Modifying effects of 5-azacytidine on metal-containing proteins profile in guerin carcinoma with different sensitivity to cytostatics

Aim: To assess the influence of the treatment with 5-azacytidine (5-aza) on the profile of metal-containing proteins and factors of their regulation in Guerin carcinoma cells in vivo. Materials and Methods: The study was conducted on Wistar rats transplanted with wild-type Guerin carcinoma (Guerin/WT) and its strains resistant to cisplatin (Guerin/CP) or doxorubicin (Guerin/Dox). Animals were distributed in 6 groups treated with 5-aza and control animals without treatment. 5-Aza was injected by i.v. route (1 injection in 4 days at a dose of 2 mg/kg starting from the 4th day after tumor transplantation, 4 injections in total). Ferritin levels in blood serum and tumor tissue were measured by ELISA, transferrin and free iron complexes — by low-temperature EPR, miRNA-200b, -133a and -320a levels and promoter methylation — by real-time quantitative reverse transcription polymerase chain reaction. Results: The study has shown that 5-aza treatment caused demethylation of promoter regions of fth1 and tfr1 genes in all studied Guerin carcinoma strains. 5-Aza treatment resulted in a significant decrease of ferritin levels in tumor tissue (by 32.1% in Guerin/WT strain, by 29.8% in Guerin/Dox and by 69.1% in Guerin/CP). These events were accompanied by 3.5-fold and 2-fold increase of free iron complexes levels in tumor tissue of doxorubicin and cisplatin resistant strains, respectively. Also, 5-aza treatment resulted in significantly elevated levels of miR-200b, -133a, 320a expression in tumor tissue. After 5-aza treatment, ferritin levels in blood serum of animals with Guerin/Dox were increased by 23.9%, while in Guerin/Wt and Guerin/CP they were decreased by 17 and 16%, respectively. Conclusion: Alterations of epigenetic regulation upon in vivo treatment with 5-aza change the levels of metal-containing proteins due to DNA demethylation and altered miRNA expression profiles in Guerin carcinoma cells

A brief survey on singularities of geodesic flows in smooth signature changing metrics on 2-surfaces

We present a survey on generic singularities of geodesic flows in smooth signature changing metrics (often called pseudo-Riemannian) in dimension 2. Generically, a pseudo-Riemannian metric on a 2-manifold S changes its signature (degenerates) along a curve S0, which locally separates S into a Riemannian (R) and a Lorentzian (L) domain. The geodesic flow does not have singularities over R and L, and for any point q∈ R∪ L and every tangential direction p∈ ℝℙ there exists a unique geodesic passing through the point q with the direction p. On the contrary, geodesics cannot pass through a point q∈ S0 in arbitrary tangential directions, but only in some admissible directions; the number of admissible directions is 1 or 2 or 3. We study this phenomenon and the local properties of geodesics near q∈ S0. © Springer International Publishing AG, part of Springer Nature 2018

Communications of the Moscow mathematical society: Geodesics on hypersurfaces in Minkowski space: Singularities of signature change

[No abstract available

A complete classification of generic singularities of geodesic flows on 2-surfaces with pseudo-Riemannian metrics

[No abstract available

On isomorphisms of pseudo-Euclidean spaces with signature (p,n − p) for p = 2,3

As is well known, for every orthogonal transformation of the Euclidean space there exists an orthogonal basis such that the matrix of the transformation is block-diagonal with first order blocks ±1 and second order blocks that are rotations of the Euclidean plane. There exists a natural generalization of this theorem for Lorentz transformations of pseudo-Euclidean spaces with signature (1,n−1). In addition to invariant subspaces appearing in the Euclidean case, Lorentz transformations can have invariant subspaces of two new types: invariant plane with the Lorenz rotation and 3-dimensional cyclic subspace with isotropic eigenvector and eigenvalue ±1. In this paper, we present similar results about the structure of isomorphisms of pseudo-Euclidean spaces with signature (p,n−p) for p=2,3. © 2017 Elsevier Inc

On isomorphisms of pseudo-Euclidean spaces with signature (p,n − p) for p = 2,3

As is well known, for every orthogonal transformation of the Euclidean space there exists an orthogonal basis such that the matrix of the transformation is block-diagonal with first order blocks ±1 and second order blocks that are rotations of the Euclidean plane. There exists a natural generalization of this theorem for Lorentz transformations of pseudo-Euclidean spaces with signature (1,n−1). In addition to invariant subspaces appearing in the Euclidean case, Lorentz transformations can have invariant subspaces of two new types: invariant plane with the Lorenz rotation and 3-dimensional cyclic subspace with isotropic eigenvector and eigenvalue ±1. In this paper, we present similar results about the structure of isomorphisms of pseudo-Euclidean spaces with signature (p,n−p) for p=2,3. © 2017 Elsevier Inc

Hyperbolic Roussarie fields with degenerate quadratic part

[No abstract available

A brief survey on singularities of geodesic flows in smooth signature changing metrics on 2-surfaces

We present a survey on generic singularities of geodesic flows in smooth signature changing metrics (often called pseudo-Riemannian) in dimension 2. Generically, a pseudo-Riemannian metric on a 2-manifold S changes its signature (degenerates) along a curve S0, which locally separates S into a Riemannian (R) and a Lorentzian (L) domain. The geodesic flow does not have singularities over R and L, and for any point q∈ R∪ L and every tangential direction p∈ ℝℙ there exists a unique geodesic passing through the point q with the direction p. On the contrary, geodesics cannot pass through a point q∈ S0 in arbitrary tangential directions, but only in some admissible directions; the number of admissible directions is 1 or 2 or 3. We study this phenomenon and the local properties of geodesics near q∈ S0. © Springer International Publishing AG, part of Springer Nature 2018

SMOOTH LOCAL NORMAL FORMS OF HYPERBOLIC ROUSSARIE VECTOR FIELDS

In 1975, Roussarie studied a special class of vector fields, whose singular points fill a submanifold of codimension two and the ratio between two non-zero eigenvalues lambda(1) : lambda(2) = 1 : -1 He established a smooth orbital normal form for such fields at points where lambda(1,2) are real and the quadratic part of the field satisfied a certain genericity condition. In this paper, we establish smooth orbital normal forms for such fields at points where this condition fails. Moreover, we prove similar results for vector fields, whose singular points fill a submanifold of codimension two and the ratio between two non-zero eigenvalues lambda(1) : lambda(2) = p : -q with arbitrary integers p, q >= 1