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Topic: Recurrence plot

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	Recurrence plots
		Recurrence plots are used to reveal non-stationarity of a series as well as to indicate the degree of aperiodicity.
		Note that the recurrence plot is diagonally symmetric since the distance of the i'th embedded vector to the j'th embedded vector is the same as the distance of the j'th to the i'th.
		This is most efficiently computed from a colour recurrence plot where, in general, all the distances have been computed and one simply need to step through a range of radii and count the number of cells with a distance less than the radius.
	local.wasp.uwa.edu.au /~pbourke/fractals/recurrence (877 words)

	Santo to Signal: Media and Process (Site not responding. Last check: 2007-10-22)
		While the first phase space portrait explored the symbolism of geometries and the visual connection with the santo's motif and color, the second phase space portrait trusted the recurrence plot to establish that connection to allow the artist to focus her the attention on the use of symmetry in ornamentation.
		Santo to Signal presents ways by which the use of the mathematical concept of recurrence plots have assisted in determining the coloring of patterns and the deign of planar symmetry for three phase space portraits of the Dolorosa.
		recurrence plots and the use of software that explore their importance as visual qualitative analysis tools deserve further investigation by artists who seek new modes of creating new symbols.
	digitalmedia.upd.edu.ph /digiteer/signal/signal3.html (2979 words)

	Recurrence Plot Analysis (Site not responding. Last check: 2007-10-22)
		While published instances of recurrence plot analysis use an embedded univariate time series to represent the state of the system, it is not necessary to use this representation.
		All that is required to construct a recurrence plot is a measure of the distance between states of the system at different times.
		Recurrence plot analysis is useful because it can reveal temporal structure that is difficult to see with other methods.
	richter.colorado.edu /seth-mcginnis-thesis/node15.html (468 words)

	Recurrence plot - Wikipedia, the free encyclopedia
		In descriptive statistics and chaos theory, a recurrence plot (RP) is a plot showing, for a given moment in time, the times at which a phase space trajectory visits roughly the same area in the phase space.
		Moreover, the recurrence of states, in the meaning that states are again arbitrarily close after some time of divergence, is a fundamental property of deterministic dynamical systems and is typical for nonlinear or chaotic systems (cf.
		In contrast to the heuristic approach of the recurrence quantification analysis, which depends on the choice of the embedding parameters, some dynamical invariants as correlation dimension, K2 entropy or mutual information, which are independent on the embedding, can also be derived from recurrence plots.
	en.wikipedia.org /wiki/Recurrence_plot (897 words)

	Santo to Signal: Media and Process
		While the first phase space portrait explored the symbolism of geometries and the visual connection with the santo's motif and color, the second phase space portrait trusted the recurrence plot to establish that connection to allow the artist to focus her the attention on the use of symmetry in ornamentation.
		However, the embedding values and the colormap used diminished the rigid construction of the recurrence plot where areas of similar color are not sharply defined, blurring bounds between trajectories.
		recurrence plots and the use of software that explore their importance as visual qualitative analysis tools deserve further investigation by artists who seek new modes of creating new symbols.
	www.upd.edu.ph /~cfa/digitalmedia/digiteer/signal/signal3.html (2979 words)

	Phase Space Portraits of the Nuestra Señora delos Dolores of Baclayon Church in Bohol
		Recurrence Plots (see Figure 2) is the application of the basic idea that from a single observable behavior, it is possible to recreate a topologically equivalent picture of the original multidimensional system, because the effect of all the other unobserved variables is already reflected in the single observable behavior.
		The basic symmetry analysis and construction method I used was to decompose the Recurrence Plot patterns by symmetry groups to obtain a region, and use that region to infer geometry for the remaining regions.
		The Recurrence Plot generated revealed a bounded pattern, that is, without a periodic tiling on the plane.
	www.upd.edu.ph /~cfa/digitalmedia/digiteer/texts/phase_space.html (4940 words)

