Generalized Mixability via Entropic Duality

Mixability is a property of a loss which characterizes when constant regret is possible in the game of prediction with expert advice. We show that a key property of mixability generalizes, and the $\exp$ and $\log$ operations present in the usual theory are not as special as one might have thought. In doing so we introduce a more general notion of $\Phi$-mixability where $\Phi$ is a general entropy (\ie, any convex function on probabilities). We show how a property shared by the convex dual of any such entropy yields a natural algorithm (the minimizer of a regret bound) which, analogous to the classical Aggregating Algorithm, is guaranteed a constant regret when used with $\Phi$-mixable losses. We characterize which $\Phi$ have non-trivial $\Phi$-mixable losses and relate $\Phi$-mixability and its associated Aggregating Algorithm to potential-based methods, a Blackwell-like condition, mirror descent, and risk measures from finance. We also define a notion of ``dominance'' between different entropies in terms of bounds they guarantee and conjecture that classical mixability gives optimal bounds, for which we provide some supporting empirical evidence

A generalized definition of reactivity for ecological systems and the problem of transient species dynamics

1. Perturbations to an ecosystem's steady state can trigger transient responses of great ecological relevance. Asymptotic stability determines whether a generic perturbation will fade out in the long run, but falls short of characterizing the dynamics immediately after an equilibrium has been perturbed. Reactivity, traditionally defined as the maximum instantaneous growth rate of small perturbations to a stable steady state, is a simple yet powerful measure of the short-term instability of a system as a whole. In many ecological applications, however, it could be important to focus on the reactivity properties of just some specific, problem-dependent state variables, such as the abundance of a focal species engaged in interspecific competition, either predators or preys in a trophic community, or infectious individuals in disease transmission. 2. We propose a generalized definition of reactivity (g-reactivity) that allows to evaluate the differential contribution of the state space components to the transient behaviour of an ecological system following a perturbation. Our definition is based on the dynamic analysis of a system output, corresponding to an ecologically motivated linear transformation of the relevant state variables. We demonstrate that the g-reactivity properties of an equilibrium are determined by the dominant eigenvalue of a Hermitian matrix that can be easily obtained from the Jacobian associated with the equilibrium and the system output transformation. 3. As a testbed for our methodological framework, we analyse the g-reactivity properties of simple spatially implicit metapopulation models of some prototypical ecological interactions, namely competition, predation and transmission of an infectious disease. We identify conditions for the temporary coexistence of an invader with a (possibly competitively superior) resident species, for transitory invasion of either prey or predator in otherwise predator- or prey-dominated ecosystems, and for transient epidemic outbreaks. 4. Through suitable examples, we show that characterizing the transient dynamics associated with an ecosystem's steady state can be, in some cases, as important as determining its asymptotic behaviour, from both theoretical and management perspective. Because g-reactivity analysis can be performed for systems of any complexity in a relatively straightforward way, we conclude that it may represent a useful addition to the toolbox of quantitative ecologists

Clinically significant chronic liver disease in people with type 2 diabetes: the Edinburgh Type 2 Diabetes Study

Background: Type 2 diabetes is an independent risk factor for chronic liver disease, however disease burden estimates and knowledge of prognostic indicators are lacking in community populations. Aims: To describe the prevalence and incidence of clinically significant chronic liver disease amongst community-based older people with Type 2 diabetes and to determine risk factors which might assist in discriminating patients with unknown prevalent or incident disease. Design: Prospective cohort study. Methods: Nine hundred and thirty-nine participants in the Edinburgh Type 2 Diabetes Study underwent investigation including liver ultrasound and non-invasive measures of non-alcoholic steatohepatitis (NASH), hepatic fibrosis and systemic inflammation. Over 6-years, cases of cirrhosis and hepatocellular carcinoma were collated from multiple sources. Results: Eight patients had known prevalent disease with 13 further unknown cases identified (prevalence 2.2%) and 15 incident cases (IR 2.9/1000 person-years). Higher levels of systemic inflammation, NASH and hepatic fibrosis markers were associated with both unknown prevalent and incident clinically significant chronic liver disease (all P < 0.001). Conclusions: Our study investigations increased the known prevalence of clinically significant chronic liver disease by over 150%, confirming the suspicion of a large burden of undiagnosed disease. The disease incidence rate was lower than anticipated but still much higher than the general population rate. The ability to identify patients both with and at risk of developing clinically significant chronic liver disease allows for early intervention and clinical monitoring strategies. Ongoing work, with longer follow-up, including analysis of rates of liver function decline, will be used to define optimal risk prediction tools

