Related papers: Discriminating chaotic and stochastic time series …
Can noise be beneficial to machine-learning prediction of chaotic systems? Utilizing reservoir computers as a paradigm, we find that injecting noise to the training data can induce a stochastic resonance with significant benefits to both…
The performance of a number of different measures of nonlinearity in a time series is compared numerically. Their power to distinguish noisy chaotic data from linear stochastic surrogates is determined by Monte Carlo simulation for a number…
The decomposition of a stochastic time series into three component series representing a dual signal - namely, the mean and dispersion - while isolating noise is presented. The decomposition is performed by applying machine learning…
Controlling Chaos could be a big factor in getting great stable amounts of energy out of small amounts of not necessarily stable resources. By definition, Chaos is getting huge changes in the system's output due to unpredictable small…
Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…
In this communication a new algorithm is proposed to produce surrogates for pseudoperiodic time series. By imposing a few constraints on the noise components of pseudoperiodic data sets, we devise an effective method to generate surrogates.…
Conventional predictive Artificial Neural Networks (ANNs) commonly employ deterministic weight matrices; therefore, their prediction is a point estimate. Such a deterministic nature in ANNs causes the limitations of using ANNs for medical…
We deal here with the issue of determinism versus randomness in time series. One wishes to identify their relative importance in a given time series. To this end we extend i) the use of ordinal patterns-based probability distribution…
Most of the time series in nature are a mixture of signals with deterministic and random dynamics. Thus the distinction between these two characteristics becomes important. Distinguishing between chaotic and aleatory signals is difficult…
A powerful tool is developed for the characterization of chaotic signals. The approach is based on the symbolic encoding of time series (according to their ordinal patterns) combined with the ensuing characterization of the corresponding…
We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the…
In this paper we suggest a new algorithm for determination of signal-to-noise ratio (SNR). SNR is a quantitative measure widely used in science and engineering. Generally, methods for determination of SNR are based on using of…
Many modern applications of the artificial neural networks ensue large number of layers making traditional digital implementations increasingly complex. Optical neural networks offer parallel processing at high bandwidth, but have the…
This paper investigates the use of probabilistic neural networks (PNNs) to model aleatoric uncertainty, which refers to the inherent variability in the input-output relationships of a system, often characterized by unequal variance or…
A common problem in time series analysis is to predict dynamics with only scalar or partial observations of the underlying dynamical system. For data on a smooth compact manifold, Takens theorem proves a time delayed embedding of the…
We use standard deep neural networks to classify univariate time series generated by discrete and continuous dynamical systems based on their chaotic or non-chaotic behaviour. Our approach to circumvent the lack of precise models for some…
A method is proposed to generate an optimal fit of a number of connected linear trend segments onto time-series data. To be able to efficiently handle many lines, the method employs a stochastic search procedure to determine optimal…
With the development of astronomical facilities, large-scale time series data observed by these facilities is being collected. Analyzing anomalies in these astronomical observations is crucial for uncovering potential celestial events and…
Stochastic networks are a plausible representation of the relational information among entities in dynamic systems such as living cells or social communities. While there is a rich literature in estimating a static or temporally invariant…
We develop a framework to track the structure of temporal networks with a signal processing approach. The method is based on the duality between networks and signals using a multidimensional scaling technique. This enables a study of the…