Binary trees, coproducts, and integrable systems

We provide a unified framework for the treatment of special integrable systems which we propose to call "generalized mean field systems". Thereby previous results on integrable classical and quantum systems are generalized. Following Ballesteros and Ragnisco, the framework consists of a unital algebra with brackets, a Casimir element, and a coproduct which can be lifted to higher tensor products. The coupling scheme of the iterated tensor product is encoded in a binary tree. The theory is exemplified by the case of a spin octahedron.Comment: 15 pages, 6 figures, v2: minor correction in theorem 1, two new appendices adde

Classical Dynamical Systems from q-algebras:"cluster" variables and explicit solutions

A general procedure to get the explicit solution of the equations of motion for N-body classical Hamiltonian systems equipped with coalgebra symmetry is introduced by defining a set of appropriate collective variables which are based on the iterations of the coproduct map on the generators of the algebra. In this way several examples of N-body dynamical systems obtained from q-Poisson algebras are explicitly solved: the q-deformed version of the sl(2) Calogero-Gaudin system (q-CG), a q-Poincare' Gaudin system and a system of Ruijsenaars type arising from the same (non co-boundary) q-deformation of the (1+1) Poincare' algebra. Also, a unified interpretation of all these systems as different Poisson-Lie dynamics on the same three dimensional solvable Lie group is given.Comment: 19 Latex pages, No figure

Gaudin Models and Bending Flows: a Geometrical Point of View

In this paper we discuss the bihamiltonian formulation of the (rational XXX) Gaudin models of spin-spin interaction, generalized to the case of sl(r)-valued spins. In particular, we focus on the homogeneous models. We find a pencil of Poisson brackets that recursively define a complete set of integrals of the motion, alternative to the set of integrals associated with the 'standard' Lax representation of the Gaudin model. These integrals, in the case of su(2), coincide wih the Hamiltonians of the 'bending flows' in the moduli space of polygons in Euclidean space introduced by Kapovich and Millson. We finally address the problem of separability of these flows and explicitly find separation coordinates and separation relations for the r=2 case.Comment: 27 pages, LaTeX with amsmath and amssym

Excursion Sets and Non-Gaussian Void Statistics

Primordial non-Gaussianity (NG) affects the large scale structure (LSS) of the universe by leaving an imprint on the distribution of matter at late times. Much attention has been focused on using the distribution of collapsed objects (i.e. dark matter halos and the galaxies and galaxy clusters that reside in them) to probe primordial NG. An equally interesting and complementary probe however is the abundance of extended underdense regions or voids in the LSS. The calculation of the abundance of voids using the excursion set formalism in the presence of primordial NG is subject to the same technical issues as the one for halos, which were discussed e.g. in arXiv:1005.1203. However, unlike the excursion set problem for halos which involved random walks in the presence of one barrier $\delta_c$, the void excursion set problem involves two barriers $\delta_v$ and $\delta_c$. This leads to a new complication introduced by what is called the "void-in-cloud" effect discussed in the literature, which is unique to the case of voids. We explore a path integral approach which allows us to carefully account for all these issues, leading to a rigorous derivation of the effects of primordial NG on void abundances. The void-in-cloud issue in particular makes the calculation conceptually rather different from the one for halos. However, we show that its final effect can be described by a simple yet accurate approximation. Our final void abundance function is valid on larger scales than the expressions of other authors, while being broadly in agreement with those expressions on smaller scales.Comment: 28 pages (18+appendices), 7 figures; v2 -- minor changes in sec 3.2, version published in PR

Elementary Darboux transformations and factorization

A general theorem on factorization of matrices with polynomial entries is proven and it is used to reduce polynomial Darboux matrices to linear ones. Some new examples of linear Darboux matrices are discussed.Comment: 10 page

MERCURY POLLUTION OF THE JURAMENTO RIVER WATER SYSTEM (SALTA PROVINCE, ARGENTINA)

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Retrospective Proteomic Screening of 100 Breast Cancer Tissues

The present investigation has been conducted on one hundred tissue fragments of breast cancer, collected and immediately cryopreserved following the surgical resection. The specimens were selected from patients with invasive ductal carcinoma of the breast, the most frequent and potentially aggressive type of mammary cancer, with the objective to increase the knowledge of breast cancer molecular markers potentially useful for clinical applications. The proteomic screening; by 2D-IPG and mass spectrometry; allowed us to identify two main classes of protein clusters: proteins expressed ubiquitously at high levels in all patients; and proteins expressed sporadically among the same patients. Within the group of ubiquitous proteins, glycolytic enzymes and proteins with anti-apoptotic activity were predominant. Among the sporadic ones, proteins involved in cell motility, molecular chaperones and proteins involved in the detoxification appeared prevalent. The data of the present study indicates that the primary tumor growth is reasonably supported by concurrent events: the inhibition of apoptosis and stimulation of cellular proliferation, and the increased expression of glycolytic enzymes with multiple functions. The second phase of the evolution of the tumor can be prematurely scheduled by the occasional presence of proteins involved in cell motility and in the defenses of the oxidative stress. We suggest that this approach on large-scale 2D-IPG proteomics of breast cancer is currently a valid tool that offers the opportunity to evaluate on the same assay the presence and recurrence of individual proteins, their isoforms and short forms, to be proposed as prognostic indicators and susceptibility to metastasis in patients operated on for invasive ductal carcinoma of the breast

Hypoxia up-regulates SERPINB3 through HIF-2\u3b1 in human liver cancer cells.

SERPINB3 is a cysteine-proteases inhibitor up-regulated in a significant number of cirrhotic patients carrying hepatocellular carcinoma (HCC) and recently proposed as a prognostic marker for HCC early recurrence. SERPINB3 has been reported to stimulate proliferation, inhibit apoptosis and, similar to what reported for hypoxia, to trigger epithelial-to-mesenchymal transition (EMT) and increased invasiveness in liver cancer cells. This study has investigated whether SERPINB3 expression is regulated by hypoxia-related mechanisms in liver cancer cells. Exposure of HepG2 and Huh7 cells to hypoxia up-regulated SERPINB3 transcription, protein synthesis and release in the extracellular medium. Hypoxia-dependent SERPINB3 up-regulation was selective (no change detected for SERPINB4) and operated through hypoxia inducible factor (HIF)-2\u3b1 (not HIF-1\u3b1) binding to SERPINB3 promoter, as confirmed by chromatin immuno-precipitation assay and silencing experiments employing specific siRNAs. HIF-2\u3b1-mediated SERPINB3 up-regulation under hypoxic conditions required intracellular generation of ROS. Immuno-histochemistry (IHC) and transcript analysis, performed in human HCC specimens, revealed co-localization of the two proteins in liver cancer cells and the existence of a positive correlation between HIF-2\u3b1 and SERPINB3 transcript levels, respectively. Hypoxia, through HIF-2\u3b1-dependent and redox-sensitive mechanisms, up-regulates the transcription, synthesis and release of SERPINB3, a molecule with a high oncogenic potential