Hamiltonian evolutions of twisted gons in \RP^n

In this paper we describe a well-chosen discrete moving frame and their associated invariants along projective polygons in \RP^n, and we use them to write explicit general expressions for invariant evolutions of projective $N$-gons. We then use a reduction process inspired by a discrete Drinfeld-Sokolov reduction to obtain a natural Hamiltonian structure on the space of projective invariants, and we establish a close relationship between the projective $N$-gon evolutions and the Hamiltonian evolutions on the invariants of the flow. We prove that {any} Hamiltonian evolution is induced on invariants by an evolution of $N$-gons - what we call a projective realization - and we give the direct connection. Finally, in the planar case we provide completely integrable evolutions (the Boussinesq lattice related to the lattice $W_3$-algebra), their projective realizations and their Hamiltonian pencil. We generalize both structures to $n$-dimensions and we prove that they are Poisson. We define explicitly the $n$-dimensional generalization of the planar evolution (the discretization of the $W_n$-algebra) and prove that it is completely integrable, providing also its projective realization

Symplectically-invariant soliton equations from non-stretching geometric curve flows

A moving frame formulation of geometric non-stretching flows of curves in the Riemannian symmetric spaces $Sp(n+1)/Sp(1)\times Sp(n)$ and $SU(2n)/Sp(n)$ is used to derive two bi-Hamiltonian hierarchies of symplectically-invariant soliton equations. As main results, multi-component versions of the sine-Gordon (SG) equation and the modified Korteweg-de Vries (mKdV) equation exhibiting $Sp(1)\times Sp(n-1)$ invariance are obtained along with their bi-Hamiltonian integrability structure consisting of a shared hierarchy of symmetries and conservation laws generated by a hereditary recursion operator. The corresponding geometric curve flows in $Sp(n+1)/Sp(1)\times Sp(n)$ and $SU(2n)/Sp(n)$ are shown to be described by a non-stretching wave map and a mKdV analog of a non-stretching Schr\"odinger map.Comment: 39 pages; remarks added on algebraic aspects of the moving frame used in the constructio

Quaternionic Soliton Equations from Hamiltonian Curve Flows in HP^n

A bi-Hamiltonian hierarchy of quaternion soliton equations is derived from geometric non-stretching flows of curves in the quaternionic projective space $HP^n$. The derivation adapts the method and results in recent work by one of us on the Hamiltonian structure of non-stretching curve flows in Riemannian symmetric spaces $M=G/H$ by viewing $HP^n \simeq {\rm U}(n+1,H)/{\rm U}(1,H) \times {\rm U}(n,H)\simeq {\rm Sp}(n+1)/{\rm Sp}(1)\times {\rm Sp}(n)$ as a symmetric space in terms of compact real symplectic groups and quaternion unitary groups. As main results, scalar-vector (multi-component) versions of the sine-Gordon (SG) equation and the modified Korteveg-de Vries (mKdV) equation are obtained along with their bi-Hamiltonian integrability structure consisting of a shared hierarchy of quaternionic symmetries and conservation laws generated by a hereditary recursion operator. The corresponding geometric curve flows in $HP^n$ are shown to be described by a non-stretching wave map and a mKdV analog of a non-stretching Schrodinger map.Comment: 25 pages; typos correcte

The biomarker HE4 (WFDC2) promotes a pro-angiogenic and immunosuppressive tumor microenvironment via regulation of STAT3 target genes

© 2020, The Author(s). Epithelial ovarian cancer (EOC) is a highly lethal gynecologic malignancy arising from the fallopian tubes that has a high rate of chemoresistant recurrence and low five-year survival rate. The ovarian cancer biomarker HE4 is known to promote proliferation, metastasis, chemoresistance, and suppression of cytotoxic lymphocytes. In this study, we sought to examine the effects of HE4 on signaling within diverse cell types that compose the tumor microenvironment. HE4 was found to activate STAT3 signaling and promote upregulation of the pro-angiogenic STAT3 target genes IL8 and HIF1A in immune cells, ovarian cancer cells, and endothelial cells. Moreover, HE4 promoted increases in tube formation in an in vitro model of angiogenesis, which was also dependent upon STAT3 signaling. Clinically, HE4 and IL8 levels positively correlated in ovarian cancer patient tissue. Furthermore, HE4 serum levels correlated with microvascular density in EOC tissue and inversely correlated with cytotoxic T cell infiltration, suggesting that HE4 may cause deregulated blood vessel formation and suppress proper T cell trafficking in tumors. Collectively, this study shows for the first time that HE4 has the ability to affect signaling events and gene expression in multiple cell types of the tumor microenvironment, which could contribute to angiogenesis and altered immunogenic responses in ovarian cancer

