Reconstruction of Phase Space and Eigenvalue Decomposition from a Biological Time Series: A Malayalam Speech Signal Case Study

2021 ◽  
Author(s):  
K. M. Muraleedharan ◽  
K. T. Bibish Kumar ◽  
Sunil Kumar ◽  
R. K. Sunil John
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Age Groups ◽  
Principal Component ◽  
Eigenvalue Decomposition ◽  
Embedding Dimension ◽  
System Perspective ◽  
Biological Time ◽  
Non Linear ◽  
Pca Method

Our objective is to describe the speech production system from a non-linear physiological system perspective and reconstruct the attractor from the experimental speech data. Mutual information method is utilized to find out the time delay for embedding. The False Nearest Neighbour (FNN) method and Principal Component Analysis (PCA) method are used for optimizing the embedding dimension of time series. The time series obtained from the typical non-linear systems, Lorenz system and Rössler system, is used to standardize the methods and the Malayalam speech vowel time series of both genders of different age groups, sampled at three sampling frequencies (16[Formula: see text]kHz, 32[Formula: see text]kHz, 44.1[Formula: see text]kHz), are taken for analysis. It was observed that time delay varies from sample to sample and, it ought to be better to figure out the time delay with the embedding dimension analysis. The embedding dimension is shown to be independent of gender, age and sampling frequency and can be projected as five. Hence a five-dimensional hyperspace will probably be adequate for reconstructing attractor of speech time series.

Identification of Synchronicity in Deterministic Chaotic Attractors for the Downscaling Process in the Bogotá River Basin

2021 ◽  
Author(s):  
Santiago Duarte ◽  
Gerald Corzo ◽  
Germán Santos
Keyword(s):  
Time Series ◽  
Time Delay ◽  
River Basin ◽  
Spatial Scales ◽  
Climatic Variables ◽  
Chaotic Attractors ◽  
Multiple Attractors ◽  
Nearest Neighbours ◽  
Basin Scale ◽  
Non Linear

<p>Bogotá’s River Basin, it’s an important basin in Cundinamarca, Colombia’s central region. Due to the complexity of the dynamical climatic system in tropical regions, can be difficult to predict and use the information of GCMs at the basin scale. This region is especially influenced by ENSO and non-linear climatic oscillation phenomena. Furthermore, considering that climatic processes are essentially non-linear and possibly chaotic, it may reduce the effectiveness of downscaling techniques in this region. </p><p>In this study, we try to apply chaotic downscaling to see if we could identify synchronicity that will allow us to better predict. It was possible to identify clearly the best time aggregation that can capture at the best the maximum relations between the variables at different spatial scales. Aside this research proposes a new combination of multiple attractors. Few analyses have been made to evaluate the existence of synchronicity between two or more attractors. And less analysis has considered the chaotic behaviour in attractors derived from climatic time series at different spatial scales. </p><p>Thus, we evaluate general synchronization between multiple attractors of various climate time series. The Mutual False Nearest Neighbours parameter (MFNN) is used to test the “Synchronicity Level” (existence of any type of synchronization) between two different attractors. Two climatic variables were selected for the analysis: Precipitation and Temperature. Likewise, two information sources are used: At the basin scale, local climatic-gauge stations with daily data and at global scale, the output of the MPI-ESM-MR model with a spatial resolution of 1.875°x1.875° for both climatic variables (1850-2005). In the downscaling process, two RCP (Representative Concentration Pathways)  scenarios are used, RCP 4.5 and RCP 8.5.</p><p>For the attractor’s reconstruction, the time-delay is obtained through the  Autocorrelation and the Mutual Information functions. The False Nearest Neighbors method (FNN) allowed finding the embedding dimension to unfold the attractor. This information was used to identify deterministic chaos at different times (e.g. 1, 2, 3 and 5 days) and spatial scales using the Lyapunov exponents. These results were used to test the synchronicity between the various chaotic attractor’s sets using the MFNN method and time-delay relations. An optimization function was used to find the attractor’s distance relation that increases the synchronicity between the attractors.  These results provided the potential of synchronicity in chaotic attractors to improve rainfall and temperature downscaling results at aggregated daily-time steps. Knowledge of loss information related to multiple reconstructed attractors can provide a better construction of downscaling models. This is new information for the downscaling process. Furthermore, synchronicity can improve the selection of neighbours for nearest-neighbours methods looking at the behaviour of synchronized attractors. This analysis can also allow the classification of unique patterns and relationships between climatic variables at different temporal and spatial scales.</p>

scholarly journals Challenges in estimating the impact of vaccination with sparse data

