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

A Loop Grammar to Understand the roles of miRNAs in the Tumor Cell

A miRNA is a small non-coding RNA molecule that regulates gene expression. Current studies showed that miRNAs may function both as oncogenes and as tumor suppressors, but not revealed the precise conditions that cause miRNAs to alter gene expression of the cancer cells. In this study, we introduce a context-free grammar, Loop Grammar, that formalizes the primary and secondary structure as a composition of loops, corresponding to concatenation or nesting of hairpins. We also formalize the concatenation and nesting on fatgraphs, oriented surfaces with boundary, and we define a Surface Loop Grammar, whose algebraic expressions uniquely identify such surfaces associated to given RNA structures. The Loop Grammar has been used to model tumor and healthy miRNAs of the mir-515 family, and we observed that the mutations of elements of primary structure involved in loops formation changed the secondary structure of tumor miRNAs. The Surface Loop Grammar is useful to classify RNA structures in terms of loops and relations among them. References: 1) Peng, Y., Croce, C. M. The role of MicroRNAs in human cancer. Signal transduction and targeted therapy, 2016, 1, 15004. 2) Penner, R.C., Knudsen, M., Wiuf, C., Andersen, J.E., Fatgraph models of proteins. Communications on Pure and Applied Mathematics, 2010, 63(10), 1249–1297 3) Quadrini, M., Culmone, R., Merelli, E.: Topological Classification of RNA Structures via Intersection Graph. In: International Conference on Theory and Practice of Natural Computing, Springer, 2017, 203–215 4) Quadrini, M., Merelli, E.: Loop-loop interaction metrics on RNA secondary structures with pseudoknotsth International Conference on Bioinformatics Models, Methods and Algorithms, Proceedings; Part of 11th International Joint Conference on Biomedical Engineering Systems and Technologies, BIOSTEC 2018 3, 2018

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

Exploring event horizons and Hawking radiation through deformed graphene membranes

Analogue gravitational systems are becoming an increasing popular way of studying the behaviour of quantum systems in curved spacetime. Setups based on ultracold quantum gases in particular, have been recently harnessed to explore the thermal nature of Hawking's and Unruh's radiation that was theoretically predicted almost 50 years ago. For solid state implementations, a promising system is graphene, in which a link between the Dirac-like low-energy electronic excitations and relativistic quantum field theories has been unveiled soon after its discovery. This link could be extended to the case of curved quantum field theory when the graphene sheet is shaped in a surface of constant negative curvature, known as Beltrami's pseudosphere. Here we provide numerical evidence that energetically stable negative curvature graphene surfaces can be realized. Owing to large-scale simulations, our geometrical realizations are characterized by a ratio between the carbon-carbon bond length and the pseudosphere radius small enough to allow the formation of an analog of a black hole event horizon. Additionally, from the energy dependence of the spatially resolved density of states, we infer some thermal properties of the corresponding gravitational system, which could be investigated using low temperature scanning tunnelling microscopy or optical near field spectroscopy. These findings pave the way to the realization of a solid-state system in which the curved spacetime dynamics of quantum many body systems can be investigated