We demonstrate an efficient high-precision optical spectroscopy technique for single trapped ions with nonclosed transitions. In a double-shelving technique, the absorption of a single photon is first amplified to several phonons of a normal motional mode shared with a cotrapped cooling ion of a different species, before being further amplified to thousands of fluorescence photons emitted by the cooling ion using the standard electron shelving technique. We employ this extension of the photon recoil spectroscopy technique to perform the first high precision absolute frequency measurement of the ${}^2{D}_{3/2}\to {}^2{P}_{1/2}$ transition in calcium, resulting in a transition frequency of $f=346000234867(96)\mathrm{kHz}$. Furthermore, we determine the isotope shift of this transition and the ${}^2{S}_{1/2}\to {}^2{P}_{1/2}$ transition for ${}^{42}{\mathrm{Ca}}^{+}$, ${}^{44}{\mathrm{Ca}}^{+}$, and ${}^{48}{\mathrm{Ca}}^{+}$ ions relative to ${}^{40}{\mathrm{Ca}}^{+}$ with an accuracy below 100 kHz. Improved field and mass shift constants of these transitions as well as changes in mean square nuclear charge radii are extracted from this high resolution data.

The TGF-b superfamily cytokine MIC-1/GDF15 circulates in the blood of healthy humans. Its levels rise substantially in cancer and other diseases and this may sometimes lead to development of an anorexia/cachexia syndrome. This is mediated by a direct action of MIC-1/GDF15 on feeding centres in the hypothalamus and brainstem. More recent studies in germline gene deleted mice also suggest that this cytokine may play a role in physiological regulation of energy homeostasis. To further characterize the role of MIC-1/GDF15 in physiological regulation of energy homeostasis in man, we have examined diurnal and food associated variation in serum levels and whether variation in circulating levels relate to BMI in human monozygotic twin pairs. We found that the within twin pair differences in serum MIC-1/GDF15 levels were significantly correlated with within twin pair differences in BMI, suggesting a role for MIC-1/GDF15 in the regulation of energy balance in man. MIC-1/GDF15 serum levels altered slightly in response to a meal, but comparison with variation its serum levels over a 24hour period suggested that these changes are likely to be due to bimodal diurnal variation which can alter serum MIC-1/GDF15 levels by about plus or minus 10% from the mesor. The lack of a rapid and substantial postprandial increase in MIC-1/GDF15 serum levels suggests that MIC1/GDF15 is unlikely to act as a satiety factor. Taken together, our findings suggest that MIC-1/GDF15 may be a physiological regulator of energy homeostasis in man, most probably due to actions on long-term regulation of energy homeostasis.

One of the central results in Einstein’s theory of Brownian motion is that the mean square displacement of a randomly moving Brownian particle scales linearly with time. Over the past few decades sophisticated experiments and data collection in numerous biological, physical and financial systems have revealed anomalous sub-diffusion in which the mean square displacement grows slower than linearly with time. A major theoretical challenge has been to derive the appropriate evolution equation for the probability density function of sub-diffusion taking into account further complications from force fields and reactions. Here we present a derivation of the generalised master equation for an ensemble of particles undergoing reactions whilst being subject to an external force field. From this general equation we show reductions to a range of well known special cases, including the fractional reaction diffusion equation and the fractional Fokker-Planck equation.