Spin Foams and Noncommutative Geometry

We extend the formalism of embedded spin networks and spin foams to include topological data that encode the underlying three-manifold or four-manifold as a branched cover. These data are expressed as monodromies, in a way similar to the encoding of the gravitational field via holonomies. We then describe convolution algebras of spin networks and spin foams, based on the different ways in which the same topology can be realized as a branched covering via covering moves, and on possible composition operations on spin foams. We illustrate the case of the groupoid algebra of the equivalence relation determined by covering moves and a 2-semigroupoid algebra arising from a 2-category of spin foams with composition operations corresponding to a fibered product of the branched coverings and the gluing of cobordisms. The spin foam amplitudes then give rise to dynamical flows on these algebras, and the existence of low temperature equilibrium states of Gibbs form is related to questions on the existence of topological invariants of embedded graphs and embedded two-complexes with given properties. We end by sketching a possible approach to combining the spin network and spin foam formalism with matter within the framework of spectral triples in noncommutative geometry.Comment: 48 pages LaTeX, 30 PDF figure

DNA damage in lens epithelial cells exposed to occupationally-relevant X-ray doses and role in cataract formation

The current framework of radiological protection of occupational exposed medical workers reduced the eye-lens equivalent dose limit from 150 to 20 mSv per year requiring an accurate dosimetric evaluation and an increase understanding of radiation induced effects on Lens cells considering the typical scenario of occupational exposed medical operators. Indeed, it is widely accepted that genomic damage of Lens epithelial cells (LEC) is a key mechanism of cataractogenesis. However, the relationship between apoptosis and cataractogenesis is still controversial. In this study biological and physical data are combined to improve the understanding of radiation induced effects on LEC. To characterize the occupational exposure of medical workers during angiographic procedures an INNOVA 4100 (General Electric Healthcare) equipment was used (scenario A). Additional experiments were conducted using a research tube (scenario B). For both scenarios, the frequencies of binucleated cells, micronuclei, p21-positive cells were assessed with different doses and dose rates. A Monte-Carlo study was conducted using a model for the photon generation with the X-ray tubes and with the Petri dishes considering the two different scenarios (A and B) to reproduce the experimental conditions and validate the irradiation setups to the cells. The simulation results have been tallied using the Monte Carlo code MCNP6. The spectral characteristics of the different X-ray beams have been estimated. All irradiated samples showed frequencies of micronuclei and p21-positive cells higher than the unirradiated controls. Differences in frequencies increased with the delivered dose measured with Gafchromic films XR-RV3. The spectrum incident on eye lens and Petri, as estimated with MCNP6, was in good agreement in the scenario A (confirming the experimental setup), while the mean energy spectrum was higher in the scenario B. Nevertheless, the response of LEC seemed mainly related to the measured absorbed dose. No effects on viability were detected. Our results support the hypothesis that apoptosis is not responsible for cataract induced by low doses of X-ray (i.e. 25 mGy) while the induction of transient p21 may interfere with the disassembly of the nuclear envelop in differentiating LEC, leading to cataract formation. Further studies are needed to better clarify the relationship we suggested between DNA damage, transient p21 induction and the inability of LEC enucleation

Compact 3-manifolds via 4-colored graphs

We introduce a representation of compact 3-manifolds without spherical boundary components via (regular) 4-colored graphs, which turns out to be very convenient for computer aided study and tabulation. Our construction is a direct generalization of the one given in the eighties by S. Lins for closed 3-manifolds, which is in turn dual to the earlier construction introduced by Pezzana's school in Modena. In this context we establish some results concerning fundamental groups, connected sums, moves between graphs representing the same manifold, Heegaard genus and complexity, as well as an enumeration and classification of compact 3-manifolds representable by graphs with few vertices ($\le 6$ in the non-orientable case and $\le 8$ in the orientable one).Comment: 25 pages, 11 figures; changes suggested by referee: references added, figure 2 modified, results about classification of the manifolds in Proposition 17 announced at the end of section 9. Accepted for publication in RACSAM. The final publication is available at Springer (see DOI

Branchfold and rational conifolds

We extend the concept of orbifold to that of branchfold, in order to allow cone singularities with rational angles, and we show why branchfolds naturally fit in the theory of branched coverings. Then, we obtain a geometric goodness theorem for branchfolds and apply it to prove that a conifold can be endowed with a branchfold structure if and only if it has locally finite holonomy

Clinical trial on the efficacy of dental polishing in oral hygiene maintenance procedures (Studio clinico sull'efficacia del polishing nelle sedute di mantenimento)

Procedure di mantenimento dell'igiene dental