Using several methods for detection of causality in time series, we show in a numerical study that coupled chaotic dynamical systems violate the first principle of Granger causality that the cause precedes the effect. While such a violation can be observed in formal applications of time series analysis methods, it cannot occur in nature, due to the relation between entropy production and temporal irreversibility. The obtained knowledge, however, can help to understand the type of causal relations observed in experimental data, namely, it can help to distinguish linear transfer of time-delayed signals from nonlinear interactions. We illustrate these findings in causality detected in experimental time series from the climate system and mammalian cardio-respiratory interactions.

In this comparative study, six causality detection methods were compared, namely, the Granger vector autoregressive test, the extended Granger test, the kernel version of the Granger test, the conditional mutual information (transfer entropy), the evaluation of cross mappings between state spaces, and an assessment of predictability improvement due to the use of mixed predictions. Seven test data sets were analyzed: linear coupling of autoregressive models, a unidirectional connection of two Hénon systems, a unidirectional connection of chaotic systems of Rössler and Lorenz type and of two different Rössler systems, an example of bidirectionally connected two-species systems, a fishery model as an example of two correlated observables without a causal relationship, and an example of mediated causality. We tested not only 20000 points long clean time series but also noisy and short variants of the data. The standard and the extended Granger tests worked only for the autoregressive models. The remaining methods were more successful with the more complex test examples, although they differed considerably in their capability to reveal the presence and the direction of coupling and to distinguish causality from mere correlation.

In this study, the information flow time arrow is investigated for stochastic data defined by vector autoregressive models. The time series are analyzed forward and backward by different Granger causality detection methods. Besides the normal distribution, which is usually required for the validity of Granger causality analysis, several other distributions of predictive errors are considered. A clear effect of a change in the order of cause and effect on the time-reversed series of unidirectionally connected variables was detected with standard Granger causality test (GC), when the product of the connection strength and the ratio of the predictive errors of the driver and the recipient was below a certain level, otherwise bidirectional causal connection was detected. On the other hand, opposite causal link was detected unconditionally by the methods based on the time reversal testing, but they were not able to detect correct bidirectional connection. The usefulness of the backward analysis is manifested in cases where falsely detected unidirectional connections can be rejected by applying the result obtained after the time reversal, and in cases of uncorrelated causally independent variables, where the absence of a causal link detected by GC on the original series should be confirmed on the time-reversed series.

Objective. The aim of this study was to validate a survival analysis assessing the effect of type of rotary system, canal curvature, and instrument size on cyclic resistance.Materials and Methods. Cyclic fatigue testing was carried out in stainless steel artificial canals with radii of curvature of 3 or 5 mm and the angle of curvature of 60 degrees. All the instruments were new and 25 mm in working length, and ISO colour coding indicated the instrument size (yellow for size 20; red for size 25).Wizard Navigatorinstruments,Mtwoinstruments,ProTaperinstruments, andRevo-Sinstruments were passively rotated at 250 rotations per minute, and the time fracture was being recorded. Subsequently, fractographic analysis of broken tips was performed by scanning electron microscope. The data were then analysed by the Kaplan-Meier estimator of the survival function, the Cox proportional hazards model, the Wald test for regression covariates, and the Wald test for significance of regression model.Conclusion. The lifespan registered for the tested instruments wasMtwo>Wizard Navigator>Revo-S>ProTaper; 5 mm radius > 3 mm radius; and yellow > red in ISO colour coding system.

Human body movement has been under continuous research for many years due to its potential application as a novel biometric system to identify individuals. It is possible to utilize various techniques, not only to obtain requested movement data, but also to analyse movement data. This paper uses functional data analysis on data obtained from 12 volunteers and uses 20 markers from the 3D motion capture system VICON MX T020. The functional data analysis was chosen as a suitable tool to obtain more information about an individual's movement because it uses a technique for real-time data, which corresponds to continuous time process. The results show that all markers, under any walking speed and condition, identify a significantly high percentage of individual pairs. Further, our results discriminate between markers, where some markers are highly dependent on walking speed and condition, and also on the influence of body part asymmetry. In addition, regular movement patterns in almost all participants' data shows a potential to identify individuals based on gait recognition with a 1:1 matching result.

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In this paper we present an exact likelihood ratio test (LRT) for testing the simple null hypothesis on all parameters of the linear regression model with normally distributed errors. In particular, we consider the simultaneous test for the regression parameters, β, and the error standard deviation, σ. The critical values of the LRT are presented for small sample sizes and a small number of explanatory variables for usual significance levels, α = 0.1, 0.05, and 0.01. The test is directly applicable for construction of the (1 − α)-confidence region for the parameters (β, σ) and the simultaneous tolerance intervals for future observations in linear regression models. For comparison, the suggested method for construction of the tolerance factors of the symmetric (1 − γ)-content simultaneous (1 − α)-tolerance intervals is illustrated by a simple numerical example.

In the paper titled "Survival Analysis of Factors Influencing Cyclic Fatigue of Nickel-Titanium Endodontic Instruments" [1], there was missing the second affiliation of (Martina Chvosteková) and is corrected above and there was an error in "Acknowledgments," which should be corrected as follows.