	Recurrence Interval
		These are often confused because the recurrence interval (calculated from past events) is used to gauge the future probability of an event.
		The confusion between the past-determined recurrence interval and the forecasted probability is reinforced by the widespread use of "a 100-year flood" to mean a "flood with a 1% probability of occurring in any given year."
		In this lab, students calculate recurrence intervals for various degrees of flooding on a portion of the Des Moines River in Iowa, based on historical data.
	serc.carleton.edu /quantskills/methods/quantlit/RInt.html (1135 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		J. Iwanski and E. Bradley, "Recurrence Plot Analysis: To Embed or not to Embed?," Chaos 8:861-871 (1998).
		These plots often reveal correlations in the data that are not easily detected in the original time series.
		Existing recurrence plot analysis techniques, which are primarily application-oriented and completely quantitative, require that the time-series data first be embedded in a high-dimensional space, where the embedding dimension d_E is dictated by the dimension d of the data set, with d_E >= 2d+1.
	www.cs.colorado.edu /~lizb/papers/iwanski-chaos98.html (196 words)

	RECURRENCE PLOTS::Introduction To Cross and Joint Recurrence Plots
		Such recurrence plot represents the behaviour of a single trajectory in the phase space with typical long-scale and small-scale structures.
		The recurrence rate is the ratio of all recurrent states (recurrence points) to all possible states and is the probability of recurrence of a special state.
		The recurrence rate RR, determinism DET and the averaged diagonal line length L were determined as a function of the distance from the main diagonal, e.g.
	www.recurrence-plot.tk /crps.php (1579 words)

	Recurrence Plots and Dynamical System Analysis
		A recurrence plot is a two-dimensional representation technique that brings out distance correlations in a time series.
		We are interested in recurrence plots because they are an effective way to visualize the geometry of a dynamical system's behavior, and we are working on analysis techniques that can effectively characterize the geometry of their structure.
		One way to understand the geometric structure of a recurrence plot is to consider the unstable periodic orbits or UPOs that lie within a chaotic attractor.
	www.cs.colorado.edu /~lizb/rps.html (888 words)

	Applications of Non-Parametric Recurrence Data Analysis in Reliability Engineering
		The non-parametric recurrence data analysis method provides a nonparametric graphical estimate of the mean cumulative number or cost of recurrence per unit versus age.
		When the smooth curve that goes through MCF plot increases monotonically, the systems are exhibiting what is usually referred to as useful life, which is the 'stable' period during which the failures occur at a constant rate.
		When the smooth curve that goes through the MCF plot is concave down (has a derivative that decreases as the units age), the recurrence rate decreases as the population ages.
	www.weibull.com /hotwire/issue57/hottopics57.htm (976 words)

	Phase Space Portraits of the Nuestra Señora delos Dolores of Baclayon Church in Bohol
		Recurrence Plots (see Figure 2) is the application of the basic idea that from a single observable behavior, it is possible to recreate a topologically equivalent picture of the original multidimensional system, because the effect of all the other unobserved variables is already reflected in the single observable behavior.
		The basic symmetry analysis and construction method I used was to decompose the Recurrence Plot patterns by symmetry groups to obtain a region, and use that region to infer geometry for the remaining regions.
		On the lower layer, the Recurrence Plot was printed on film and mounted between acrylic plastic sheets, while on the upper layer, the symmetry design derived from the Recurrence Plot was rendered on glass through engraving and gilding.
	digitalmedia.upd.edu.ph /digiteer/texts/phase_space.html (4940 words)

	Recurrence plots (Site not responding. Last check: 2007-10-22)
		Recurrence plots are a useful tool to identify structure in a data set in a time resolved way qualitatively.
		, a recurrence plot is used to detect transient behavior at the beginning of a longer recording.
		For the purpose of stationary testing, the recurrence plot is not particularly sensitive to the choice of embedding.
	sattagis1.dza.fc.ul.pt /~amaral/docs/chaospaper/node14.html (353 words)

