Limit theorems for empirical Fréchet means of independent and non-identically distributed manifold-valued random variables

We prove weak laws of large numbers and central limit theorems of Lindeberg type for empirical centres of mass (empirical Fréchet means) of independent nonidentically distributed random variables taking values in Riemannian manifolds. In order to prove these theorems we describe and prove a simple kind of Lindeberg–Feller central approximation theorem for vector-valued random variables, which may be of independent interest and is therefore the subject of a self-contained section. This vector-valued result allows us to clarify the number of conditions required for the central limit theorem for empirical Fréchet means, while extending its scope

The Universal Aspect Ratio of Vortices in Rotating Stratifi?ed Flows: Experiments and Observations

We validate a new law for the aspect ratio $\alpha = H/L$ of vortices in a rotating, stratified flow, where $H$ and $L$ are the vertical half-height and horizontal length scale of the vortices. The aspect ratio depends not only on the Coriolis parameter f and buoyancy (or Brunt-Vaisala) frequency $\bar{N}$ of the background flow, but also on the buoyancy frequency $N_c$ within the vortex and on the Rossby number $Ro$ of the vortex such that $\alpha = f \sqrt{[Ro (1 + Ro)/(N_c^2- \bar{N}^2)]}$. This law for $\alpha$ is obeyed precisely by the exact equilibrium solution of the inviscid Boussinesq equations that we show to be a useful model of our laboratory vortices. The law is valid for both cyclones and anticyclones. Our anticyclones are generated by injecting fluid into a rotating tank filled with linearly-stratified salt water. The vortices are far from the top and bottom boundaries of the tank, so there is no Ekman circulation. In one set of experiments, the vortices viscously decay, but as they do, they continue to obey our law for $\alpha$, which decreases over time. In a second set of experiments, the vortices are sustained by a slow continuous injection after they form, so they evolve more slowly and have larger |Ro|, but they also obey our law for $\alpha$. The law for $\alpha$ is not only validated by our experiments, but is also shown to be consistent with observations of the aspect ratios of Atlantic meddies and Jupiter's Great Red Spot and Oval BA. The relationship for $\alpha$ is derived and examined numerically in a companion paper by Hassanzadeh et al. (2012).Comment: Submitted to the Journal of Fluid Mechanics. Also see the companion paper by Hassanzadeh et al. "The Universal Aspect Ratio of Vortices in Rotating Stratifi?ed Flows: Theory and Simulation" 201

A probabilistic model for information and sensor validation

This paper develops a new theory and model for information and sensor validation. The model represents relationships between variables using Bayesian networks and utilizes probabilistic propagation to estimate the expected values of variables. If the estimated value of a variable differs from the actual value, an apparent fault is detected. The fault is only apparent since it may be that the estimated value is itself based on faulty data. The theory extends our understanding of when it is possible to isolate real faults from potential faults and supports the development of an algorithm that is capable of isolating real faults without deferring the problem to the use of expert provided domain-specific rules. To enable practical adoption for real-time processes, an any time version of the algorithm is developed, that, unlike most other algorithms, is capable of returning improving assessments of the validity of the sensors as it accumulates more evidence with time. The developed model is tested by applying it to the validation of temperature sensors during the start-up phase of a gas turbine when conditions are not stable; a problem that is known to be challenging. The paper concludes with a discussion of the practical applicability and scalability of the model

DsJ(2860)D_{sJ}(2860) and DsJ(2715)D_{sJ}(2715)

Recently Babar Collaboration reported a new $c\bar{s}$ state $D_{sJ}(2860)$ and Belle Collaboration observed $D_{sJ}(2715)$. We investigate the strong decays of the excited $c\bar{s}$ states using the $^{3}P_{0}$ model. After comparing the theoretical decay widths and decay patterns with the available experimental data, we tend to conclude: (1) $D_{sJ}(2715)$ is probably the $1^{-}(1^{3}D_{1})$ $c\bar{s}$ state although the $1^{-}(2^{3}S_{1})$ assignment is not completely excluded; (2) $D_{sJ}(2860)$ seems unlikely to be the $1^{-}(2^{3}S_{1})$ and $1^{-}(1^{3}D_{1})$ candidate; (3) $D_{sJ}(2860)$ as either a $0^{+}(2^{3}P_{0})$ or $3^{-}(1^{3}D_{3})$ $c\bar{s}$ state is consistent with the experimental data; (4) experimental search of $D_{sJ}(2860)$ in the channels $D_s\eta$, $DK^{*}$, $D^{*}K$ and $D_{s}^{*}\eta$ will be crucial to distinguish the above two possibilities.Comment: 18 pages, 7 figures, 2 tables. Some discussions added. The final version to appear at EPJ

Valuing the voluntary sector: rethinking economic analysis

The voluntary sector plays an important role in the sports industry, as a provider of sporting opportunities and in the development of sport, from increasing participation through to supporting excellence and elite performance. However, despite this importance, research on its contribution to sport-related economic activity is limited, with information on this sector remaining the weakest part of current economic assessments of the UK sports industry. The research presented in this article examines the economic importance of the voluntary sector, using a case study of Sheffield. It demonstrates that the sports voluntary sector in the city is considerably smaller than was predicted when using national estimates, and that this is largely a consequence of methodological issues relating to previous research. The article suggests that in the light of the findings and the increasing use of sport in urban policy, there is a need to rethink the methodology used to evaluate the economic contribution of the voluntary sector in the future.</p

Innovation and research in organic farming: A multi‐level approach to facilitate cooperation among stakeholders

A wider range of stakeholders is expected to be involved in organic research. A decision‐support tool is needed to define priorities and to allocate tasks among institutions. Based on research and management experience in organic research, the authors have developed a framework for experimental and research projects. The framework is based on a multi‐level approach. Each level is defined according to the directness of the innovation impact on the organic systems. The projects carried out for each level were assessed over a ten-year period. Two applications are presented: analysis of crop protection strategies in horticulture and plant breeding programmes. When combined with four development models of organic farming, this multi‐level analysis appears to be promising for defining research agendas