On the data consumption benefits of accepting increased uncertainty

In the context of learning paradigms of identification in the limit, we address the question: why is uncertainty sometimes desirable? We use mind change bounds on the output hypotheses as a measure of uncertainty and interpret ‘desirable’ as reduction in data memorization, also defined in terms of mind change bounds. The resulting model is closely related to iterative learning with bounded mind change complexity, but the dual use of mind change bounds — for hypotheses and for data — is a key distinctive feature of our approach. We show that situations exist where the more mind changes the learner is willing to accept, the less the amount of data it needs to remember in order to converge to the correct hypothesis. We also investigate relationships between our model and learning from good examples, set-driven, monotonic and strong-monotonic learners, as well as class-comprising versus class-preserving learnability.

The impact of nonlinear exposure risk relationships on seasonal time series data: modelling danish neonatal birth anthropometric data

Background Birth weight and length have seasonal fluctuations. Previous analyses of birth weight by latitude effects identified seemingly contradictory results, showing both 6 and 12 monthly periodicities in weight. The aims of this paper are twofold: (a) to explore seasonal patterns in a large, Danish Medical Birth Register, and (b) to explore models based on seasonal exposures and a non-linear exposure-risk relationship. Methods Birth weight and birth lengths on over 1.5 million Danish singleton, live births were examined for seasonality. We modelled seasonal patterns based on linear, U- and J-shaped exposure-risk relationships. We then added an extra layer of complexity by modelling weighted population-based exposure patterns. Results The Danish data showed clear seasonal fluctuations for both birth weight and birth length. A bimodal model best fits the data, however the amplitude of the 6 and 12 month peaks changed over time. In the modelling exercises, U- and J-shaped exposure-risk relationships generate time series with both 6 and 12 month periodicities. Changing the weightings of the population exposure risks result in unexpected properties. A J-shaped exposure-risk relationship with a diminishing population exposure over time fitted the observed seasonal pattern in the Danish birth weight data. Conclusion In keeping with many other studies, Danish birth anthropometric data show complex and shifting seasonal patterns. We speculate that annual periodicities with non-linear exposure-risk models may underlie these findings. Understanding the nature of seasonal fluctuations can help generate candidate exposures.

Rural and Urban Differentials in Primary Care Management of Chronic Heart Failure: New Data from the CASE Study

Objective: To determine whether primary care management of chronic heart failure (CHF) differed between rural and urban areas in Australia. Design: A cross-sectional survey stratified by Rural, Remote and Metropolitan Areas (RRMA) classification. The primary source of data was the Cardiac Awareness Survey and Evaluation (CASE) study. Setting: Secondary analysis of data obtained from 341 Australian general practitioners and 23 845 adults aged 60 years or more in 1998. Main outcome measures: CHF determined by criteria recommended by the World Health Organization, diagnostic practices, use of pharmacotherapy, and CHF-related hospital admissions in the 12 months before the study. Results: There was a significantly higher prevalence of CHF among general practice patients in large and small rural towns (16.1%) compared with capital city and metropolitan areas (12.4%) (P < 0.001). Echocardiography was used less often for diagnosis in rural towns compared with metropolitan areas (52.0% v 67.3%, P < 0.001). Rates of specialist referral were also significantly lower in rural towns than in metropolitan areas (59.1% v 69.6%, P < 0.001), as were prescribing rates of angiotensin-converting enzyme inhibitors (51.4% v 60.1%, P < 0.001). There was no geographical variation in prescribing rates of β-blockers (12.6% [rural] v 11.8% [metropolitan], P = 0.32). Overall, few survey participants received recommended “evidence-based practice” diagnosis and management for CHF (metropolitan, 4.6%; rural, 3.9%; and remote areas, 3.7%). Conclusions: This study found a higher prevalence of CHF, and significantly lower use of recommended diagnostic methods and pharmacological treatment among patients in rural areas.

Time-dependent fractional advection–diffusion equations by an implicit MLS meshless method

Recently, many new applications in engineering and science are governed by a series of fractional partial differential equations (FPDEs). Unlike the normal partial differential equations (PDEs), the differential order in a FPDE is with a fractional order, which will lead to new challenges for numerical simulation, because most existing numerical simulation techniques are developed for the PDE with an integer differential order. The current dominant numerical method for FPDEs is Finite Difference Method (FDM), which is usually difficult to handle a complex problem domain, and also hard to use irregular nodal distribution. This paper aims to develop an implicit meshless approach based on the moving least squares (MLS) approximation for numerical simulation of fractional advection-diffusion equations (FADE), which is a typical FPDE. The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless strong-forms. The stability and convergence related to the time discretization of this approach are then discussed and theoretically proven. Several numerical examples with different problem domains and different nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the FADE.