The symmetric representation of the rigid body equations and their discretization

This paper analyses continuous and discrete versions of the generalized rigid body equations and the role of these equations in numerical analysis, optimal control and integrable Hamiltonian systems. In particular, we present a symmetric representation of the rigid body equations on the Cartesian product SO(n)×SO(n) and study its associated symplectic structure. We describe the relationship of these ideas with the Moser-Veselov theory of discrete integrable systems and with the theory of variational symplectic integrators. Preliminary work on the ideas discussed in this paper may be found in Bloch et al (Bloch A M, Crouch P, Marsden J E and Ratiu T S 1998 Proc. IEEE Conf. on Decision and Control 37 2249-54).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/49076/2/no2416.pd

Morphological assessment of colon polyp using flexible spectral imaging color enhancement

The article is devoted to the study of the efficacy of the flexible spectral imaging color enhancement (FICE) in the visual assessment of the polyp morphology. A group of 166 patients had undergone screening colonoscopy, which showed polyps of different sizes and histological structure in different parts of the intestine. The accuracy of the visual assessment of the polyp type performed using FICE was compared with the histological examination results. 255 polyps in various parts of the colon were identified in 166 patients. Comparative analysis of the results of visual assessment and histological examination of the identified polyps showed that the diagnoses agreed in 190 (74.5%) cases, and preliminary diagnoses proved to be erroneous in 65 (25.5%) cases. The size of the polyp was found to be inversely correlated with the number of erroneous diagnoses, i.e. the smaller the size of the polyp, the greater the probability of error. The erroneous diagnosis was made most frequently in the cases of small and smallest tubular adenomas and hyperplastic polyps, which were taken as serrated one (p <0.05 – significant differences), and also in the case of small and smallest hyperplastic polyps, which were taken as tubular ones (p < 0.05). Based on the results of evaluation of the FICE informativeness in the visual assessment of colon polyps, the method has been shown to have high diagnostic accuracy with respect to tubular, serrated and hyperplastic polyps equal to 83.1, 81.2, 83.9%, respectively. The study showed the high efficacy of flexible spectral imaging colour enhancement in recognizing the morphological structure of epithelial neoplasms, which can be used as a screening method for the preliminary classification of colonic epithelial neoplasia