The purpose of this study was to establish GENEA (Gravity Estimator of Normal Everyday Activity) cut-points for discriminating between six relative-intensity activity levels in middle-aged recreational marathoners. Nighty-eight (83 males and 15 females) recreational marathoners, aged 30–45 years, completed a cardiopulmonary exercise test running on a treadmill while wearing a GENEA accelerometer on their non-dominant wrist. The breath-by-breath V̇O2 data was also collected for criterion measure of physical activity categories (sedentary, light, moderate, vigorous, very vigorous and extremely vigorous). GENEA cut-points for physical activity classification was performed via Receiver Operating Characteristic (ROC) analysis. Spearman’s correlation test was applied to determine the relationship between estimated and measured intensity classifications. Statistical analysis were done for all individuals, and separating samples by sex. The GENEA cut-points established were able to distinguish between all six-relative intensity levels with an excellent classification accuracy (area under the ROC curve (AUC) values between 0.886 and 0.973) for all samples. When samples were separated by sex, AUC values were 0.881–0.973 and 0.924–0.968 for males and females, respectively. The total variance in energy expenditure explained by GENEA accelerometer data was 78.50% for all samples, 78.14% for males, and 83.17% for females. In conclusion, the wrist-worn GENEA accelerometer presents a high capacity of classifying the intensity of physical activity in middle-aged recreational marathoners when examining all samples together, as well as when sample set was separated by sex. This study suggests that the triaxial GENEA accelerometers (worn on the non-dominant wrist) can be used to predict energy expenditure for running activities.

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were discarded from further analyses. The entire process of sampling (contact approach and criteria for inclusion and exclusion of volunteers) has been previously described 25. ethics statement. All individuals included in the current study were fully informed and gave their written consent to participate. The research was conducted according to the Declaration of Helsinki, and it was approved by the Research Ethics Committee of the University Jaume I of Castellon. This study is enrolled in the ClinicalTrails.gov database, with the code number NCT03155633 (www.clinicaltrials.gov).

In this paper, we introduce a new notion of generalized companion pencils for scalar polynomials over an arbitrary field expressed in the monomial basis. Our definition is quite general and extends the notions of companion pencil in [F.

In this paper, we introduce a general class of quasi-sparse potential companion pencils for arbitrary square matrix polynomials over an arbitrary field, which extends the class introduced in [B. Eastman, I.-J. Kim, B. L. Shader, K.N. Vander Meulen, Companion matrix patterns. Linear Algebra Appl. 436 (2014) 255-272]for monic scalar polynomials. We provide a canonical form, up to permutation, for companion pencils in this class. We also relate these companion pencils with other relevant families of companion linearizations known so far. Finally, we determine the number of different sparse companion pencils in the class, up to permutation.