Differential Entropy on Statistical Spaces

We show that the previously introduced concept of distance on statistical spaces leads to a straightforward definition of differential entropy on these statistical spaces. These spaces are characterized by the fact that their points can only be localized within a certain volume and exhibit thus a feature of fuzziness. This implies that Riemann integrability of relevant integrals is no longer secured. Some discussion on the specialization of this formalism to quantum states concludes the paper.Comment: 4 pages, to appear in the proceedings of the joint meeting of the 2nd International Conference on Cybernetics and Information Technologies, Systems and Applications (CITSA 2005) and the 11th International Conference on Information Systems Analysis and Synthesis (ISAS 2005), to be held in Orlando, USA, on July 14-17, 200

UV solar irradiance in observations and the NRLSSI and SATIRE-S models

Total solar irradiance and UV spectral solar irradiance have been monitored since 1978 through a succession of space missions. This is accompanied by the development of models aimed at replicating solar irradiance by relating the variability to solar magnetic activity. The NRLSSI and SATIRE-S models provide the most comprehensive reconstructions of total and spectral solar irradiance over the period of satellite observation currently available. There is persistent controversy between the various measurements and models in terms of the wavelength dependence of the variation over the solar cycle, with repercussions on our understanding of the influence of UV solar irradiance variability on the stratosphere. We review the measurement and modelling of UV solar irradiance variability over the period of satellite observation. The SATIRE-S reconstruction is consistent with spectral solar irradiance observations where they are reliable. It is also supported by an independent, empirical reconstruction of UV spectral solar irradiance based on UARS/SUSIM measurements from an earlier study. The weaker solar cycle variability produced by NRLSSI between 300 and 400 nm is not evident in any available record. We show that although the method employed to construct NRLSSI is principally sound, reconstructed solar cycle variability is detrimentally affected by the uncertainty in the SSI observations it draws upon in the derivation. Based on our findings, we recommend, when choosing between the two models, the use of SATIRE-S for climate studies

Liquid-to-liquid phase transition in pancake vortex systems

We study the thermodynamics of a model of pancake vortices in layered superconductors. The model is based on the effective pair potential for the pancake vortices derived from the London approximation of a version of the Lawrence-Doniach model which is valid for extreme type-II superconductors. Using the hypernetted-chain (HNC) approximation, we find that there is a temperature below which multiple solutions to the HNC equations exist. By explicitly evaluating the free energy for each solution we find that the system undergoes a first-order transition between two vortex liquid phases. The low-temperature phase has larger correlations along the field direction than the high-temperature phase. We discuss the possible relation of this phase transition to the liquid-to-liquid phase transition recently observed in Y-Ba-Cu-O superconductors in high magnetic fields in the presence of disorder.Comment: 7 pages, 6 figure

Metastable Dynamics of the Hard-Sphere System

The reformulation of the mode-coupling theory (MCT) of the liquid-glass transition which incorporates the element of metastability is applied to the hard-sphere system. It is shown that the glass transition in this system is not a sharp one at the special value of the density or the packing fraction, which is in contrast to the prediction by the conventional MCT. Instead we find that the slowing down of the dynamics occurs over a range of values of the packing fraction. Consequently, the exponents governing the sequence of time relaxations in the intermediate time regime are given as functions of packing fraction with one additional parameter which describes the overall scale of the metastable potential energy for defects in the hard-sphere system. Implications of the present model on the recent experiments on colloidal systems are also discussed.Comment: 21 pages, 5 figures (available upon request), RevTEX3.0, JFI Preprint

COVID-19 Related Mobility Reduction: Heterogenous Effects on Sleep and Physical Activity Rhythms

Mobility restrictions imposed to suppress coronavirus transmission can alter physical activity (PA) and sleep patterns. Characterization of response heterogeneity and their underlying reasons may assist in tailoring customized interventions. We obtained wearable data covering baseline, incremental movement restriction and lockdown periods from 1824 city-dwelling, working adults aged 21 to 40 years, incorporating 206,381 nights of sleep and 334,038 days of PA. Four distinct rest activity rhythms (RARs) were identified using k-means clustering of participants' temporally distributed step counts. Hierarchical clustering of the proportion of time spent in each of these RAR revealed 4 groups who expressed different mixtures of RAR profiles before and during the lockdown. Substantial but asymmetric delays in bedtime and waketime resulted in a 24 min increase in weekday sleep duration with no loss in sleep efficiency. Resting heart rate declined 2 bpm. PA dropped an average of 38%. 4 groups with different compositions of RAR profiles were found. Three were better able to maintain PA and weekday/weekend differentiation during lockdown. The least active group comprising 51 percent of the sample, were younger and predominantly singles. Habitually less active already, this group showed the greatest reduction in PA during lockdown with little weekday/weekend differences. Among different mobility restrictions, removal of habitual social cues by lockdown had the largest effect on PA and sleep. Sleep and resting heart rate unexpectedly improved. RAR evaluation uncovered heterogeneity of responses to lockdown and can identify characteristics of persons at risk of decline in health and wellbeing.Comment: 30 pages, 3 main figures, 3 tables, 4 supplementary figure