2018 ◽  
Author(s):  
Kayoko Shioda ◽  
Cynthia Schuck-Paim ◽  
Robert J. Taylor ◽  
Roger Lustig ◽  
Lone Simonsen ◽  
...  
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Simulation Analysis ◽  
Principal Component ◽  
Population Level ◽  
Series Data ◽  
Synthetic Control ◽  
Vaccine Impact ◽  
Pca Method ◽  
The Impact

ABSTRACTBackgroundThe synthetic control (SC) model is a powerful tool to quantify the population-level impact of vaccines, because it can adjust for trends unrelated to vaccination using a composite of control diseases. Because vaccine impact studies are often conducted using smaller subnational datasets, we evaluated the performance of SC models with sparse time series data. To obtain more robust estimates of vaccine effects from noisy time series, we proposed a possible alternative approach, “STL+PCA” method (seasonal-trend decomposition plus principal component analysis), which first extracts smoothed trends from the control time series and uses them to adjust the outcome.MethodsUsing both the SC and STL+PCA models, we estimated the impact of 10-valent pneumococcal conjugate vaccine (PCV10) on pneumonia hospitalizations among cases <12 months and 80+ years of age during 2004-2014 at the subnational level in Brazil. The performance of these models was also compared using simulation analyses.ResultsThe SC model was able to adjust for trends unrelated to PCV10 in larger states but not in smaller states. The simulation analysis confirmed that the SC model failed to select an appropriate set of control diseases when the time series were sparse and noisy, thereby generating biased estimates of the impact of vaccination when secular trends were present. The STL+PCA approach decreased bias in the estimates for smaller populations.ConclusionsEstimates from the SC model might be biased when data are sparse. The STL+PCA model provides more accurate evaluations of vaccine impact in smaller populations.

scholarly journals Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 221
Author(s):  
Mariano Matilla-García ◽  
Isidro Morales ◽  
Jose Miguel Rodríguez ◽  
Manuel Ruiz Marín
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Phase Space ◽  
Mutual Information ◽  
Phase Space Reconstruction ◽  
Chaotic Time Series ◽  
Optimal Time ◽  
Embedding Dimension ◽  
Simple Method ◽  
Correlation Integral

The modeling and prediction of chaotic time series require proper reconstruction of the state space from the available data in order to successfully estimate invariant properties of the embedded attractor. Thus, one must choose appropriate time delay τ∗ and embedding dimension p for phase space reconstruction. The value of τ∗ can be estimated from the Mutual Information, but this method is rather cumbersome computationally. Additionally, some researchers have recommended that τ∗ should be chosen to be dependent on the embedding dimension p by means of an appropriate value for the time delay τw=(p−1)τ∗, which is the optimal time delay for independence of the time series. The C-C method, based on Correlation Integral, is a method simpler than Mutual Information and has been proposed to select optimally τw and τ∗. In this paper, we suggest a simple method for estimating τ∗ and τw based on symbolic analysis and symbolic entropy. As in the C-C method, τ∗ is estimated as the first local optimal time delay and τw as the time delay for independence of the time series. The method is applied to several chaotic time series that are the base of comparison for several techniques. The numerical simulations for these systems verify that the proposed symbolic-based method is useful for practitioners and, according to the studied models, has a better performance than the C-C method for the choice of the time delay and embedding dimension. In addition, the method is applied to EEG data in order to study and compare some dynamic characteristics of brain activity under epileptic episodes

scholarly journals Symplectic Principal Component Analysis: A New Method for Time Series Analysis

