Recently a new framework has been proposed to explore the dynamics of pseudoperiodic time series by constructing a complex network [Phys. Rev. Lett. 96, 238701 (2006)]. Essentially, this is a transformation from the time domain to the network domain, which allows for the dynamics of the time series to be studied via the organization of the network. In this paper, we focus on the deterministic chaotic Rössler time series and stochastic noisy periodic data that yield substantially different structures of the networks. In particular, we test an extensive range of network topology statistics, which have not be discussed in previous works, but which are capable of providing a comprehensive statistical characterization of the dynamics from different angles. Our goal is to find out how they reflect and quantify different aspects of specific dynamics, and how they can be used to distinguish different dynamical regimes. For example, we find that the joint degree distribution appears to fundamentally characterize the spatial organizations of the cycles in phase space, and this is quantified via assortativity coefficient. We applied the network statistics to the electrocardiograms of a healthy individual and an arrythmia patient. Such time series are typically pseudoperiodic, but are noisy and nonstationary and degrade traditional phase-space based methods. These time series are, however, better differentiated by our network-based statistics.

We describe a method for investigating nonlinearity in irregular fluctuations ͑short-term variability͒ of time series even if the data exhibit long-term trends ͑periodicities͒. Such situations are theoretically incompatible with the assumption of previously proposed methods. The null hypothesis addressed by our algorithm is that irregular fluctuations are generated by a stationary linear system. The method is demonstrated for numerical data generated by known systems and applied to several actual time series.

We describe a method for identifying dynamics in irregular time series ͑short term variability͒. The method we propose focuses attention on the flow of information in the data. We can apply the method even for irregular fluctuations which exhibit long term trends ͑periodicities͒: situations in which previously proposed surrogate methods would give erroneous results. The null hypothesis addressed by our algorithm is that irregular fluctuations are independently distributed random variables ͑in other words, there is no short term dynamics͒. The method is demonstrated for numerical data generated by known systems, and applied to several actual time series. There are many natural phenomena that show irregular fluctuations ͑short term variability͒. The question of whether the fluctuations are random or not is an old one and extremely important. If the fluctuations are not random, then they are due to some kind of dynamical structure and then it might be possible to build deterministic models or model systems from the time series. Clearly, such models are of immense value for both understanding and predicting the time series. To investigate whether the data can be fully described by independent and identically distributed ͑IID͒ random variables, the random-shuffle surrogate ͑RSS͒ method has been proposed ͓1͔. Although this method is effective for time series with no trends ͑periodicities͒ like that shown in Figs. 1͑a͒ and 1͑b͒, the algorithm is ineffective for data exhibing slow trends or periodicities ͓see Figs. 1͑c͒ and 1͑d͔͒. Such cases are theoretically incompatible with the assumption of the RSS method as well as other linear surrogate tests ͓1,2͔. There is currently no method which can tackle this problem. In this Communication, to investigate whether there is dynamics in data which also exhibits irregular fluctuations, we introduce such a method.The basic premise of this technique is that if irregular fluctuations are not random, then there is some kind of underlying dynamical system: whatever trending is contaminating the data. In such a case, the data index ͑order͒ itself has important implications irrespective of whether time series are linear or nonlinear. Hence, whenever the index changes, the flow of information also changes and the resultant time series no longer reflects the original dynamics. We focus our attention on this point and propose a surrogate method using this idea. The purpose of our method is to distinguish between irregular fluctuations with or without dynamics.After describing our technique, we will present our choice of discriminating statistic. Then, we will apply this algorithm to two cases using simulated time series data. One case is that data have no trend ͑this case can also be adequately addressed with the standard surrogate methods͒. The other case is that data have trends ͑this case is not consistent with existing surrogate techniques͒. In each case, the data we use are both noise free and subsequently contaminated by 10% Gaussian observational noise. Also, we apply the method t...

To build good models, we need to know the appropriate model size. To handle this problem, a variety of information criteria have already been proposed, each with a different background. In this paper, we consider the problem of model selection and investigate the performance of a number of proposed information criteria and whether the assumption to obtain the formulae that fitting errors are normally distributed hold or not in some conditions (different data points and noise levels). The results show that although the application of information criteria prevents over-fitting and under-fitting in most cases, there are cases where we cannot avoid even involving many data points and low noise levels in ideal situations. The results also show that the distribution of the fitting errors is not always normally distributed, although the observational noise is Gaussian, which contradicts an assumption of the information criteria.

This population-based study shows that, in addition to high temperature, rainfall and holidays are associated with the occurrence of trauma including motor vehicle collisions.

We describe a method for constructing networks for multivariate nonlinear time series. We approach the interaction between the various scalar time series from a deterministic dynamical system perspective and provide a generic and algorithmic test for whether the interaction between two measured time series is statistically significant. The method can be applied even when the data exhibit no obvious qualitative similarity: a situation in which the naive method utilizing the cross correlation function directly cannot correctly identify connectivity. To establish the connectivity between nodes we apply the previously proposed small-shuffle surrogate (SSS) method, which can investigate whether there are correlation structures in short-term variabilities (irregular fluctuations) between two data sets from the viewpoint of deterministic dynamical systems. The procedure to construct networks based on this idea is composed of three steps: (i) each time series is considered as a basic node of a network, (ii) the SSS method is applied to verify the connectivity between each pair of time series taken from the whole multivariate time series, and (iii) the pair of nodes is connected with an undirected edge when the null hypothesis cannot be rejected. The network constructed by the proposed method indicates the intrinsic (essential) connectivity of the elements included in the system or the underlying (assumed) system. The method is demonstrated for numerical data sets generated by known systems and applied to several experimental time series.

In this paper a different 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. Unlike other algorithms, this method properly copes with pseudoperiodic orbits contaminated with linear colored observational noise. We will demonstrate the ability of this algorithm to distinguish chaotic orbits from pseudoperiodic orbits through simulation data sets from the Rössler system. As an example of application of this algorithm, we will also employ it to investigate a human electrocardiogram record.

We describe a method for identifying correlation structures in irregular fluctuations ͑short-term variabilities͒ of multivariate time series, even if they exhibit long-term trends. This method is based on the previously proposed small shuffle surrogate method. The null hypothesis addressed by this method is that there is no short-term correlation structure among data or that the irregular fluctuations are independent. The method is demonstrated for numerical data generated by known systems and applied to several experimental time series.