scholarly journals Phase Space Reconstruction from a Biological Time Series: A Photoplethysmographic Signal Case Study

2020 ◽  
Vol 10 (4) ◽  
pp. 1430
Author(s):  
Javier de Pedro-Carracedo ◽  
David Fuentes-Jimenez ◽  
Ana María Ugena ◽  
Ana Pilar Gonzalez-Marcos
Keyword(s):  
Time Series ◽  
Phase Space ◽  
State Space ◽  
The State ◽  
Time Interval ◽  
Physiological System ◽  
Dynamic Complexity ◽  
Biological Time ◽  
Correct Determination

In the analysis of biological time series, the state space is comprised of a framework for the study of systems with presumably deterministic and stationary properties. However, a physiological experiment typically captures an observable that characterizes the temporal response of the physiological system under study; the dynamic variables that make up the state of the system at any time are not available. Only from the acquired observations should state vectors be reconstructed to emulate the different states of the underlying system. This is what is known as the reconstruction of the state space, called the phase space in real-world signals, in many cases satisfactorily resolved using the method of delays. Each state vector consists of m components, extracted from successive observations delayed a time τ . The morphology of the geometric structure described by the state vectors, as well as their properties depends on the chosen parameters τ and m. The real dynamics of the system under study is subject to the correct determination of the parameters τ and m. Only in this way can be deduced features have true physical meaning, revealing aspects that reliably identify the dynamic complexity of the physiological system. The biological signal presented in this work, as a case study, is the photoplethysmographic (PPG) signal. We find that m is five for all the subjects analyzed and that τ depends on the time interval in which it is evaluated. The Hénon map and the Lorenz flow are used to facilitate a more intuitive understanding of the applied techniques.

scholarly journals Chaotic Patterns in Aeroelastic Signals

2009 ◽  
Vol 2009 ◽  
pp. 1-19 ◽  
Author(s):  
F. D. Marques ◽  
R. M. G. Vasconcellos
Keyword(s):  
Time Series ◽  
State Space ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Separated Flow ◽  
Direct Analysis ◽  
Surrogate Data ◽  
The State ◽  
Aeroelastic System ◽  
Value Decomposition

This work presents the analysis of nonlinear aeroelastic time series from wing vibrations due to airflow separation during wind tunnel experiments. Surrogate data method is used to justify the application of nonlinear time series analysis to the aeroelastic system, after rejecting the chance for nonstationarity. The singular value decomposition (SVD) approach is used to reconstruct the state space, reducing noise from the aeroelastic time series. Direct analysis of reconstructed trajectories in the state space and the determination of Poincaré sections have been employed to investigate complex dynamics and chaotic patterns. With the reconstructed state spaces, qualitative analyses may be done, and the attractors evolutions with parametric variation are presented. Overall results reveal complex system dynamics associated with highly separated flow effects together with nonlinear coupling between aeroelastic modes. Bifurcations to the nonlinear aeroelastic system are observed for two investigations, that is, considering oscillations-induced aeroelastic evolutions with varying freestream speed, and aeroelastic evolutions at constant freestream speed and varying oscillations. Finally, Lyapunov exponent calculation is proceeded in order to infer on chaotic behavior. Poincaré mappings also suggest bifurcations and chaos, reinforced by the attainment of maximum positive Lyapunov exponents.

A State Space Method for Optimal Design of Vibration Isolators

1979 ◽  
Vol 101 (2) ◽  
pp. 309-314 ◽  
Author(s):  
M. H. Hsiao ◽  
E. J. Haug ◽  
J. S. Arora
Keyword(s):  
Nonlinear Programming ◽  
Optimal Design ◽  
State Space ◽  
The State ◽  
Programming Approach ◽  
Time Interval ◽  
Numerical Comparison ◽  
State Space Method ◽  
Continuous State ◽  
Space Method

A state space method of optimal design of dynamic systems subjected to transient loads is developed and applied. In contrast to the conventional nonlinear programming approach of discretizing the time interval and constructing a high dimension nonlinear programming problem, a state space approach is employed which develops the sensitivity analysis and optimization algorithm in continuous state space, resorting to discretization only for efficient numerical integration of differential equations. A numerical comparison of the state space and conventional nonlinear programming methods is carried out for two test problems, in which the state space method requires only one-tenth the computing time reported for the nonlinear programming approach.

scholarly journals Behavior of Attractors During Surge in Centrifugal Compression System

