Consensus analysis with large and multiple communication delays using spectral delay space concept

In this study, we consider the consensus problem for a group of second-order agents interacting under a fixed, undirected communication topology. Communication lines are affected by two rationally independent delays. The first delay is assumed to be in the position information channels, whereas the second delay is in the velocity information exchange. The delays are assumed to be large and uniform throughout the entire network. The stability analysis of such systems becomes quickly intractable as the number of agents increases and the delays enlarge. To resolve this dilemma, we first reduce the complexity of the problem dramatically, by decomposing the characteristic equation of the system into a set of second-order factors. Then, we assess the stability of the resulting subsystems exactly and exhaustively in the domain of the time delays using the cluster treatment of characteristic roots (CTCR) paradigm. CTCR requires the determination of all the potential stability switching loci in the domain of the delays. For this, a surrogate domain, called the ‘spectral delay space (SDS)’, is used. The result is a computationally efficient stability analysis of the given dynamics within the domain of the delays. Illustrative cases are provided to verify the analytical conclusions. On these examples, we also study the consensus speeds through eigenvalue analysis.     

Daily dietary lithium intake in Belgium using duplicate portion sampling

 For the first time, daily dietary lithium intake for adults in Belgium has been evaluated by duplicate portion sampling, the heating of the samples in a microwave oven and atomic absorption spectrometric determination of the element. The mean intake value for adults (8.6±4.6 μg/day) is very low compared to the scarce literature data. Since the lithium requirement of humans and animals is still unknown, no comparison could be made with RDA values.     

Reliability as Tool for Hydraulic Network Planning

This paper presents a methodology to evaluate the reliability of water distribution systems that can be used in the design phase and for identifying repair works to be carried out on existing systems. The methodology is based on the statistical analysis of dimensionless performance indices (hydraulic performance indices) derived from a large number of simulations of various water system demand scenarios and∕or operating conditions. The hydraulic reliability index is assumed as the probability that, under a given operating condition, the hydraulic performance index will be above a certain threshold. Finally, the system's overall reliability (mechanical + hydraulic) is estimated using the overall reliability index, which is defined by the weighted mean of the hydraulic performance indices obtained for the various operating conditions. A case study using this methodology shows the concrete possibilities of applying this approach to a wide spectrum of cases, and the small influence on overall system reliability normally exerted by such events as the failure of links, pipes, and valves.     

Understanding consumer heterogeneity: A business intelligence application of neural networks

This paper describes a business intelligence application of neural networks in analyzing consumer heterogeneity in the context of eating-out behavior in Taiwan. We apply a neural network rule extraction algorithm which automatically groups the consumers into identifiable segments according to their socio-demographic information. Within each of these segments, the consumers are distinguished between those who eat-out frequently from those who do not based on their psychological traits and eat-out considerations. The data set for this study has been collected through a survey of 800 Taiwanese consumers. Demographic information such as gender, age and income were recorded. In addition, information about their psychological traits and eating-out considerations that might influence the frequency of eating-out were obtained. The results of our data analysis show that the neural network rule extraction algorithm is able to find distinct consumer segments and predict the consumers within each segment with good accuracy.     

Multicategory classification of body surface potential maps

A statistical classification method is suggested for body surface potential maps (BSPM). The initial data reduction utilizes the Fourier expansion and time integration, resulting in physiological-oriented features. Based on Fischer's criterion, optimal discriminant vectors are used to map the features to an optimal subdomain. Experimental criteria determine the dimensionality of the subdomain and the number of features to be mapped into it. Classification is performed in two steps. In the first, a k-nearest neighbor (k-NN) rule is used for every two-category problem, the results of which are fed into a voting rule for final classification. The method is tested with 123 patients divided into four categories: normal (NR), ischemia (IS), myocardial infarction (MI), and left bundle branch block (LB) patients. The success is between 88% (for IS) and 100% (for LB) for QRS segment integration. Departure maps were used to explain the misclassified patterns.     

The use of splines to calculate jerk for a lifting task involving chronic lower back pain patients

Motion differences in a repetitive lifting task have been described previously using differences in the timing of body angle changes during the lift. These timing changes relied on small differences of motion and are difficult to measure. The purpose of this study was to evaluate shoulder jerk (rate of change of acceleration) in a repetitive lifting task as an alternative parameter to detect differences of motion between controls and chronic lower back pain (CLBP) patients and to measure the impact of a rehabilitation program on jerk. The jerk calculation was a noisy measure, since jerk is the third derivative of position; consequently a simulation was performed to evaluate smoothing methods. Woltring's generalized cross-validation spline produced the best estimates of the third derivative and was fit to subject data. The root mean square (rms) amplitude of jerk was used for comparison. Significant group differences were found. CLBP patients performed lifts with lower jerk values than controls and, as the task progressed, both groups increased jerk. After completion of a rehabilitation program, CLBP patients performed lifts with greater rms jerk. In general, patients performed lifts with lower jerk values than controls, suggesting that pain impacts lifting style.