - Press yourself or use free services offered on the web today. This is a service where people write articles using a specific keyword you have given them. If you're using Wordpress and want to make your blog a "dofollow" blog, meaning that links from your blog pass on the benefits of Google pagerank, you can install one of the many dofollow plugins available. Understanding how Word - Press works can be a challenge, but it is not too difficult when you learn more about it.

These websites can be easily customized and can appear in the top rankings of the major search engines. If a newbie missed a certain part of the video then they could always rewind. A Wordpress plugin is a software that you can install into your Wordpress site. You can up your site's rank with the search engines by simply taking a bit of time with your site. Now a days it has since evolved into a fully capable CMS platform which make it, the best platform in the world for performing online business.

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