scholarly journals Synchronization Measure Based on a Geometric Approach to Attractor Embedding Using Finite Observation Windows

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Inga Timofejeva ◽  
Kristina Poskuviene ◽  
Maosen Cao ◽  
Minvydas Ragulskis
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Time Delays ◽  
Geometric Approach ◽  
Optimal Time ◽  
Effective Algorithm ◽  
Geometrical Properties ◽  
Finite Observation

A simple and effective algorithm for the identification of optimal time delays based on the geometrical properties of the embedded attractor is presented in this paper. A time series synchronization measure based on optimal time delays is derived. The approach is based on the comparison of optimal time delay sequences that are computed for segments of the considered time series. The proposed technique is validated using coupled chaotic Rössler systems.

scholarly journals Extracting Low-Dimensional Latent Structure from Time Series in the Presence of Delays

2015 ◽  
Vol 27 (9) ◽  
pp. 1825-1856 ◽  
Author(s):  
Karthik C. Lakshmanan ◽  
Patrick T. Sadtler ◽  
Elizabeth C. Tyler-Kabara ◽  
Aaron P. Batista ◽  
Byron M. Yu
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Motor Cortex ◽  
Dimensionality Reduction ◽  
Gaussian Process ◽  
Latent Variables ◽  
Time Delays ◽  
High Dimensional ◽  
Latent Space ◽  
Low Dimensional

Noisy, high-dimensional time series observations can often be described by a set of low-dimensional latent variables. Commonly used methods to extract these latent variables typically assume instantaneous relationships between the latent and observed variables. In many physical systems, changes in the latent variables manifest as changes in the observed variables after time delays. Techniques that do not account for these delays can recover a larger number of latent variables than are present in the system, thereby making the latent representation more difficult to interpret. In this work, we introduce a novel probabilistic technique, time-delay gaussian-process factor analysis (TD-GPFA), that performs dimensionality reduction in the presence of a different time delay between each pair of latent and observed variables. We demonstrate how using a gaussian process to model the evolution of each latent variable allows us to tractably learn these delays over a continuous domain. Additionally, we show how TD-GPFA combines temporal smoothing and dimensionality reduction into a common probabilistic framework. We present an expectation/conditional maximization either (ECME) algorithm to learn the model parameters. Our simulations demonstrate that when time delays are present, TD-GPFA is able to correctly identify these delays and recover the latent space. We then applied TD-GPFA to the activity of tens of neurons recorded simultaneously in the macaque motor cortex during a reaching task. TD-GPFA is able to better describe the neural activity using a more parsimonious latent space than GPFA, a method that has been used to interpret motor cortex data but does not account for time delays. More broadly, TD-GPFA can help to unravel the mechanisms underlying high-dimensional time series data by taking into account physical delays in the system.

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 An ensemble approach based on transformation functions for natural gas price forecasting considering optimal time delays

2021 ◽  
Vol 7 ◽  
pp. e409
Author(s):  
Faramarz Saghi ◽  
Mustafa Jahangoshai Rezaee
Keyword(s):  
Time Series ◽  
Natural Gas ◽  
Time Delays ◽  
Wavelet Decomposition ◽  
Vital Role ◽  
Optimal Time ◽  
Price Forecasting ◽  
Fuzzy Transform ◽  
Economic Sectors ◽  
Gas Price

Natural gas, known as the cleanest fossil fuel, plays a vital role in the economies of producing and consuming countries. Understanding and tracking the drivers of natural gas prices are of significant interest to the many economic sectors. Hence, accurately forecasting the price is very important not only for providing an effective factor for implementing energy policy but also for playing an extremely significant role in government strategic planning. The purpose of this study is to provide an approach to forecast the natural gas price. First, optimal time delays are identified by a new approach based on the Euclidean Distance between input and target vectors. Then, wavelet decomposition has been implemented to reduce noise. Moreover, fuzzy transform with different membership functions has been used for modeling uncertainty in time series. The wavelet decomposition and fuzzy transform have been integrated into the preprocessing stage. An ensemble method is used for integrating the outputs of various neural networks. The results depict that the proposed preprocessing methods used in this paper cause to improve the accuracy of natural gas price forecasting and consider uncertainty in time series.

