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Markov models are important tools for quantitative social research. In this article, new methods for discrete Markov chains are presented. These methods allow us to calculate the distribution of the occupation time in a subset of the state space, the distribution of the waiting time to first entry into a subset of the state space, and the distribution of the waiting time to final exit from a subset of the state space. To demonstrate the usefulness of these methods, we apply them to working life tables for Spanish males to assess how the recent financial crisis affected the length of working life. The results show that the duration of working life decreased considerably, a pattern that can largely be explained by later entry to and earlier exit from the labor market. The findings also indicate that inequality in the length of working life increased. [ABSTRACT FROM AUTHOR]

Summary: We investigate the effect of taking up daily use of cannabis on the onset of homelessness by using Australian data. We use a bivariate simultaneous mixed proportional hazard model to address potential biases due to common unobservable factors and reverse causality. We find that taking up daily use of cannabis substantially increases the probability of transitioning into homelessness for young men but not young women. In contrast, the onset of homelessness increases the probability of taking up daily use of cannabis for young women but not for young men. In a trivariate extension we find that the use of other illicit drugs at least weekly has no additional effect on transitions into homelessness for either gender but there is a large if imprecisely estimated effect of onset of homelessness on taking up weekly use of such drugs for young women. [ABSTRACT FROM AUTHOR]

The features of the interpolation method of the measurement of the time instants based on digital processing of the samples of the reaction of a circuit of impact excitation are considered. The samples processing is the estimation of the coefficients of a regression function that approximates the damped oscillation. It is shown that a small number of samples has not the systematic error in nonlinear transformations. The accuracy capabilities of the method are illustrated by the results of the computational experiment. [ABSTRACT FROM AUTHOR]

1. Understanding ecological phenomena often requires an accurate assessment of the timing of events. To estimate the time since a diet shift in animals without knowledge on the isotope ratios of either the old or the new diet, isotope ratio measurements in two different tissues (e.g. blood plasma and blood cells) at a single point in time can be used. For this ‘isotopic-clock’ principle, we present here a mathematical model that yields an analytical and easily calculated outcome. 2. Compared with a previously published model, our model assumes the isotopic difference between the old and new diets to be constant if multiple measurements are taken on the same subject at different points in time. Furthermore, to estimate the time since diet switch, no knowledge of the isotopic signature of tissues under the old diet, but only under the new diet is required. 3. The two models are compared using three calibration data sets including a novel one based on a diet shift experiment in a shorebird (red knot Calidris canutus); sensitivity analyses were conducted. The two models behaved differently and each may prove rather unsatisfactory depending on the system under investigation. A single-tissue model, requiring knowledge of both the old and new diets, generally behaved quite reliably. 4. As blood (cells) and plasma are particularly useful tissues for isotopic-clock research, we trawled the literature on turnover rates in whole blood, cells and plasma. Unfortunately, turnover rate predictions using allometric relations are too unreliable to be used directly in isotopic-clock calculations. 5. We advocate that before applying the isotopic-clock methodology, the propagation of error in the ‘time-since-diet-shift’ estimation is carefully assessed for the system under scrutiny using a sensitivity analysis as proposed here. [ABSTRACT FROM AUTHOR]