On Poisson quasi-Nijenhuis Lie algebroids

We propose a definition of Poisson quasi-Nijenhuis Lie algebroids as a natural generalization of Poisson quasi-Nijenhuis manifolds and show that any such Lie algebroid has an associated quasi-Lie bialgebroid. Therefore, also an associated Courant algebroid is obtained. We introduce the notion of a morphism of quasi-Lie bialgebroids and of the induced Courant algebroids morphism and provide some examples of Courant algebroid morphisms. Finally, we use paired operators to deform doubles of Lie and quasi-Lie bialgebroids and find an application to generalized complex geometry.Comment: 12 page

Toda systems and exponents of simple Lie groups

Results on the finite nonperiodic An Toda lattice are extended to the Bogoyavlesky Toda systems of type Bn and Cn. The areas investigated, include master symmetries, recursion operators, higher Poisson brackets and invariants. The results are presented both in Flaschka coordinates (a,b) as well as in the natural (q,p) coordinates. A conjecture which relates the degrees of higher Poisson brackets and the exponents of the corresponding Lie group is verified for these systems.http://www.sciencedirect.com/science/article/B6VKR-42BT0VX-3/1/5111b82cd06e6016a123f286071a5d6

On Jacobi quasi-Nijenhuis algebroids and Courant-Jacobi algebroid morphisms

We propose a definition of Jacobi quasi-Nijenhuis algebroid and show that any such Jacobi algebroid has an associated quasi-Jacobi bialgebroid. Therefore, also an associated Courant-Jacobi algebroid is obtained. We introduce the notions of quasi-Jacobi bialgebroid morphism and Courant-Jacobi algebroid morphism providing also some examples of Courant-Jacobi algebroid morphisms.Comment: 14 pages, to appear in Journal of Geometry and Physic

Reduction of Jacobi manifolds via Dirac structures theory

We first recall some basic definitions and facts about Jacobi manifolds, generalized Lie bialgebroids, generalized Courant algebroids and Dirac structures. We establish an one-one correspondence between reducible Dirac structures of the generalized Lie bialgebroid of a Jacobi manifold $(M,\Lambda,E)$ for which 1 is an admissible function and Jacobi quotient manifolds of $M$. We study Jacobi reductions from the point of view of Dirac structures theory and we present some examples and applications.Comment: 18 page

Reduction and construction of Poisson quasi-Nijenhuis manifolds with background

We extend the Falceto-Zambon version of Marsden-Ratiu Poisson reduction to Poisson quasi-Nijenhuis structures with background on manifolds. We define gauge transformations of Poisson quasi-Nijenhuis structures with background, study some of their properties and show that they are compatible with reduction procedure. We use gauge transformations to construct Poisson quasi-Nijenhuis structures with background.Comment: to appear in IJGMM

Hierarchies and compatibility on Courant algebroids

We extend to the context of Courant algebroids several hierarchies that can be constructed on Poisson-Nijenhuis manifolds. More precisely, we introduce several notions (Poisson-Nijenhuis, deformation-Nijenhuis and Nijenhuis pairs) that extend to Courant algebroids the notion of a Poisson-Nijenhuis manifold, by using the idea that both the Poisson and the Nijenhuis structures, although they seem to be different in nature when considered on manifolds, are just $(1,1)$-tensors on the usual Courant algebroid $TM \oplus T^*M$ satisfying several constraints. For each of the generalizations mentioned, we show that there are natural hierarchies obtained by successive deformation by one of the $(1,1)$-tensor

Jacobi-Nijenhuis algebroids and their modular classes

Jacobi-Nijenhuis algebroids are defined as a natural generalization of Poisson-Nijenhuis algebroids, in the case where there exists a Nijenhuis operator on a Jacobi algebroid which is compatible with it. We study modular classes of Jacobi and Jacobi-Nijenhuis algebroids

Sublineage A1 Drives Multi-Organ Carcinogenesis

by Fundação para a Ciência e Tecnologia/Ministério da Ciência, Tecnologia e Ensino Superior (FCT/MCTES, Portugal) through national funds to iNOVA4Health (UIDB/04462/2020 and UIDP/ 04462/2020); from the GenomePT project (POCI-01-0145-FEDER-022184), supported by COMPETE 2020—Operational Programme for Competitiveness and Internationalisation (POCI), Lisboa Portugal Regional Operational Programme (Lisboa2020), Algarve Portugal Regional Operational Pro- Int. J. Mol. Sci. 2022, 23, 12371 8 of 10 gramme (CRESC Algarve2020), under the PORTUGAL 2020 Partnership Agreement, through the European Regional Development Fund (ERDF), and by Fundação para a Ciência e a Tecnologia (FCT). This work was also supported by Fundos FEDER through the Programa Operacional Factores de Competitividade—COMPETE and by Fundos Nacionais through the Fundação para a Ciência e a Tecnologia within the scope of the project UID/BIM/00009/2019 (Centre for Toxicogenomics and Human Health-ToxOmics); and from LA/P/0045/2020 (ALiCE), UIDB/00511/2020 and UIDP/00511/2020 (LEPABE), funded by national funds through FCT/MCTES (PIDDAC); 2SMART (NORTE-01-0145- FEDER-000054), supported by Norte Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, through the European Regional Development Fund (ERDF).The study of human papillomavirus (HPV)-induced carcinogenesis uses multiple in vivo mouse models, one of which relies on the cytokeratin 14 gene promoter to drive the expression of all HPV early oncogenes. This study aimed to determine the HPV16 variant and sublineage present in the K14HPV16 mouse model. This information can be considered of great importance to further enhance this K14HPV16 model as an essential research tool and optimize its use for basic and translational studies. Our study evaluated HPV DNA from 17 samples isolated from 4 animals, both wild-type (n = 2) and HPV16-transgenic mice (n = 2). Total DNA was extracted from tissues and the detection of HPV16 was performed using a qPCR multiplex. HPV16-positive samples were subsequently whole-genome sequenced by next-generation sequencing techniques. The phylogenetic positioning clearly shows K14HPV16 samples clustering together in the sub-lineage A1 (NC001526.4). A comparative genome analysis of K14HPV16 samples revealed three mutations to the human papillomaviruses type 16 sublineage A1 representative strain. Knowledge of the HPV 16 variant is fundamental, and these findings will allow the rational use of this animal model to explore the role of the A1 sublineage in HPV-driven cancer.publishersversionpublishe