We investigate a generalised version of the recently proposed ordinal partition time series to network transformation algorithm. First, we introduce fixed lag for elements each that is selected using techniques from traditional delay embedding. The resulting partitions define regions in embedding phase space are mapped nodes space. Edges allocated between based on temporal succession thus creating Markov chain representation series. then apply this new algorithm generated by Rössler system...

The East Asian-Indonesian-Australian summer monsoon (EAIASM) links the Earth's hemispheres and provides a heat source that drives global circulation. At seasonal inter-seasonal timescales, of one hemisphere is linked via outflows from winter opposing hemisphere. Long-term phase relationships between Asian (EASM) Indonesian-Australian (IASM) are poorly understood, raising questions long-term adjustments to future greenhouse-triggered climate change whether these changes could 'lock in'...

Delay embedding methods are a staple tool in the field of time series analysis and prediction. However, selection parameters can have big impact on resulting analysis. This has led to creation large number optimise such as lag. paper aims provide comprehensive overview fundamentals theory for readers who new subject. We outline collection existing selecting lag both uniform non-uniform delay cases. Highlighting poor dynamical explainability lags, we an alternative method lags that includes...

In this study, we propose a new information theoretic measure to quantify the complexity of biological systems based on time-series data. We demonstrate potential our method using two distinct applications human cardiac dynamics. Firstly, show that clearly discriminates between segments electrocardiogram records characterized by normal sinus rhythm, ventricular tachycardia and fibrillation. Secondly, investigate multiscale dynamics with respect age in healthy individuals interbeat interval...

Forecasting complex systems is important for understanding and predicting phenomena. Due to the complexity error sensitivity inherent in these predictive models, forecasting proves challenging. This paper presents a novel approach assimilate system observations into models. The makes use of recursive partitioning algorithm facilitate computation local sets model corrections as well provide data structure traverse space. These act sample from piecewise stochastic process. Appending...

Recently proposed ordinal networks not only afford novel methods of nonlinear time series analysis but also constitute stochastic approximations the deterministic flow from which network models are constructed. In this paper, we construct discrete sampled continuous chaotic and then regenerate new by taking random walks on network. We investigate extent to dynamics original encoded in retained through process regenerating using several distinct quantitative approaches. First, use recurrence...

It has been established that the count of ordinal patterns, which do not occur in a time series, called forbidden is an effective measure for detection determinism noisy data. A very recent study shown this also partially robust against effects irregular sampling. In paper, we extend said research with emphasis on exploring parameter space method's sole parameter—the length patterns—and find more to under-sampling and sampling than previously reported. Using numerically generated data from...

We are motivated by real-world data that exhibit severe sampling irregularities such as geological or paleoclimate measurements. Counting forbidden patterns has been shown to be a powerful tool towards the detection of determinism in noisy time series. They constitute set ordinal symbolic cannot realised series generated deterministic systems. The reliability estimator relative count from irregularly sampled explored two recent studies. In this paper, we explore highly irregular frequency...

Mapping time series to complex networks analyze observables has recently become popular, both at the theoretical and practitioner's level. The intent is use network metrics characterize dynamics of underlying system. Applications cover a wide range problems, from geoscientific measurements biomedical data financial series. It been observed that different can produce with distinct topological characteristics under variety time-series-to-network transforms have proposed in literature. direct...

Consistency is an extension to generalized synchronization which quantifies the degree of functional dependency a driven nonlinear system its input. We apply this concept echo-state networks, are artificial-neural network version reservoir computing. Through replica test we measure consistency levels high-dimensional response, yielding comprehensive portrait property.

Irregular sampling of data sets is one the challenges often encountered in time-series analysis, since traditional methods cannot be applied and frequently used interpolation approach can corrupt bias subsequence analysis. Here we present TrAnsformation-Cost Time-Series (TACTS) method, which allows us to analyze irregularly sampled without degenerating quality set. Instead using consider segments determine how close they are each other by determining cost needed transform segment into...

Preferential attachment, by which new nodes attach to existing with probability proportional the nodes' degree, has become standard growth model for scale-free networks, where asymptotic of a node having degree k is k^{-γ}. However, motivation this entirely ad hoc. We use exact likelihood arguments and show that optimal way build network most links low degree. Curiously, leads single dominant hub: starlike structure we call superstar network. Asymptotically, strategy each one...

Significance Science and engineering have benefited greatly from the ability of finite element methods (FEMs) to simulate nonlinear, time-dependent complex systems. The recent advent extensive data collection such systems now raises question how systematically incorporate these into models, consistently updating solution in face mathematical model misspecification with physical reality. This article describes general widely applicable methodology for coherent synthesis FEM providing a...

Sequential Bayesian filters, such as particle are often presented an ideal means of tracking the state nonlinear systems. Here shadowing filters demonstrated to perform better than sequential at under specific circumstances. The success is attributed avoiding both well-known deficiencies and some newly identified problems.

Statistical learning additions to physically derived mathematical models are gaining traction in the literature. A recent approach has been augment underlying physics of governing equations with data driven Bayesian statistical methodology. Coined statFEM, method acknowledges a priori model misspecification, by embedding stochastic forcing within equations. Upon receipt additional data, posterior distribution discretised finite element solution is updated using classical filtering...

Methods developed recently to obtain stochastic models of low-dimensional chaotic systems are tested in electronic circuit experiments. We demonstrate that reliable drift and diffusion coefficients can be obtained even when no excessive time scale separation occurs. Crisis induced intermittent motion described terms a model showing tunneling which is dominated by state space dependent diffusion. Analytical solutions the corresponding Fokker-Planck equation excellent agreement with experimental data.

Natural and man-made networks often possess locally treelike substructures. Taking such tree as our starting point, we show how the addition of links changes synchronization properties network. We focus on two different methods link addition. The first method adds single that create cycles a well-defined length. Following topological approach, introduce varying length analyze this feature, well position in network, alters synchronous behavior. particular short can lead to maximum change...

The concept of scale-free networks has been widely applied across natural and physical sciences. Many claims are made about the properties these networks, even though is often vaguely defined. We present tools procedures to analyse statistical defined by arbitrary degree distributions other constraints. Doing so reveals highly likely properties, some unrecognised richness, casts doubt on previously claimed being due a characteristic.

Positioning and tracking a moving target from limited positional information is frequently-encountered problem. For given noisy observations of the target's position, one wants to estimate true trajectory reconstruct full phase space including velocity acceleration. The shadowing filter offers robust methodology achieve such an estimation reconstruction. Here, we highlight validate important merits this for real-life applications. In particular, explore filter's performance when dealing with...

Non-recurrent congestion disrupts normal traffic operations and lowers travel time (TT) reliability, which leads to many negative consequences such as difficulties in trip planning, missed appointments, loss productivity, driver frustration. Traffic incidents are one of the six causes non-recurrent congestion. Early accurate detection helps reduce incident duration, but it remains a challenge due limitation current sensor technologies. In this paper, we employ recurrence-based technique,...