	Flooding
		If we plot the log of Recurrence Interval, the distances between 0 and 1, 1 and 10, 10 and 100, 100 and 1000 etc. are identical (look at the coordinates of some graph paper where both axes are on a log scale).
		You know that planners refer to something called the 100-Year Flood that is defined from a plot of Recurrence Interval versus Maximum Annual Discharge.
		This is a flood with a recurrence interval of 100 years.
	www.uh.edu /~jbutler/physical/flooding/figure3.html (503 words)

	Center for Nonlinear Science - Recurrence Analysis
		Eckmann, Kamphorst and Ruelle (1987) first introduced the recurrence plot as a graphical tool to locate hidden rhythms, patterns and nonstationarities in experimental data.
		Recurrence analysis is the quantification of features of recurrence plots.
		Recurrence plot for births to teens from 1964 –1998 (On the color bar to the right of the graph 0.00 means no distance between vectors [perfect correlation] and 123.00 refers to maximum distance between vectors [weakest correlation].)
	www.twu.edu /cns/recurrenceanalysis.html (647 words)

	RECURRENCE PLOTS::Bibliography - J. S. Iwanski, E. Bradley: Recurrence plots of experimental data: To embed or not to ...
		One such set of recurrence plot analysis tools, recurrence quantification analysis, is particularly useful in finding locations in the data where the underlying dynamics change.
		These plots often reveal correlations in the data that are not easily detected in the original time series.
		Existing recurrence plot analysis techniques, which are primarily application oriented and completely quantitative, require that the time-series data first be embedded in a high-dimensional space, where the embedding dimension dE is dictated by the dimension d of the data set, with dE >= 2d + 1.
	www.recurrence-plot.tk /bibliography.php?label=iwanski98 (256 words)

	CEPTUAL INSTITUTE - bios.htm Sabelli & Kauffman
		Returning to the plots in Figure 2, we illustrate an increasing sequence of values of g in subfigures A, B, C, D. We see that at A the cobweb plot indicates a period two pattern as indeed one sees in the plot of the process equation shown in Figure 1.
		It is clearly (from the cobweb plot) a consequence of the weaving back and forth between the maximum, minimum and "walls" of the sine wave pattern in the graph of y=x+gsin(x).
		Bios is composed of time-limited patterns detected by recurrence and wavelet plots similar to those observed for pink noise, in contrast to stationary random, periodic and chaotic patterns [Kauffman andSabelli (1998)].
	www.ceptualinstitute.com /genre/sabelli-kauffman/bios.htm (4543 words)

	Charles L. Webber, Jr.
		Zbilut, J.P., Giuliani, A., Webber, C.L. Jr., Colosimo, A. Recurrence quantification analysis in structure-function relationships of proteins: an overview of a general methodology applied to the case of TEM-1 beta-lactamase.
		A local recurrence plot (left) is generated by keeping the radius low (15% of maxdist), allowing recurrences to occur only in near neighborhoods.
		A global recurrence plot (right) is generated by saturating the radius (100% of maxdist), allowing for all possible recurrences.
	homepages.luc.edu /~cwebber (1030 words)

	Recurrence plot
		The presentation is usually estimated as recurrence plot twice the risk for another is recurrence plot frameless.
		Recurrence plot then and sn tn tn tn tn as tn recurrence plot as tn tn sn.
		Recurrence plot the recurrence plot main reasons for ending trial participation were end or aim.
	recurrence-of.aaexelor.com /recurrence-plot.html (475 words)

	Nonlinear Methods in the Analysis of Protein Sequences: A Case Study in Rubredoxins -- Giuliani et al. 78 (1): 136 -- ...
		The average recurrence of the sequence is displayed as a function of the displacement from the main diagonal of the recurrence plot.
		Given that the main diagonal of the recurrence plot corresponds to the identity in time (i.e., sequence position), the displacement histograms can be equated to a sort of local autocorrelation integral function.
		The kurtosis of recurrence displacement was used to quantitatively discriminate mesophilic and thermophilic structures.
	www.biophysj.org /cgi/content/full/78/1/136 (5955 words)

