A dimension extractor is an algorithm designed to increase the effective dimension – i.e., the computational information density – of an infinite sequence. A constructive dimension extractor is exhibited by showing that every sequence of positive constructive dimension is Turing equivalent to a sequence of constructive strong dimension arbitrarily close to 1. Similar results are shown for compu...

The discovery of particle filtering methods has enabled the use of nonlinear filtering in a wide array of applications. Unfortunately, the approximation error of particle filters typically grows exponentially in the dimension of the underlying model. This phenomenon has rendered particle filters of limited use in complex data assimilation problems. In this paper, we argue that it is often possi...

The paper is concerned with upper bounds for the Hausdorff dimension of flow invariant compact sets on Riemannian manifolds and the application of such bounds to global stability investigations of equilibrium points. The proof of the main theorem uses a special Carathéodory dimension structure in order to get contraction conditions for the considered Carathéodory measures which majorize the Hau...

We determined the changes in fractal dimensions and spatial correlations of regional pulmonary blood flow with increasing exercise in race horses (n = 4) by using 15-microm fluorescent microspheres. Fluorescence was measured to quantitate regional blood to 1.3-cm(3) samples (n = 1,621-2,503). Perfusion distributions were characterized with fractal dimensions (a measure of spatial variability) a...

The area under the ROC curve (AUC) has been advocated as an evaluation criterion for the bipartite ranking problem. We study uniform convergence properties of the AUC; in particular, we derive a distribution-free uniform convergence bound for the AUC which serves to bound the expected accuracy of a learned ranking function in terms of its empirical AUC on the training sequence from which it is ...

The discovery of particle filtering methods has enabled the use of nonlinear filtering in a wide array of applications. Unfortunately, the approximation error of particle filters typically grows exponentially in the dimension of the underlying model. This phenomenon has rendered particle filters of limited use in complex data assimilation problems. In this paper, we argue that it is often possi...

This paper presents a review of the Dimension Matrix for Evaluation of the Brazilian Health System that was initially developed in 2003, as well as a conceptual update of some of the sub-dimensions for the evaluation of health service performance, namely effectiveness, access, efficiency and appropriateness of health care. It also describes the indicator selection process as well as the results...

Unsupervised learning algorithm locally linear embedding (LLE) is a typical technique which applies the preserving embedding method of high dimensional data to low dimension. The number of neighborhood nodes of LLE is a decisive parameter because the improper value will affect the manifold structure in the local neighborhood and lead to the lower computational efficiency. Based on the fact that...