In the assessment of nodules in CT scans of the lungs, a number of image-derived features are diagnostically relevant. Currently, many of these features are defined only qualitatively, so they are difficult to quantify from first principles. Nevertheless, these features (through their qualitative definitions and interpretations thereof) are often quantified via a variety of mathematical methods for the purpose of computer-aided diagnosis (CAD). To determine the potential usefulness of quantified diagnostic image features as inputs to a CAD system, we investigate the predictive capability of statistical learning methods for classifying nodule malignancy. We utilize the Lung Image Database Consortium dataset and only employ the radiologist-assigned diagnostic feature values for the lung nodules therein, as well as our derived estimates of the diameter and volume of the nodules from the radiologists' annotations. We calculate theoretical upper bounds on the classification accuracy that are achievable by an ideal classifier that only uses the radiologist-assigned feature values, and we obtain an accuracy of 85.74 [Formula: see text], which is, on average, 4.43% below the theoretical maximum of 90.17%. The corresponding area-under-the-curve (AUC) score is 0.932 ([Formula: see text]), which increases to 0.949 ([Formula: see text]) when diameter and volume features are included and has an accuracy of 88.08 [Formula: see text]. Our results are comparable to those in the literature that use algorithmically derived image-based features, which supports our hypothesis that lung nodules can be classified as malignant or benign using only quantified, diagnostic image features, and indicates the competitiveness of this approach. We also analyze how the classification accuracy depends on specific features and feature subsets, and we rank the features according to their predictive power, statistically demonstrating the top four to be spiculation, lobulation, subtlety, and calcification.

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We analyze the dynamics of the Poincaré map associated with the center manifold equations of double-diffusive thermosolutal convection near a codimension-four bifurcation point when the values of the thermal and solute Rayleigh numbers, [Formula: see text] and [Formula: see text], are comparable. We find that the bifurcation sequence of the Poincaré map is analogous to that of the (continuous) Lorenz equations. Chaotic solutions are found, and the emergence of strange attractors is shown to occur via three different routes: (1) a discrete Lorenz-like attractor of the three-dimensional Poincaré map of the four-dimensional center manifold equations that forms as the result of a quasi-periodic homoclinic explosion; (2) chaos that follows quasi-periodic intermittency occurring near saddle-node bifurcations of tori; and, (3) chaos that emerges from the destruction of a 2-torus, preceded by frequency locking.

Abstract. A wind-driven numerical model of the Indian Ocean is used to examine the horizontal statistics of hundreds of passive tracers spread evenly over the model domain. The distribution covers several dynamically distinct regions, revealing a variety of Lagrangian behaviours associated with different geographic locations. In particular, a cluster of trajectories with scaling dimension as large as 1.3 exists throughout the equatorial zone. Spectral analysis of trajectory displacements indicates mixed Rossby-gravity waves are involved in the production of some fractal trajectories.

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