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Strong laws for recurrence quantification analysis  [PDF]
Marian Grendár,Jana Majerová,Vladimír ?pitalsky
Mathematics , 2013, DOI: 10.1142/S0218127413501472
Abstract: The recurrence rate and determinism are two of the basic complexity measures studied in the recurrence quantification analysis. In this paper, the recurrence rate and determinism are expressed in terms of the correlation sums, and strong laws of large numbers are given for them.
Rough surfaces induced speckle effects on detection performance of pulsed laser radar

Guo Guan-Jun,Shao Yun,

物理学报 , 2004,
Abstract: The statistical performance of detecting optically rough surfaces with pulsed laser radar using energy detection techniques has been investigated in this paper. Under the far field condition, the analytical expressions for computing the speckle number integrated by the receiving aperture is presented, and the speckle number subtended by the telescope is found to be dependent only on the relative size of the laser beam waist and the area of the entrance pupil. A new statistics for photoelectron counts is proposed when the receiving telescope collects a large number of speckle cells and photoelectrons. The detection probabilities for airborne and space-based laser radar have been derived. The results indicate that the laser radar performance is closely related to the speckle number observed by the receiving aperture and the influence of the speckle noise is abated with the increase of integrated speckle cells.
Recurrence Quantification Analysis and Principal Components in the Detection of Short Complex Signals  [PDF]
J. P. Zbilut,A. Giuliani,C. L. Webber, Jr
Physics , 1997, DOI: 10.1016/S0375-9601(97)00843-8
Abstract: Recurrence plots were introduced to help aid the detection of signals in complicated data series. This effort was furthered by the quantification of recurrence plot elements. We now demonstrate the utility of combining recurrence quantification analysis with principal components analysis to allow for a probabilistic evaluation for the presence of deterministic signals in relatively short data lengths.
Recurrence quantification analysis to compare the machinability of steels
Ravish,Umashankar K. S.,Abhinav Alva,Gangadharan K. V.
Journal of Engineering and Applied Sciences , 2011,
Abstract: Machinability, though is a simple term, is difficult to generalize. But nevertheless, it can be realized as the ease or difficulty with which a material can be machined. Assessing the machinability of various materials before they are used in commercial manufacturing is very demanding, as the machinability affects the material removal rate, surface finish of the workpiece, cutting power consumption and tool wear rate. The present work aims at establishing Recurrence Quantification Analysis, a relatively new technique in the study of chaotic systems, as a potential tool to establish and compare the machinability of steels. The technique has its roots in quantifying the Recurrence Plots obtained by the phase space reconstruction of time domain signals. Variation in Determinism, one of the variables of the technique, is used as a mean to establish the comparison of machinability.
Anaesthesia Monitoring by Recurrence Quantification Analysis of EEG Data  [PDF]
Klaus Becker,Gerhard Schneider,Matthias Eder,Andreas Ranft,Eberhard F. Kochs,Walter Zieglg?nsberger,Hans-Ulrich Dodt
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0008876
Abstract: Appropriate monitoring of the depth of anaesthesia is crucial to prevent deleterious effects of insufficient anaesthesia on surgical patients. Since cardiovascular parameters and motor response testing may fail to display awareness during surgery, attempts are made to utilise alterations in brain activity as reliable markers of the anaesthetic state. Here we present a novel, promising approach for anaesthesia monitoring, basing on recurrence quantification analysis (RQA) of EEG recordings. This nonlinear time series analysis technique separates consciousness from unconsciousness during both remifentanil/sevoflurane and remifentanil/propofol anaesthesia with an overall prediction probability of more than 85%, when applied to spontaneous one-channel EEG activity in surgical patients.
Recurrence Quantification Analysis of Financial Market Crashes and Crises  [PDF]
Oleksandr Piskun,Sergii Piskun
Quantitative Finance , 2011,
Abstract: Financial markets are systems with the complex behavior, that can be hardly analyzed by means of linear methods. Recurrence Quantification Analysis (RQA) is a nonlinear methodology, which is able to work with the nonstationary and short data series. Thus, we apply RQA for the studying of the critical events on financial markets. For the present research, stock crashes of DJI 1929; DJI, NYSE and S&P500 1987; NASDAQ 2000; HSI 1994, 1997 and Spanish 1992, Portuguese 1992, British 1992, German 1992, Italian 1992, Mexican 1994, Brazilian 1999, Indonesian 1997, Thai 1997, Malaysian 1997, Philippine 1997, Russian 1998, Turkish 2001, Argentine 2002 currency devaluations were taken. The recent world financial crisis of 2007-2010 was considered as well. The possibility of LAM measure to serve as a tool for the revealing, monitoring, analysing and precursoring of financial bubbles, crises and crashes was asserted.
