A variational problem on Stiefel manifolds

In their paper on discrete analogues of some classical systems such as the rigid body and the geodesic flow on an ellipsoid, Moser and Veselov introduced their analysis in the general context of flows on Stiefel manifolds. We consider here a general class of continuous time, quadratic cost, optimal control problems on Stiefel manifolds, which in the extreme dimensions again yield these classical physical geodesic flows. We have already shown that this optimal control setting gives a new symmetric representation of the rigid body flow and in this paper we extend this representation to the geodesic flow on the ellipsoid and the more general Stiefel manifold case. The metric we choose on the Stiefel manifolds is the same as that used in the symmetric representation of the rigid body flow and that used by Moser and Veselov. In the extreme cases of the ellipsoid and the rigid body, the geodesic flows are known to be integrable. We obtain the extremal flows using both variational and optimal control approaches and elucidate the structure of the flows on general Stiefel manifolds.Comment: 30 page

Conductivity of underdoped YBa2Cu3O7-d : evidence for incoherent pair correlations in the pseudogap regime

Conductivity due to superconducting fluctuations studied in optimally doped YBa2Cu3O7-d films displays a stronger decay law in temperature than explainable by theory. A formula is proposed, which fits the data very well with two superconductive parameters, Tc and the coherence length ksi_c0, and an energy scale Delta*. This is also valid in underdoped materials and enables to describe the conductivity up to 300 K with a single-particle excitations channel in parallel with a channel whose contribution is controlled by ksi_c0, Tc and Delta*. This allows to address the nature of the pseudogap in favour of incoherent pairing.Comment: 14 pages, 4 figures, 1 tabl

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

SARS-CoV-2 infects the human kidney and drives fibrosis in kidney organoids

Kidney failure is frequently observed during and after COVID-19, but it remains elusive whether this is a direct effect of the virus. Here, we report that SARS-CoV-2 directly infects kidney cells and is associated with increased tubule-interstitial kidney fibrosis in patient autopsy samples. To study direct effects of the virus on the kidney independent of systemic effects of COVID-19, we infected human-induced pluripotent stem-cell-derived kidney organoids with SARS-CoV-2. Single-cell RNA sequencing indicated injury and dedifferentiation of infected cells with activation of profibrotic signaling pathways. Importantly, SARS-CoV-2 infection also led to increased collagen 1 protein expression in organoids. A SARS-CoV-2 protease inhibitor was able to ameliorate the infection of kidney cells by SARS-CoV-2. Our results suggest that SARS-CoV-2 can directly infect kidney cells and induce cell injury with subsequent fibrosis. These data could explain both acute kidney injury in COVID-19 patients and the development of chronic kidney disease in long COVID

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