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Min Lei ◽  
Guang Meng
Keyword(s):  
Dynamical System ◽  
Principal Component Analysis ◽  
Time Series ◽  
Symplectic Geometry ◽  
Time Series Data ◽  
Principal Component ◽  
Component Analysis ◽  
Series Data ◽  
Pca Method ◽  
Value Decomposition

Experimental data are often very complex since the underlying dynamical system may be unknown and the data may heavily be corrupted by noise. It is a crucial task to properly analyze data to get maximal information of the underlying dynamical system. This paper presents a novel principal component analysis (PCA) method based on symplectic geometry, called symplectic PCA (SPCA), to study nonlinear time series. Being nonlinear, it is different from the traditional PCA method based on linear singular value decomposition (SVD). It is thus perceived to be able to better represent nonlinear, especially chaotic data, than PCA. Using the chaotic Lorenz time series data, we show that this is indeed the case. Furthermore, we show that SPCA can conveniently reduce measurement noise.

scholarly journals Measurement of pulse transit time using ultra-wideband radar

2020 ◽  
pp. 1-10
Author(s):  
Hui-Sup Cho ◽  
Young-Jin Park
Keyword(s):  
Blood Pressure ◽  
Principal Component Analysis ◽  
Time Series ◽  
Time Delay ◽  
Transit Time ◽  
Principal Component ◽  
Pulse Transit Time ◽  
Ultra Wideband ◽  
Transit Times ◽  
Wideband Radar

BACKGROUND: The pulse transit time is an important factor that can be used to estimate the blood pressure indirectly. In many studies, pressures in the artery near and far from the heart are measured or the electrocardiogram and photoplethysmography are used to calculate the pulse transit time. In other words, the so-called contact measurements have been mainly used in these studies. OBJECTIVE: In this paper, a new method based on radar technology to measure the pulse transit time in a non-contact manner is proposed. METHODS: Radar pulses were simultaneously emitted to the chest and the wrist, and the reflected pulses were accumulated. Heartbeats were extracted by performing principal component analysis on each time series belonging to the accumulated pulses. Then, the matched heartbeat pairs were found among the heartbeats obtained from the chest and wrist and the time delay between them, i.e. the pulse transit time, was obtained. RESULTS: By comparing the pulse transit times obtained by the proposed method with those obtained by conventional methods, it is confirmed that the proposed method using the radar can be used to obtain the pulse transit time in a non-contact manner.

Spearman's Law of Diminishing Returns

2006 ◽  
Vol 27 (4) ◽  
pp. 199-207 ◽  
Author(s):  
Peter Hartmann
Keyword(s):  
Principal Axis ◽  
Age Groups ◽  
Principal Component ◽  
Longitudinal Survey ◽  
Male And Female ◽  
Two Samples ◽  
Diminishing Returns ◽  
The One ◽  
Armed Services ◽  
Principal Axis Factor

Spearman's Law of Diminishing Returns (SLODR) with regard to age was tested in two different databases from the National Longitudinal Survey of Youth. The first database consisted of 6,980 boys and girls aged 12–16 from the 1997 cohort ( NLSY 1997 ). The subjects were tested with a computer-administered adaptive format (CAT) of the Armed Services Vocational Aptitude Battery (ASVAB) consisting of 12 subtests. The second database consisted of 11,448 male and female subjects aged 15–24 from the 1979 cohort ( NLSY 1979 ). These subjects were tested with the older 10-subtest version of the ASVAB. The hypothesis was tested by dividing the sample into Young and Old age groups while keeping IQ fairly constant by a method similar to the one developed and employed by Deary et al. (1996) . The different age groups were subsequently factor-analyzed separately. The eigenvalue of the first principal component (PC1) and the first principal axis factor (PAF1), and the average intercorrelation of the subtests were used as estimates of the g saturation and compared across groups. There were no significant differences in the g saturation across age groups for any of the two samples, thereby pointing to no support for this aspect of Spearman's “Law of Diminishing Returns.”

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