Time series analysis complex systems

The first level of complexity corresponds to simple, low uncertainty systems, where the issue to be solved has limited scope. Single perspective and simple models would be sufficient to warrant with satisfactory descriptions of the system. Regarding water scarcity, this level corresponds, for example, to the description of precipitation using a time-series analysis or a numerical mathematical model to analyze water consumption evolution. In these cases, the information arising from the analysis may be used for more wide-reaching purposes beyond the scope of the particular researcher. 

The empirical evidence overwhelmingly supports the interpretation of the time series analysis that complex physiologic phenomena are described by fractal stochastic processes. Furthermore, the fractal nature of these time series is not constant in time but changes with the vagaries of the interaction of the system with its environment, and therefore these phenomena are multifractal. 

Chaotic behavior and synchronization in heterogeneous catalysis are closely related. Partial synchronization can lead to a complex time series, generated by superposition of several periodic oscillators, and can in some cases result in deterministically chaotic behavior. In addition to the fact that macroscopically observable oscillations exist (which demonstrates that synchronization occurs in these systems), a number of experiments show the influence of a synchronizing force on all the hierarchical levels mentioned earlier. Sheintuch (294) analyzed on a general level the problem of communication between two cells. He concluded that if the gas-phase concentration is the autocatalytic variable, then synchronization is attained in all cases. However, if the gas-phase concentration were the nonautocatalytic variable, then this would lead to symmetry breaking and the formation of spatial structures. When surface variables are the model variables, the existence of synchrony is dependent upon the size scale. Only two-variable models were analyzed, and no such strict analysis has been provided for models with two or more surface concentrations, mass balances, or heat balances. There are, however, several studies that focused on a certain system and a certain synchronization mechanism. 

Complexity is used in very different fields (dynamical systems, time series, quantum wavefunctions in disordered systems, spatial patterns, language, analysis of multielectronic systems, cellular automata, neuronal networks, self-organization, molecular or DNA analyses, social sciences, etc.) [25-27]. Although there is no general agreement about the definition of what complexity is, its quantitative characterization is a very important subject of research in nature and has received considerable attention over the past years [28,29]. 

To evaluate HRV, several measures have been proposed. These measures are roughly classifiable into time domain analysis [5], frequency domain analysis, and nonlinear and fractal analysis [5]. Time domain analysis includes tone-entropy method [6]. Nonlinear and fractal analysis include de-trended fluctuation analysis (DFA) [7]. Frequency domain analysis is based on estimation of the power spectrum of RRI series. Depending on the estimation method of power spectrum, frequency domain analysis is classified into FFT method [8], AR model method [9], maximum entropy method [10], and complex de-modulation method [11]. Akselrod et al. [3] investigated the relation between spectral component of HRV and ANS activity [12]. They classified spectral component of HRV into a high-frequency (HF) band of 0.14-0.4 Hz, a low-frequency (LF) band of 0.04-0.14 Hz, a very-low-frequency (VLF) band of 0.003-0.04 Hz, and a ultra-low-frequency (ULF) band under 0.003 Hz. They further show that LF and HF components are affected from both sympathetic and parasympathetic nervous system activity and the parasympathetic nervous system activity, respectively [12]. Furthermore, VLF and ULF components are affected by the thermoregulation system [13],... 

Artificial Neural Networks (ANNs) have been deemed successful in applications involving classification, identiflcation, pattern recognition, time series forecasting and optimisation. ANNs are distributed information-processing systems composed of many simple computational elements interacting across weighted connections. It was inspired by the architecture of the human brain. The ability of ANNs to model a complex stochastic system could be utilised in risk prediction and decision-making research, especially in areas where multi-variate statistical analysis is carried out. 

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