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A fundamental goal of cometary studies is to determine the exact relationship between these bodies and the Solar System – the question(s) can be summarised as follows: did comets originate during the same events that spawned the Sun and planets, are they more primitive bodies that record a pre-solar history, or are they interstellar materials collected in relatively more recent times? Now, whatever the origin of comets, it is entirely possible that they could, in part, contain interstellar or pre-solar components – indeed, it seems rather likely in light of the fact that primitive meteorites contain such entities. These particular components are likely to be refractory (dust, macromolecular organic complexes, etc.). Of more relevance to the issues above are the volatile constituents, which make up the bulk of a comet's mass. Since these materials, by their very nature, volatilise during perihelion passage of a comet they can, in some instances, be detected and measured spectroscopically. Perhaps the most useful species for isotopic investigations are C2, HCN and CN. Unfortunately, spectroscopic measurements can only currently be made with accuracies of ±10 to ±20%. As such it is very often not practical to conclude anything further than the fact that isotopic measurements are compatible with ‘`solar’' values, which tends to imply an origin from the margins of the solar accretion disk. But there is another problem with the spectroscopic measurements – since these are made on gaseous species in the coma (and relatively minor species at that) it is impossible to be certain that these represent the true nuclear values. In other words, if the processes of sublimation, active jetting, and photochemistry in the coma impart isotopic fractionation, the spectroscopic measurements could give a false impression of the true isotope ratios. What is required is an experiment capable of measuring isotopic ratios at the very surface of a comet. Herein we describe the Ptolemy instrument, which is included on the Philae lander as part of the Rosetta mission to 67P/Churyumov-Gerasimenko. The major objective of Ptolemy is a detailed appraisal of the nature and isotopic compositions of all materials present at the surface of a comet. [ABSTRACT FROM AUTHOR]

For Markov models of single channel kinetics, a sojourn time in a class of states has a density function which is usually a linear combination of exponential densities. There are many instances in the single channel literature where the time constants of exponentials fitted to sojourn time data have been used as estimated mean sojourn times in individual states, though the two may be very different. In the present study the nature and magnitude of this difference in the case of a two state class is illustrated analytically and numerically. The time constants should be viewed at best as approximations, possibly poor, to the estimated mean sojourn times. Estimates of kinetic parameters cannot in general be obtained explicitly from the fitted parameters of the density alone. However, this is shown to be possible in some special cases and enables direct estimation of, for example, the channel opening rate constant β (or an upper limit to the estimate of β in the case of multiple channels) in standard sequential three or four state models of nicotinic receptor kinetics, using only the fitted parameters of the closed-time density. [ABSTRACT FROM AUTHOR]