1998 ◽  
Author(s):  
A. Mutou ◽  
S. Mizuki ◽  
Y. Komatsubara ◽  
H. Tsujita
Keyword(s):  
Time Series ◽  
State Space ◽  
System Analysis ◽  
Spline Interpolation ◽  
Finite Difference Methods ◽  
The State ◽  
Least Square ◽  
Band Pass Filter ◽  
Pass Filter ◽  
Compression System

A dynamical system analysis method is presented, that permits the characterization of unsteady phenomena in a centrifugal compression system. The method maps one experimental time series of data into a state space in which behaviors of the compression system should be represented, and reconstructs an attractor that geometrically characterizes a state of the compression system. The time series of data were obtained by using a high response pressure transducer and an analog to digital converter at surge condition. For the reconstruction of attractors, a noise free differentiation method in time was employed. The differentiation was made by high order finite difference methods. To remove the influence of noise, the data were passed through a filter using a third order spline interpolation. In this study, the dimension of the state space was restricted to three. The measured data itself and their first and second derivatives in time are used to represent an attractor in the state space. The modeling of the system behavior from the time series of data by second order ordinary differential equations was attempted. It is assumed that the data and their derivatives satisfy the equations at each time. Then, appropriate coefficients are determined by a least square method. The reconstructed attractor showed complex cyclic trajectories at a first glance. However, by applying a band pass filter to the original signal, it was found that the attractor consisted of three independent wave forms and formed an attractor with torus-like behavior. In contrast, the solution by the modeled equations showed a type of limit cycle.

scholarly journals Unobserved Components Model for Forecasting Sugarcane Yield in Haryana

2019 ◽  
Vol 11 (3) ◽  
pp. 661-665 ◽  
Author(s):  
Ekta Hooda ◽  
Urmil Verma
Keyword(s):  
Time Series ◽  
State Space ◽  
The State ◽  
State Space Models ◽  
Stationary Time Series ◽  
Component Model ◽  
Series Data ◽  
Unobserved Component ◽  
Sugarcane Yield ◽  
Unobserved Component Model

Unlike classical regression analysis, the state space models have time-dependent parameters and provide a flexible class of dynamic and structural time series models. The unobserved component model (UCM) is a special type of state space models widely used to analyze and forecast time series. The present investigation has been carried out to study the trend of sugarcane(gur) yield in five districts (Ambala, Karnal, Panipat, Yamunanagar and Kurukshetra) of Haryana state using the unobserved component models with level, trend and irregular components. For this purpose, the time series data on sugarcane yield from 1966-67 to 2016-17 of Ambala and Karnal, 1971-72 to 2016-17 of Kurukshetra and 1980-81 to 2016-17 of Panipat and Yamunanagar districts have been used.   For all the districts, the irregular component was found to be highly significant (p=0.01) while both level and trend component variances were observed non-significant. Significance analysis of the individual component(s) has also been performed for possible dropping of the level and trend components by setting their variances equal to zero. The state space models may be effectively used pertaining to Indian agriculture data, as it takes into account the time dependency of the underlying parameters which may further enhance the predictive accuracy of the most popularly used ARIMA models with parameter constancy. Moreover, the unobserved component model is capable of handling both stationary as well as non-stationary time series and thus found more suitable for sugarcane yield modeling which is a trended yield (i.e. non-stationary in nature).

scholarly journals Modelling and forecasting of potato sales prices in Ukraine

2021 ◽  
Vol 7 (4) ◽  
pp. 160-179
Author(s):  
Inna Koblianska ◽  
Larysa Kalachevska ◽  
Stanisław Minta ◽  
Nataliia Strochenko ◽  
Svitlana Lukash
Keyword(s):  
Time Series ◽  
State Space ◽  
Security Policy ◽  
Exponential Smoothing ◽  
Food Prices ◽  
Information Criteria ◽  
The State ◽  
Agricultural Enterprises ◽  
Use Of Resources ◽  
Modelling And Forecasting

