Related papers: Don't bleach chaotic data
Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be…
Causality analysis is an important problem lying at the heart of science, and is of particular importance in data science and machine learning. An endeavor during the past 16 years viewing causality as real physical notion so as to…
In this work the significance of treating a set of measurements as a time series is being explored. Time Series Analysis (TSA) techniques, part of the Exploratory Data Analysis (EDA) approach, can provide much insight regarding the…
Extracting reliable indicators of chaos from a single experimental time series is a challenging task, in particular, for systems with many degrees of freedom. The techniques available for this purpose often require unachievably long time…
A particular example of chaos can be conceived in the interaction of non-linear oscillator with a harmonic gravitational wave. When we replace the linear potential forces by the therm SIN(x), the type of solution becomes subject to external…
Avoiding aliasing in time-resolved flow data obtained through high fidelity simulations while keeping the computational and storage costs at acceptable levels is often a challenge. Well-established solutions such as increasing the sampling…
Chaotic systems that decompose into two cells connected only by a narrow channel exhibit characteristic deviations of their quantum spectral statistics from the canonical random-matrix ensembles. The equilibration between the cells…
Many practical systems can be described by dynamic networks, for which modern technique can measure their output signals, and accumulate extremely rich data. Nevertheless, the network structures producing these data are often deeply hidden…
Optical chaos is a topic of current research characterized by high-dimensional nonlinearity which is attributed to the delay-induced dynamics, high bandwidth and easy modular implementation of optical feedback. In light of these facts,…
Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…
The problem of statistical inference for open chaotic systems measured with error is complicated by the interaction of the uncertainty introduced by chaos, and the various sources of random or external variation. Here a method of…
Cross-spectral analysis is a mathematical tool for extracting the power spectral density of a correlated signal from two time series in the presence of uncorrelated interfering signals. We demonstrate and explain a set of conditions where…
The deep learning revolution has spurred a rise in advances of using AI in sciences. Within physical sciences the main focus has been on discovery of dynamical systems from observational data. Yet the reliability of learned surrogates and…
We study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum…
A signal processing method designed for the detection of linear (coherent) behaviors among random fluctuations is presented. It is dedicated to the study of data recorded from nonlinear physical systems. More precisely the method is suited…
Data quality issues have attracted widespread attention due to the negative impacts of dirty data on data mining and machine learning results. The relationship between data quality and the accuracy of results could be applied on the…
Low-order thermoacoustic models are qualitatively correct, but they are typically quantitatively inaccurate. We propose a time-domain bias-aware method to make qualitatively low--order models quantitatively (more) accurate. First, we…
Correlation matrices contain a wide variety of spatio-temporal information about a dynamical system. Predicting correlation matrices from partial time series information of a few nodes characterizes the spatio-temporal dynamics of the…
Errors are prevalent in time series data, such as GPS trajectories or sensor readings. Existing methods focus more on anomaly detection but not on repairing the detected anomalies. By simply filtering out the dirty data via anomaly…
In this research the technology of complex Markov chains is applied to predict financial time series. The main distinction of complex or high-order Markov Chains and simple first-order ones is the existing of aftereffect or memory. The…