A novel approach to exponential stability of nonlinear non-autonomous difference equations with variable delays

In this paper, by using a novel approach, we first prove a new generalization of discrete-type Halanay inequality. Based on our new generalized inequality, a novel criterion for the exponential stability of a certain class of nonlinear non-autonomous difference equations is proposed. Numerical examples are given to illustrate the effectiveness of the obtained results.

Modeling the propagation of peer-to-peer worms

Propagation of Peer-to-Peer (P2P) worms in the Internet is posing a serious challenge to network security research because of P2P worms' increasing complexity and sophistication. Due to the complexity of the problem, no existing work has solved the problem of modeling the propagation of P2P worms, especially when quarantine of peers is enforced. This paper presents a study on modeling the propagation of P2P worms. It also presents our applications of the proposed approach in worm propagation research.

Motivated by our aspiration to invent an easy-to-employ instrument for worm propagation research, the proposed approach models the propagation processes of P2P worms by difference equations of a logic matrix, which are essentially discrete-time deterministic propagation models of P2P worms. To the best of our knowledge, we are the first using a logic matrix in network security research in general and worm propagation modeling in particular.

Our major contributions in this paper are firstly, we propose a novel logic matrix approach to modeling the propagation of P2P worms under three different conditions; secondly, we find the impacts of two different topologies on a P2P worm's attack performance; thirdly, we find the impacts of the network-related characteristics on a P2P worm's attack performance in structured P2P networks; and fourthly, we find the impacts of the two different quarantine tactics on the propagation characteristics of P2P worms in unstructured P2P networks. The approach's ease of employment, which is demonstrated by its applications in our simulation experiments, makes it an attractive instrument to conduct worm propagation research.

Stability analysis of a general family of nonlinear positive discrete time-delay systems

In this paper, we propose a new approach to analyse the stability of a general family of nonlinear positive discrete time-delay systems. First, we introduce a new class of nonlinear positive discrete time-delay systems, which generalises some existing discrete time-delay systems. Second, through a new technique that relies on the comparison and mathematical induction method, we establish explicit criteria for stability and instability of the systems. Three numerical examples are given to illustrate the feasibility of the obtained results.

Predictive validity and classification accuracy of ActiGraph energy expenditure equations and cut-points in young children

Objectives
Evaluate the predictive validity of ActiGraph energy expenditure equations and the classification accuracy of physical activity intensity cut-points in preschoolers.

Methods
Forty children aged 4–6 years (5.3±1.0 years) completed a ~150-min room calorimeter protocol involving age-appropriate sedentary, light and moderate-to vigorous-intensity physical activities. Children wore an ActiGraph GT3X on the right mid-axillary line of the hip. Energy expenditure measured by room calorimetry and physical activity intensity classified using direct observation were the criterion methods. Energy expenditure was predicted using Pate and Puyau equations. Physical activity intensity was classified using Evenson, Sirard, Van Cauwenberghe, Pate, Puyau, and Reilly, ActiGraph cut-points.

Results
The Pate equation significantly overestimated VO2 during sedentary behaviors, light physical activities and total VO2 (P<0.001). No difference was found between measured and predicted VO2 during moderate-to vigorous-intensity physical activities (P = 0.072). The Puyau equation significantly underestimated activity energy expenditure during moderate-to vigorous-intensity physical activities, light-intensity physical activities and total activity energy expenditure (P<0.0125). However, no overestimation of activity energy expenditure during sedentary behavior was found. The Evenson cut-point demonstrated significantly higher accuracy for classifying sedentary behaviors and light-intensity physical activities than others. Classification accuracy for moderate-to vigorous-intensity physical activities was significantly higher for Pate than others.

Conclusion
Available ActiGraph equations do not provide accurate estimates of energy expenditure across physical activity intensities in preschoolers. Cut-points of ≤25counts⋅15 s−1 and ≥420 counts⋅15 s−1 for classifying sedentary behaviors and moderate-to vigorous-intensity physical activities, respectively, are recommended.

Evaluation of Actical equations and thresholds to predict physical activity intensity in young children

This study examined the validity of current Actical activity energy expenditure (AEE) equations and intensity cut-points in preschoolers using AEE and direct observation as criterion measures. Forty 4–6-year-olds (5.3 ± 1.0 years) completed a ~150-min room calorimeter protocol involving age-appropriate sedentary behaviours (SBs), light intensity physical activities (LPAs) and moderate-to-vigorous intensity physical activities (MVPAs). AEE and/or physical activity intensity were calculated using Actical equations and cut-points by Adolph, Evenson, Pfeiffer and Puyau. Predictive validity was examined using paired sample t-tests. Classification accuracy was evaluated using weighted kappas, sensitivity, specificity and area under the receiver operating characteristic curve. The Pfeiffer equation significantly overestimated AEE during SB and underestimated AEE during LPA (P < 0.0125 for both). There was no significant difference between measured and predicted AEEs during MVPA. The Adolph cut-point showed significantly higher accuracy for classifying SB, LPA and MVPA than all others. The available Actical equation does not provide accurate estimates of AEE across all intensities in preschoolers. However, the Pfeiffer equation performed reasonably well for MVPA. Using cut-points of ≤6 counts · 15 s−1, 7–286 counts · 15 s−1 and ≥ 287 counts · 15 s−1 when classifying SB, LPA and MVPA, respectively, is recommended.