Purpose. Under the background of the climate change and other crises, the world food system is becoming increasingly vulnerable to price fluctuations. This highlights the need to consider and better manage the risks associated with price volatility in accordance with the principles of a market economy and simultaneously protecting the most vulnerable groups of population. Responding to these challenges, in this study we aim to determine the main parameters of time series of potato sales prices in agricultural enterprises in Ukraine, to build an appropriate model, and to form a short-term (one-year) forecast. Methodology / approach. We used in the research the data from the State Statistics Service of Ukraine on average monthly sales prices of potatoes in agricultural enterprises from December 2012 to July 2021 (104 observations) adjusted for the price index of crop products sold by enterprises for the month (with December 2012 base period). Decomposition was used to determine the characteristics of the time series; exponential smoothing methods (Holt-Winters and State Space Framework – ETS) and autoregressive-moving average were used to find the model that fits the actual data the best and has high prognostic quality. We applied the Rstudio forecast package to model and to forecast the time series. Results. The time series of potato sales prices in enterprises is characterized by seasonality (mainly related to seasonal production) with the lowest prices in November, and the highest – in June; although, other periods of price growth were identified during the year: in January and April. The ARMA (2, 2) (1,0)12 with a non-zero mean was found to be the best model for forecasting potatoes sales prices. ARMA (2, 2) (1,0)12, compared to the state-space exponential smoothing model with additive errors – ETS (A), better fits the observed data and provides more accurate forecasting model (with lower errors). Forecast made with ARMA (2, 2) (1,0)12 shows that potato sale prices in agricultural enterprises in November 2021 (months with the lowest price) will range from 2154.76 UAH/t to 7414.57 UAH/t, in June 2022 – from 3016.72 UAH/t to 14051.63 UAH/t (prices of July 2021) with a probability of 95%. The forecast’s mean absolute percentage error is 14.87%. Originality / scientific novelty. This research deepens the methodological basis for food prices modelling and forecasting, thus contributing to the agricultural economics science development. The obtained results confirm the previous research findings on the better quality of food prices forecasts made with autoregressive models (for univariate time series) compared with exponential smoothing. Additionally, the study reveals advantages of the state space framework for exponential smoothing (ETS) compared to Holt-Winters methods in case of time series with seasonality: although the ETS model overlaps with the observed (train) data, it is better in terms of information criteria and forecasting (for the test data). Practical value / implications. The obtained results can serve as an information basis for decision-making on potato production and sales by producers, on more efficient use of resources by the population, on more effective measures to support industrial potato growing, to implement social programs and food security policy by the government.

scholarly journals Strict deformation quantization of the state space of Mk(ℂ) with applications to the Curie–Weiss model

2020 ◽  
Vol 32 (10) ◽  
pp. 2050031 ◽  
Author(s):  
Klaas Landsman ◽  
Valter Moretti ◽  
Christiaan J. F. van de Ven
Keyword(s):  
Phase Space ◽  
State Space ◽  
Deformation Quantization ◽  
Classical Limit ◽  
Poisson Manifold ◽  
Quantum Spin ◽  
The State ◽  
Symmetric Convex ◽  
Algebraic Vector ◽  
Classical Phase Space

Increasing tensor powers of the [Formula: see text] matrices [Formula: see text] are known to give rise to a continuous bundle of [Formula: see text]-algebras over [Formula: see text] with fibers [Formula: see text] and [Formula: see text], where [Formula: see text], the state space of [Formula: see text], which is canonically a compact Poisson manifold (with stratified boundary). Our first result is the existence of a strict deformation quantization of [Formula: see text] à la Rieffel, defined by perfectly natural quantization maps [Formula: see text] (where [Formula: see text] is an equally natural dense Poisson subalgebra of [Formula: see text]). We apply this quantization formalism to the Curie–Weiss model (an exemplary quantum spin with long-range forces) in the parameter domain where its [Formula: see text] symmetry is spontaneously broken in the thermodynamic limit [Formula: see text]. If this limit is taken with respect to the macroscopic observables of the model (as opposed to the quasi-local observables), it yields a classical theory with phase space [Formula: see text] (i.e. the unit three-ball in [Formula: see text]). Our quantization map then enables us to take the classical limit of the sequence of (unique) algebraic vector states induced by the ground state eigenvectors [Formula: see text] of this model as [Formula: see text], in which the sequence converges to a probability measure [Formula: see text] on the associated classical phase space [Formula: see text]. This measure is a symmetric convex sum of two Dirac measures related by the underlying [Formula: see text]-symmetry of the model, and as such the classical limit exhibits spontaneous symmetry breaking, too. Our proof of convergence is heavily based on Perelomov-style coherent spin states and at some stage it relies on (quite strong) numerical evidence. Hence the proof is not completely analytic, but somewhat hybrid.

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