On the string Lie algebra

We construct an abelian representative for the crossed module associated to the string Lie algebra. We show how to apply this construction in order to define quasi-invariant tensors which serve to categorify the infinitesimal braiding on the category of g-modules given by an r-matrix, following Cirio-Martins.Comment: 29 page

Algebraic deformations of toric varieties II. Noncommutative instantons

We continue our study of the noncommutative algebraic and differential geometry of a particular class of deformations of toric varieties, focusing on aspects pertinent to the construction and enumeration of noncommutative instantons on these varieties. We develop a noncommutative version of twistor theory, which introduces a new example of a noncommutative four-sphere. We develop a braided version of the ADHM construction and show that it parametrizes a certain moduli space of framed torsion free sheaves on a noncommutative projective plane. We use these constructions to explicitly build instanton gauge bundles with canonical connections on the noncommutative four-sphere that satisfy appropriate anti-selfduality equations. We construct projective moduli spaces for the torsion free sheaves and demonstrate that they are smooth. We define equivariant partition functions of these moduli spaces, finding that they coincide with the usual instanton partition functions for supersymmetric gauge theories on C^2.Comment: 62 pages; v2: typos corrected, references updated; Final version to be published in Advances in Theoretical and Mathematical Physic

Algebraic deformations of toric varieties I. General constructions

We construct and study noncommutative deformations of toric varieties by combining techniques from toric geometry, isospectral deformations, and noncommutative geometry in braided monoidal categories. Our approach utilizes the same fan structure of the variety but deforms the underlying embedded algebraic torus. We develop a sheaf theory using techniques from noncommutative algebraic geometry. The cases of projective varieties are studied in detail, and several explicit examples are worked out, including new noncommutative deformations of Grassmann and flag varieties. Our constructions set up the basic ingredients for thorough study of instantons on noncommutative toric varieties, which will be the subject of the sequel to this paper.Comment: 54 pages; v2: Presentation of Grassmann and flag varieties improved, minor corrections; v3: Presentation of some parts streamlined, minor corrections, references added; final version to appear in Advances in Mathematic

Kidney regeneration: common themes from the embryo to the adult

The vertebrate kidney has an inherent ability to regenerate following acute damage. Successful regeneration of the injured kidney requires the rapid replacement of damaged tubular epithelial cells and reconstitution of normal tubular function. Identifying the cells that participate in the regeneration process as well as the molecular mechanisms involved may reveal therapeutic targets for the treatment of kidney disease. Renal regeneration is associated with the expression of genetic pathways that are necessary for kidney organogenesis, suggesting that the regenerating tubular epithelium may be “reprogrammed” to a less-differentiated, progenitor state. This review will highlight data from various vertebrate models supporting the hypothesis that nephrogenic genes are reactivated as part of the process of kidney regeneration following acute kidney injury (AKI). Emphasis will be placed on the reactivation of developmental pathways and how our understanding of the resulting regeneration process may be enhanced by lessons learned in the embryonic kidney.Fil: Cirio, Maria Cecilia. University of Pittsburgh; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: de Groh, Eric D.. University of Pittsburgh; Estados UnidosFil: de Caestecker, Mark P.. Vanderbilt University; Estados UnidosFil: Davidson, Alan J.. The University of Auckland; Nueva ZelandaFil: Hukriede, Neil A.. University of Pittsburgh; Estados Unido

Connected components of compact matrix quantum groups and finiteness conditions

We introduce the notion of identity component of a compact quantum group and that of total disconnectedness. As a drawback of the generalized Burnside problem, we note that totally disconnected compact matrix quantum groups may fail to be profinite. We consider the problem of approximating the identity component as well as the maximal normal (in the sense of Wang) connected subgroup by introducing canonical, but possibly transfinite, sequences of subgroups. These sequences have a trivial behaviour in the classical case. We give examples, arising as free products, where the identity component is not normal and the associated sequence has length 1. We give necessary and sufficient conditions for normality of the identity component and finiteness or profiniteness of the quantum component group. Among them, we introduce an ascending chain condition on the representation ring, called Lie property, which characterizes Lie groups in the commutative case and reduces to group Noetherianity of the dual in the cocommutative case. It is weaker than ring Noetherianity but ensures existence of a generating representation. The Lie property and ring Noetherianity are inherited by quotient quantum groups. We show that A_u(F) is not of Lie type. We discuss an example arising from the compact real form of U_q(sl_2) for q<0.Comment: 43 pages. Changes in the introduction. The relation between our and Wang's notions of central subgroup has been clarifie

Thin low-gain avalanche detectors for particle therapy applications

none18The University of Torino (UniTO) and the National Institute for Nuclear Physics (INFN-TO) are investigating the use of Ultra Fast Silicon Detectors (UFSD) for beam monitoring in radiobiological experiments with therapeutic proton beams. The single particle identification approach of solid state detectors aims at increasing the sensitivity and reducing the response time of the conventional monitoring devices, based on gas detectors. Two prototype systems are being developed to count the number of beam particles and to measure the beam energy with time-of-flight (ToF) techniques. The clinically driven precision (&lt; 1%) in the number of particles delivered and the uncertainty &lt; 1 mm in the depth of penetration (range) in radiobiological experiments (up to 108 protons/s fluxes) are the goals to be pursued. The future translation into clinics would allow the implementation of faster and more accurate treatment modalities, nowadays prevented by the limits of state-of-the-art beam monitors. The experimental results performed with clinical proton beams at CNAO (Centro Nazionale di Adroterapia Oncologica, Pavia) and CPT (Centro di Protonterapia, Trento) showed a counting inefficiency &lt;2% up to 100 MHz/cm2, and a deviation of few hundreds of keV of measured beam energies with respect to nominal ones. The progresses of the project are reported.noneVignati, A.; Donetti, M.; Fausti, F.; Ferrero, M.; Giordanengo, S.; Hammad Ali, O.; Mart Villarreal, O.A.; Mas Milian, F.; Mazza, G.; Monaco, V.; Sacchi, R.; Shakarami, Z.; Sola, V.; Staiano, A.; Tommasino, F.; Verroi, E.; Wheadon, R.; Cirio, R.Vignati, A.; Donetti, M.; Fausti, F.; Ferrero, M.; Giordanengo, S.; Hammad Ali, O.; Mart Villarreal, O. A.; Mas Milian, F.; Mazza, G.; Monaco, V.; Sacchi, R.; Shakarami, Z.; Sola, V.; Staiano, A.; Tommasino, F.; Verroi, E.; Wheadon, R.; Cirio, R

The quantum Cartan algebra associated to a bicovariant differential calculus

We associate to any (suitable) bicovariant differential calculus on a quantum group a Cartan Hopf algebra which has a left, respectively right, representation in terms of left, respectively right, Cartan calculus operators. The example of the Hopf algebra associated to the $4D_+$ differential calculus on $SU_q(2)$ is described.Comment: 20 pages, no figures. Minor corrections in the example in Section 4