Trust and control interrelations: New perspectives on the trust control nexus

This article is the post-print version of the published article that may be accessed at the link below. Copyright @ 2007 Sage Publications.This article introduces the special issue on New Perspectives on the Trust-Control Nexus in Organizational Relations. Trust and control are interlinked processes commonly seen as key to reach effectiveness in inter- and intraorganizational relations. The relation between trust and control is, however, a complex one, and research into this relation has given rise to various and contradictory interpretations of how trust and control relate. A well-known discussion is directed at whether trust and control are better conceived as substitutes, or as complementary mechanisms of governance. The articles in this special issue bring the discussion on the relationship between both concepts a step further by identifying common factors, distinctive mechanisms, and key implications relevant for theory building and empirical research. By studying trust and control through different perspectives and at different levels of analysis, the articles provide new theoretical insights and empirical evidence on the foundations of the trust-control interrelations

Extended Superscaling of Electron Scattering from Nuclei

An extended study of scaling of the first and second kinds for inclusive electron scattering from nuclei is presented. Emphasis is placed on the transverse response in the kinematic region lying above the quasielastic peak. In particular, for the region in which electroproduction of resonances is expected to be important, approximate scaling of the second kind is observed and the modest breaking of it is shown probably to be due to the role played by an inelastic version of the usual scaling variable.Comment: LaTeX, 36 pages including 5 color postscript figures and 4 postscript figure

Stochastic modelling of hydraulic conductivity derived from geotechnical data: an example applied to central Glasgow

Characterising the three-dimensional (3D) distribution of hydraulic conductivity and its variability in the shallow subsurface is fundamental to understanding groundwater behaviour and to developing conceptual and numerical groundwater models to manage the subsurface. However, directly measuring in situ hydraulic conductivity can be difficult and expensive and is rarely carried out with sufficient density in urban environments. In this study we model hydraulic conductivity for 603 sites in the unconsolidated Quaternary deposits underlying Glasgow using particle size distribution and density description widely available from geotechnical investigations. Six different models were applied and the MacDonald formula was found to be most applicable in this heterogeneous environment, comparing well with the few available in situ hydraulic conductivity data. The range of the calculated hydraulic conductivity values between the 5th and 95th percentile was 1.56×10–2–4.38mday–1 with a median of 2.26×10–1 mday–1. These modelled hydraulic conductivity data were used to develop a suite of stochastic 3D simulations conditioned to existing 3D representations of lithology. Ten per cent of the input data were excluded from the modelling process for use in a split-sample validation test, which demonstrated the effectiveness of this approach compared with non-spatial or lithologically unconstrained models. Our spatial model reduces the mean squared error between the estimated and observed values at the excluded data locations over those predicted using a simple homogeneous model by 73 %. The resulting 3D hydraulic conductivity model is of a much higher resolution than would have been possible from using only direct measurements, and will improve understanding of groundwater flow in Glasgow and reduce the spatial uncertainty of hydraulic parameters in groundwater process models. The methodology employed could be replicated in other regions where significant volumes of suitable geotechnical and site investigation data are available to predict ground conditions in areas with complex superficial deposits

Superscaling of Inclusive Electron Scattering from Nuclei

We investigate the degree to which the concept of superscaling, initially developed within the framework of the relativistic Fermi gas model, applies to inclusive electron scattering from nuclei. We find that data obtained from the low energy loss side of the quasielastic peak exhibit the superscaling property, i.e., the scaling functions f(\psi') are not only independent of momentum transfer (the usual type of scaling: scaling of the first kind), but coincide for A \geq 4 when plotted versus a dimensionless scaling variable \psi' (scaling of the second kind). We use this behavior to study as yet poorly understood properties of the inclusive response at large electron energy loss.Comment: 33 pages, 12 color EPS figures, LaTeX2e using BoxedEPSF macros; email to [email protected]

Charmless Bs→PP,PV,VVB_s\to PP, PV, VV Decays Based on the six-quark Effective Hamiltonian with Strong Phase Effects II

We provide a systematic study of charmless $B_s \to PP, PV, VV$ decays ($P$ and $V$ denote pseudoscalar and vector mesons, respectively) based on an approximate six-quark operator effective Hamiltonian from QCD. The calculation of the relevant hard-scattering kernels is carried out, the resulting transition form factors are consistent with the results of QCD sum rule calculations. By taking into account important classes of power corrections involving "chirally-enhanced" terms and the vertex corrections as well as weak annihilation contributions with non-trivial strong phase, we present predictions for the branching ratios and CP asymmetries of $B_s$ decays into PP, PV and VV final states, and also for the corresponding polarization observables in VV final states. It is found that the weak annihilation contributions with non-trivial strong phase have remarkable effects on the observables in the color-suppressed and penguin-dominated decay modes. In addition, we discuss the SU(3) flavor symmetry and show that the symmetry relations are generally respected