Constant Curvature Coefficients and Exact Solutions in Fractional Gravity and Geometric Mechanics

We study fractional configurations in gravity theories and Lagrange mechanics. The approach is based on Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical interactions and we formulate a method of nonholonomic deformations to other types of fractional derivatives. The main result of this paper consists in a proof that for corresponding classes of nonholonomic distributions a large class of physical theories are modelled as nonholonomic manifolds with constant matrix curvature. This allows us to encode the fractional dynamics of interactions and constraints into the geometry of curve flows and solitonic hierarchies.Comment: latex2e, 11pt, 27 pages, the variant accepted to CEJP; added and up-dated reference

Lagrangian Curves in a 4-dimensional affine symplectic space

Lagrangian curves in R4 entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic frame for Lagrangian curves. It allows us to classify La- grangrian curves with constant symplectic curvatures, to construct a class of Lagrangian tori in R4 and determine Lagrangian geodesic

The Relative Composition of the Inflammatory Infiltrate as an Additional Tool for Synovial Tissue Classification

10.1371/journal.pone.0072494PLoS ONE88-POLN

ANK, a Host Cytoplasmic Receptor for the Tobacco mosaic virus Cell-to-Cell Movement Protein, Facilitates Intercellular Transport through Plasmodesmata

Plasmodesma (PD) is a channel structure that spans the cell wall and provides symplastic connection between adjacent cells. Various macromolecules are known to be transported through PD in a highly regulated manner, and plant viruses utilize their movement proteins (MPs) to gate the PD to spread cell-to-cell. The mechanism by which MP modifies PD to enable intercelluar traffic remains obscure, due to the lack of knowledge about the host factors that mediate the process. Here, we describe the functional interaction between Tobacco mosaic virus (TMV) MP and a plant factor, an ankyrin repeat containing protein (ANK), during the viral cell-to-cell movement. We utilized a reverse genetics approach to gain insight into the possible involvement of ANK in viral movement. To this end, ANK overexpressor and suppressor lines were generated, and the movement of MP was tested. MP movement was facilitated in the ANK-overexpressing plants, and reduced in the ANK-suppressing plants, demonstrating that ANK is a host factor that facilitates MP cell-to-cell movement. Also, the TMV local infection was largely delayed in the ANK-suppressing lines, while enhanced in the ANK-overexpressing lines, showing that ANK is crucially involved in the infection process. Importantly, MP interacted with ANK at PD. Finally, simultaneous expression of MP and ANK markedly decreased the PD levels of callose, β-1,3-glucan, which is known to act as a molecular sphincter for PD. Thus, the MP-ANK interaction results in the downregulation of callose and increased cell-to-cell movement of the viral protein. These findings suggest that ANK represents a host cellular receptor exploited by MP to aid viral movement by gating PD through relaxation of their callose sphincters

Optimizing a Massive Parallel Sequencing Workflow for Quantitative miRNA Expression Analysis

BACKGROUND: Massive Parallel Sequencing methods (MPS) can extend and improve the knowledge obtained by conventional microarray technology, both for mRNAs and short non-coding RNAs, e.g. miRNAs. The processing methods used to extract and interpret the information are an important aspect of dealing with the vast amounts of data generated from short read sequencing. Although the number of computational tools for MPS data analysis is constantly growing, their strengths and weaknesses as part of a complex analytical pipe-line have not yet been well investigated. PRIMARY FINDINGS: A benchmark MPS miRNA dataset, resembling a situation in which miRNAs are spiked in biological replication experiments was assembled by merging a publicly available MPS spike-in miRNAs data set with MPS data derived from healthy donor peripheral blood mononuclear cells. Using this data set we observed that short reads counts estimation is strongly under estimated in case of duplicates miRNAs, if whole genome is used as reference. Furthermore, the sensitivity of miRNAs detection is strongly dependent by the primary tool used in the analysis. Within the six aligners tested, specifically devoted to miRNA detection, SHRiMP and MicroRazerS show the highest sensitivity. Differential expression estimation is quite efficient. Within the five tools investigated, two of them (DESseq, baySeq) show a very good specificity and sensitivity in the detection of differential expression. CONCLUSIONS: The results provided by our analysis allow the definition of a clear and simple analytical optimized workflow for miRNAs digital quantitative analysis