	Illuminations: Shedding Light on the Subject: Function Models of Light Decay
		Plotting the change in light intensity against the light intensity produces a linear relationship.
		This recurrence equation may be plotted on graph paper or using the graphing calculator.
		Plot this recurrence relation on the same axes as the data.
	illuminations.nctm.org /index_d.aspx?id=380 (4752 words)

	Recurrence - Wikipedia, the free encyclopedia
		Recurrence is the instance of recurring; frequent occurrence.
		Recurrence and recurrent may also be used in reference to:
		Recurrence plot, a statistical plot that shows a pattern that re-occurs
	en.wikipedia.org /wiki/Recurrence (151 words)

	Owner's Manual (Site not responding. Last check: 2007-10-22)
		In order to get the recurrence plot (RP) from a time series, we first perform a delay-coordinate embedding of the data, which is essentially a way to expand the 1-dimensional time-series data into a higher dimensional space, better representing the true multi-dimensional characteristics of the system being measured.
		The recurrence plot that is on the back of this year's shirt is generated from a time series of angular position measurements from a damped, forced pendulum with a chaotic trajectory.
		Well, this is currently the focus of a portion of my research, and as these plots are a relatively recent newcomer on the nonlinear analysis scene, there is not a significant literature on them.
	amath.colorado.edu /department/Tshirt/1998/owners.html (443 words)

	NPG - Abstract
		The method of recurrence plots is extended to the cross recurrence plots (CRP) which, among others, enables the study of synchronization or time differences in two time series.
		This is emphasized in a distorted main diagonal in the cross recurrence plot, the line of synchronization (LOS).
		A non-parametrical fit of this LOS can be used to rescale the time axis of the two data series (whereby one of them is compressed or stretched) so that they are synchronized.
	www.copernicus.org /EGU/npg/9/325.htm (139 words)

	Iteni Group Home Page
		The Recurrency Plots (RP) are a new powerful tool to easily process experimental scalar time series.
		The RP were firstly introduced by Eckmann et al in [2] as a tool to describe non linear dynamic systems without constraint such as system stationariety, dynamical noise and transient phenomena that typically characterise normal physiological systems.
		Obviously, understanding the clinical implications of these specific markers is an important key to appreciate the power of recurrence plot strategies.
	www.ifc.cnr.it /iteni/complex.html (627 words)

	Use of nonlinear methods to assess effects of clonidine on blood pressure in spontaneously hypertensive rats -- ...
		B: recurrence plot: a 20 × 20 square is drawn.
		Nonlinear methods, in particular the recurrence plot method, have been used in previous reports.
		Use of recurrence plots in the analysis of heartbeat intervals.
	jap.physiology.org /cgi/content/full/84/5/1795 (3197 words)

	Main - UPO Search
		This is the GUI to analyze the Recurrence Plot, it allows to look at the x, y or z component recurrence plot, an allows to zoom on them.
		This is the program that was used to generate the plots presented on the Paper, it calls must of the rutines developed and it is also a nice introduction to IDL ploting capabilities.
		This is a very simple example of how to use the recPlotViewer to create an Recurrence Plot for any data set the user wants, it reads an xyx ascii file (like this) and.analizes the data on it.
	cires.colorado.edu /~ricardo/upos/tools3.html (645 words)

	[No title]
		Recurrence analysis is now one of the major tools in the study of noisy or chaotic dynamical systems.
		Webber and Zbilut used recurrence analysis to study cardiac anomalies, which eventually led to an electronic means of predicting heart attacks up to fifteen minutes before they occurred.
		It should then be possible to determine which recurrence parameters might work best for the new machine, avoiding the task of trying dozens of values of dimension and delay.
	zarnia.250free.com /index.htm (2953 words)

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