scholarly journals Optimal State Space Reconstruction via Monte Carlo Decision Tree Search

2021 ◽  
Author(s):  
Kai Hauke Kraemer ◽  
Maximilian Gelbrecht ◽  
Induja Pavithran ◽  
R.I. Sujith ◽  
Norbert Marwan
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Time Delay ◽  
Objective Function ◽  
State Space ◽  
Multivariate Time Series ◽  
Forecast Accuracy ◽  
Recurrence Plot ◽  
Optimal Time ◽  
State Space Reconstruction

Abstract A novel idea for an optimal time delay state space reconstruction from uni- and multivariate time series is presented. The entire embedding process is considered as a game, in which each move corresponds to an embedding cycle and is subject to an evaluation through an objective function. This way the embedding procedure can be modeled as a tree, in which each leaf holds a specific value of the objective function. By using a Monte Carlo ansatz the proposed algorithm populates the tree with many leafs by computing different possible embedding paths and the final embedding is chosen as that particular path, which ends at the leaf with the lowest achieved value of the objective function. The method aims to prevent getting stuck in a local minimum of the objective function and can be used in a modular way, enabling practitioners to choose a statistic for possible delays in each embedding cycle as well as a suitable objective function themselves. As a proof of concept, we demonstrate the superiority of the proposed method over the classical time delay embedding methods using a variety of application examples. We compare recurrence plot based statistics inferred from reconstructions of a Lorenz-96 system and highlight an improved forecast accuracy for map-like model data as well as for paleoclimate isotope time series. Finally we utilize state space reconstruction for the detection of causality and its strength between observables of a gas turbine type thermoacoustic combustor.

Construct Validity

2017 ◽  
Author(s):  
Richard McCleary ◽  
David McDowall ◽  
Bradley J. Bartos
Keyword(s):  
Time Series ◽  
Construct Validity ◽  
Hypothesis Test ◽  
Secondary Data ◽  
Time Frame ◽  
Primary Data ◽  
Optimal Time ◽  
Intervention Model ◽  
Right Hand ◽  
The Right

Chapter 8 focuses on threats to construct validity arising from the left-hand side time series and the right-hand side intervention model. Construct validity is limited to questions of whether an observed effect can be generalized to alternative cause and effect measures. The “talking out” self-injurious behavior time series, shown in Chapter 5, are examples of primary data. Researchers often have no choice but to use secondary data that were collected by third parties for purposes unrelated to any hypothesis test. Even in those less-than-ideal instances, however, an optimal time series can be constructed by limiting the time frame and otherwise paying attention to regime changes. Threats to construct validity that arise from the right-hand side intervention model, such as fuzzy or unclear onset and responses, are controlled by paying close attention to the underlying theory. Even a minimal theory should specify the onset and duration of an impact.

scholarly journals Delay-Dependent Robust Stabilization for Nonlinear Large Systems via Decentralized Fuzzy Control

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Chun-xia Dou ◽  
Zhi-sheng Duan ◽  
Xing-bei Jia ◽  
Xiao-gang Li ◽  
Jin-zhao Yang ◽  
...  
Keyword(s):  
Time Delay ◽  
Fuzzy Control ◽  
Upper Bound ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Large System ◽  
Disturbance Attenuation ◽  
Robust Controller ◽  
Large Systems ◽  
Delay Dependent

A delay-dependent robust fuzzy control approach is developed for a class of nonlinear uncertain interconnected time delay large systems in this paper. First, an equivalent T–S fuzzy model is extended in order to accurately represent nonlinear dynamics of the large system. Then, a decentralized state feedback robust controller is proposed to guarantee system stabilization with a prescribedH∞disturbance attenuation level. Furthermore, taking into account the time delays in large system, based on a less conservative delay-dependent Lyapunov function approach combining with linear matrix inequalities (LMI) technique, some sufficient conditions for the existence ofH∞robust controller are presented in terms of LMI dependent on the upper bound of time delays. The upper bound of time-delay and minimizedH∞performance index can be obtained by using convex optimization such that the system can be stabilized and for all time delays whose sizes are not larger than the bound. Finally, the effectiveness of the proposed controller is demonstrated through simulation example.

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