Three-Dimensional Shapes of Spinning Helium Nanodroplets

A significant fraction of superfluid helium nanodroplets produced in a free-jet expansion have been observed to gain high angular momentum resulting in large centrifugal deformation. We measured single-shot diffraction patterns of individual rotating helium nanodroplets up to large scattering angles using intense extreme ultraviolet light pulses from the FERMI free-electron laser. Distinct asymmetric features in the wide-angle diffraction patterns enable the unique and systematic identification of the three-dimensional droplet shapes. The analysis of a large dataset allows us to follow the evolution from axisymmetric oblate to triaxial prolate and two-lobed droplets. We find that the shapes of spinning superfluid helium droplets exhibit the same stages as classical rotating droplets while the previously reported metastable, oblate shapes of quantum droplets are not observed. Our three-dimensional analysis represents a valuable landmark for clarifying the interrelation between morphology and superfluidity on the nanometer scale

Personal probabilities of probabilities

By definition, the subjective probability distribution of a random event is revealed by the (‘rational’) subject's choice between bets — a view expressed by F. Ramsey, B. De Finetti, L. J. Savage and traceable to E. Borel and, it can be argued, to T. Bayes. Since hypotheses are not observable events, no bet can be made, and paid off, on a hypothesis. The subjective probability distribution of hypotheses (or of a parameter, as in the current ‘Bayesian’ statistical literature) is therefore a figure of speech, an ‘as if’, justifiable in the limit. Given a long sequence of previous observations, the subjective posterior probabilities of events still to be observed are derived by using a mathematical expression that would approximate the subjective probability distribution of hypotheses, if these could be bet on. This position was taken by most, but not all, respondents to a ‘Round Robin’ initiated by J. Marschak after M. H. De-Groot's talk on Stopping Rules presented at the UCLA Interdisciplinary Colloquium on Mathematics in Behavioral Sciences. Other participants: K. Borch, H. Chernoif, R. Dorfman, W. Edwards, T. S. Ferguson, G. Graves, K. Miyasawa, P. Randolph, L. J. Savage, R. Schlaifer, R. L. Winkler. Attention is also drawn to K. Borch's article in this issue.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43847/1/11238_2004_Article_BF00169102.pd

On the Probabilty Concept

As it has been already done for the Corrado Gini's works, STATISTICA has accepted the invitation of some researchers who asked to republish the English translation of some fundamental De Finetti's papers. These works were translated into English and published in the volume: Bruno De Finetti, Induction and Probability, Biblioteca di Statistica, eds. P. Monari, D. Cocchi, Clueb, Bologna, 1993. On the Probability Concept is one of the first fundamental philosophical papers in which we can find the essential basis of De Finetti's subjective approach to the Theory of probability