Appropriateness of gait analysis for biometrics: Initial study using FDA method

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. © 2017 Elsevier LtdIGA grant at Tomas Bata University in Zlin [IGA/FAI/2013/001]; European Regional Development Fund under the project CEBIA-Tech [CZ.1.05/2.1.00/03.0089]; Grant Agency of the Czech Republic [GA15-06991S]; Scientific Grant Agency of the Ministry of Education of the Slovak Republic; Slovak Academy of Sciences [VEGA 2/0011/16]; Slovak Research and Development Agency [APVV-15-0295

Survival analysis of factors influencing cyclic fatigue of nickel-titanium endodontic instruments

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 Navigator instruments, Mtwo instruments, ProTaper instruments, and Revo-S instruments 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 was Mtwo > Wizard Navigator > Revo-S > ProTaper; 5 mm radius > 3 mm radius; and yellow > red in ISO colour coding system.Ministry of Education, Youth and Sports of the Czech Republic [CZ.1.07/2.3.00/20.0170, CZ.1.07/2.3.00/30.0041

Multiple Use Confidence Intervals for a Univariate Statistical Calibration

The statistical calibration problem treated here consists of constructing the interval estimates for future unobserved values of a univariate explanatory variable corresponding to an unlimited number of future observations of a univariate response variable. An interval estimate is to be computed for a value x of an explanatory variable after observing a response Yx by using the same calibration data from a single calibration experiment, and it is called the multiple use confidence interval. It is assumed that the normally distributed response variable Yx is related to the explanatory variable x through a linear regression model, a polynomial regression is probably the most frequently used model in industrial applications. Construction of multiple use confidence intervals (MUCI’s) by inverting the tolerance band for a linear regression has been considered by many authors, but the resultant MUCI’s are conservative. A new method for determining MUCI’s is suggested straightforward from their marginal property assuming a distribution of the explanatory variable. Using simulations, we show that the suggested MUCI’s satisfy the coverage probability requirements of MUCI’s quite well and they are narrower than previously published. The practical implementation of the proposed MUCI’s is illustrated in detail on an example

Two-sided Tolerance Intervals in a Simple Linear Regression

summary:Numerical results for a simple linear regression indicate that the non-simultaneous two-sided tolerance intervals nearly satisfy the condition of multiple-use confidence intervals, see Lee and Mathew (2002), but the numerical computation of the limits of the multiple-use confidence intervals is needed. We modified the Lieberman–Miller method (1963) for computing the simultaneous two-sided tolerance intervals in a simple linear regression with independent normally distributed errors. The suggested tolerance intervals are the narrowest of all the known simultaneous two-sided tolerance intervals. The computation of the multiple-use confidence intervals based on the new simultaneous two-sided tolerance intervals is simple and fast

Granger Causality on forward and Reversed Time Series

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

Optimization of Parameters in the Menzerath–Altmann Law, II

summary:The paper continues our studies released under the same title [Andres, J., Kubáček, L., Machalová, J., Tučková, M.: Optimization of parameters in the Menzerath–Altmann law Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 51, 1 (2012), 5–27.]. As the main result justifying the conclusions in [Andres, J., Kubáček, L., Machalová, J., Tučková, M.: Optimization of parameters in the Menzerath–Altmann law Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 51, 1 (2012), 5–27.], the theorem is presented enunciating that the English original of Poe’s celebrated poem Raven is a language fractal only w.r.t. the application of the simplest truncated formulas of the Menzerath–Altmann law, but not w.r.t. other applied formulas under our consideration. Moreover, the related degree of semanticity is calculated in these cases, including the naive intervals of such a degree. A suitability of the applied formulas is discussed from the point of view of a verbal version of the Menzerath–Altmann law (i.e. the tendency of the approximating functions is to be decreasing) and by means of quantitative criteria characterizing the accuracy of fitted data. Our discussion extends the traditional approaches to the Menzerath–Altmann law

Against the Flow of Time with Multi-Output Models

Recent work has paid close attention to the first principle of Granger causality, according to which cause precedes effect. In this context, the question may arise whether the detected direction of causality also reverses after the time reversal of unidirectionally coupled data. Recently, it has been shown that for unidirectionally causally connected autoregressive (AR) processes X → Y, after time reversal of data, the opposite causal direction Y → X is indeed detected, although typically as part of the bidirectional X ↔ Y link. As we argue here, the answer is different when the measured data are not from AR processes but from linked deterministic systems. When the goal is the usual forward data analysis, cross-mapping-like approaches correctly detect X → Y, while Granger causality-like approaches, which should not be used for deterministic time series, detect causal independence X ⫫ Y . The results of backward causal analysis depend on the predictability of the reversed data. Unlike AR processes, observables from deterministic dynamical systems, even complex nonlinear ones, can be predicted well forward, while backward predictions can be difficult (notably when the time reversal of a function leads to one-to-many relations). To address this problem, we propose an approach based on models that provide multiple candidate predictions for the target, combined with a loss function that consideres only the best candidate. The resulting good forward and backward predictability supports the view that unidirectionally causally linked deterministic dynamical systems X → Y can be expected to detect the same link both before and after time reversal

Against the flow of time with multi-output models

Recent work has paid close attention to the first principle of Granger causality, according to which cause precedes effect. In this context, the question may arise whether the detected direction of causality also reverses after the time reversal of unidirectionally coupled data. Recently, it has been shown that for unidirectionally causally connected autoregressive (AR) processes X → Y, after time reversal of data, the opposite causal direction Y → X is indeed detected, although typically as part of the bidirectional X↔ Y link. As we argue here, the answer is different when the measured data are not from AR processes but from linked deterministic systems. When the goal is the usual forward data analysis, cross-mapping-like approaches correctly detect X → Y, while Granger causality-like approaches, which should not be used for deterministic time series, detect causal independence X → Y. The results of backward causal analysis depend on the predictability of the reversed data. Unlike AR processes, observables from deterministic dynamical systems, even complex nonlinear ones, can be predicted well forward, while backward predictions can be difficult (notably when the time reversal of a function leads to one-to-many relations). To address this problem, we propose an approach based on models that provide multiple candidate predictions for the target, combined with a loss function that consideres only the best candidate. The resulting good forward and backward predictability supports the view that unidirectionally causally linked deterministic dynamical systems X → Y can be expected to detect the same link both before and after time reversal

Survival Analysis of Factors Influencing Cyclic Fatigue of Nickel-Titanium Endodontic Instruments

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 Navigator instruments, Mtwo instruments, ProTaper instruments, and Revo-S instruments 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 was Mtwo > Wizard Navigator > Revo-S > ProTaper; 5 mm radius > 3 mm radius; and yellow > red in ISO colour coding system