Forecast Ergodicity: Prediction Modeling Using Algorithmic Information Theory

The capabilities of machine intelligence are bounded by the potential of data from the past to forecast the future. Deep learning tools are used to find structures in the available data to make predictions about the future. Such structures have to be present in the available data in the first place and they have to be applicable in the future. Forecast ergodicity is a measure of the ability to forecast future events from data in the past. We model this bound by the algorithmic complexity of the available data

Controllability, Observability, Realizability, and Stability of Dynamic Linear Systems

We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on generalized Laplace transform methods (e.g. shifts and convolution) from our recent work \cite{DaGrJaMaRa}. We study controllability in terms of the controllability Gramian and various rank conditions (including Kalman's) in both the time invariant and time varying settings and compare the results. We also explore observability in terms of both Gramian and rank conditions as well as realizability results. We conclude by applying this systems theory to connect exponential and BIBO stability problems in this general setting. Numerous examples are included to show the utility of these results.Comment: typos corrected; current form is as accepted in EJD

17O NMR spectroscopy as a tool to study hydrogen bonding of cholesterol in lipid bilayers

Cholesterol is a crucial component of biological membranes and can interact with other membrane components through hydrogen bonding. NMR spectroscopy has been used previously to investigate this bonding, however this study represents the first 17O NMR spectroscopy study of isotopically enriched cholesterol. We demonstrate the 17O chemical shift is dependent on hydrogen bonding, providing a novel method for the study of cholesterol in bilayers

Testing the universality of star formation - II. Comparing separation distributions of nearby star-forming regions and the field

We have measured the multiplicity fractions and separation distributions of seven young star-forming regions using a uniform sample of young binaries. Both the multiplicity fractions and separation distributions are similar in the different regions. A tentative decline in the multiplicity fraction with increasing stellar density is apparent, even for binary systems with separations too close (19-100au) to have been dynamically processed. The separation distributions in the different regions are statistically indistinguishable over most separation ranges, and the regions with higher densities do not exhibit a lower proportion of wide (300-620au) relative to close (62-300au) binaries as might be expected from the preferential destruction of wider pairs. Only the closest (19-100au) separation range, which would be unaffected by dynamical processing, shows a possible difference in separation distributions between different regions. The combined set of young binaries, however, shows a distinct difference when compared to field binaries, with a significant excess of close (19-100au) systems among the younger binaries. Based on both the similarities and differences between individual regions, and between all seven young regions and the field, especially over separation ranges too close to be modified by dynamical processing, we conclude that multiple star formation is not universal and, by extension, the star formation process is not universal.Comment: accepted for publication in MNRA