Recurrence quantification analysis as a tool for the characterization of molecular dynamics simulations  [PDF]
Cesare Manetti,Marc-Antoine Ceruso,Alessandro Giuliani,Charles L. Webber, Jr.,Joseph P. Zbilut
Physics , 1998, DOI: 10.1103/PhysRevE.59.992
Abstract: A molecular dynamics simulation of a Lennard-Jones fluid, and a trajectory of the B1 immunoglobulin G-binding domain of streptococcal protein G (B1-IgG) simulated in water are analyzed by recurrence quantification, which is noteworthy for its independence from stationarity constraints, as well as its ability to detect transients, and both linear and nonlinear state changes. The results demonstrate the sensitivity of the technique for the discrimination of phase sensitive dynamics. Physical interpretation of the recurrence measures is also discussed.
Orthographic Structuring of Human Speech and Texts: Linguistic Application of Recurrence Quantification Analysis  [PDF]
F. Orsucci,K. Walter,A. Giuliani,C. L. Webber, Jr.,J. P. Zbilut
Computer Science , 1997,
Abstract: A methodology based upon recurrence quantification analysis is proposed for the study of orthographic structure of written texts. Five different orthographic data sets (20th century Italian poems, 20th century American poems, contemporary Swedish poems with their corresponding Italian translations, Italian speech samples, and American speech samples) were subjected to recurrence quantification analysis, a procedure which has been found to be diagnostically useful in the quantitative assessment of ordered series in fields such as physics, molecular dynamics, physiology, and general signal processing. Recurrence quantification was developed from recurrence plots as applied to the analysis of nonlinear, complex systems in the physical sciences, and is based on the computation of a distance matrix of the elements of an ordered series (in this case the letters consituting selected speech and poetic texts). From a strictly mathematical view, the results show the possibility of demonstrating invariance between different language exemplars despite the apparent low-level of coding (orthography). Comparison with the actual texts confirms the ability of the method to reveal recurrent structures, and their complexity. Using poems as a reference standard for judging speech complexity, the technique exhibits language independence, order dependence and freedom from pure statistical characteristics of studied sequences, as well as consistency with easily identifiable texts. Such studies may provide phenomenological markers of hidden structure as coded by the purely orthographic level.
Multi-windowed defocused speckle photographic system for tilt measurement  [PDF]
Jose M. Diazdelacruz
Physics , 2004, DOI: 10.1364/AO.44.002250
Abstract: Defocused speckle photography has long been used to measure rotations of rough surfaces. This paper explains how, by adding a suitably perforated mask, some measurement properties, such as range or lateral resolution, may be changed at wish. Particularly, the maximum measurable tilt can be significantly raised, although at the expense of poorer lateral resolution. Advantages over previously described techniques include independent tuning of speckle size and optical system aperture and more extended adaptability to different measuring needs. The benefits and disadvantages of the new and old techniques are thoroughly compared.
Finding Trends of Airborne Harmful Pollutants by Using Recurrence Quantification Analysis
American Journal of Environmental Engineering , 2011, DOI: 10.5923/j.ajee.20110101.02
Abstract: In this work, the use of Recurrence Plots and Recurrence Quantification Analysis explores the changes in the non-linear behavior of harmful airborne particle concentration in four sites around London simultaneously. This research has been carried out for 6 years, using large datasets of raw data (hourly) for harmful particles such as CO, SO2, NO2, NO and Particulate Matter (PMx). Recurrence analysis has been shown to be a useful tool in many disciplines to find trends, rates and predictions. Nevertheless, it has not been shown before the feasibility of using these algorithms to extract information for pollution monitoring and control. Also, observations are made with the results and conclusions drawn from these observations, showing the feasibility of this approach in finding trends of airborne pollution.
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