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Purpose: Benign and malignant tumors can be classified by using texture analysis of the ultrasound B-scan image to describe the variation in the echogenicity of scatterers. The recently proposed ultrasonic Nakagami parametric image has also been used to detect the concentrations and arrangements of scatterers for tumor characterization applications. B-scan-based texture analysis and the Nakagami parametric image are functionally complementary in ultrasonic tissue characterizations and this study aimed to combine these methods in order to improve the ability to characterize breast tumors. Methods: To validate this concept, radio-frequency data obtained from 130 clinical cases were used to construct the texture-feature parametric image and the Nakagami parametric image. Four texturefeature parameters based on a gray-level co-occurrence matrix ͑homogeneity, contrast, energy, and variance͒ and the Nakagami parameters of the benign and malignant tumors were calculated. The usefulness of an individual parameter was determined and scatter graphs indicated the relationship between two selected texture-feature parameters. Fisher's linear discriminant analysis was used to combine the selected texture-feature parameters with the Nakagami parameter. The performance in classifying tumors was evaluated based on the receiver operating characteristic curve. Results: The results indicated that there is a trade-off between sensitivity and specificity when using an individual texture-feature parameter or when combining two such correlated parameters to discriminate benign and malignant cases. However, the best performance was obtained when combining selected texture-feature parameters with the Nakagami parameter. Conclusions:The study findings suggest that combining B-scan-based texture analysis and the Nakagami parametric image could improve the ability to classify benign and malignant breast tumors.

Low-dimensional materials could display anomalous thermal conduction that the thermal conductivity (κ) diverges with increasing lengths, in ways inconceivable in any bulk materials. However, previous theoretical or experimental investigations were plagued with many finite-size effects, rendering the results either indirect or inconclusive. Indeed, investigations on the anomalous thermal conduction must demand the sample length to be sufficiently long so that the phenomena could emerge from unwanted finite-size effects. Here we report experimental observations that the κ's of single-wall carbon nanotubes continuously increase with their lengths over 1 mm, reaching at least 8640  W/mK at room temperature. Remarkably, the anomalous thermal conduction persists even with the presence of defects, isotopic disorders, impurities, and surface absorbates. Thus, we demonstrate that the anomalous thermal conduction in real materials can persist over much longer distances than previously thought. The finding would open new regimes for wave engineering of heat as well as manipulating phonons at macroscopic scales.

Forces on a finite body in an incompressible viscous flow are shown to be contributed by a potential flow and fluid elements of non-zero vorticity in a revealing formulation. The present study indicates that the potential flow play also a geometric role in determining the contribution of the fluid elements. Consideration is given to a solid body moving through a fluid, fluid accelerating past a solid body and a solid body which oscillates in a uniform stream. The effects of induced-mass and inertial forces appear naturally in the formulation and are separated from the contribution due to the surface vorticity and that due to the vorticity within the flow. Physical significance of the present analysis for vortical flows about a finite body is illustrated by examples, e.g. flow past a circular cylinder or an ellipsoid of revolution.