Random Graphs Associated to some Discrete and Continuous Time Preferential Attachment Models

We give a common description of Simon, Barab\'asi--Albert, II-PA and Price growth models, by introducing suitable random graph processes with preferential attachment mechanisms. Through the II-PA model, we prove the conditions for which the asymptotic degree distribution of the Barab\'asi--Albert model coincides with the asymptotic in-degree distribution of the Simon model. Furthermore, we show that when the number of vertices in the Simon model (with parameter $\alpha$) goes to infinity, a portion of them behave as a Yule model with parameters $(\lambda,\beta) = (1-\alpha,1)$, and through this relation we explain why asymptotic properties of a random vertex in Simon model, coincide with the asymptotic properties of a random genus in Yule model. As a by-product of our analysis, we prove the explicit expression of the in-degree distribution for the II-PA model, given without proof in \cite{Newman2005}. References to traditional and recent applications of the these models are also discussed

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Gold-coated superparamagnetic nanoparticles for single methyl discrimination in DNA aptamers

Au- and iron-based magnetic nanoparticles (NPs) are promising NPs for biomedical applications due to their unique properties. The combination of a gold coating over a magnetic core puts together the benefits from adding the magnetic properties to the robust chemistry provided by the thiol functionalization of gold. Here, the use of Au-coated magnetic NPs for molecular detection of a single methylation in DNA aptamer is described. Binding of α-thrombin to two aptamers conjugated to these NPs causes aggregation, a phenomenon that can be observed by UV, DLS and MRI. These techniques discriminate a single methylation in one of the aptamers, preventing aggregation due to the inability of α-thrombin to recognize it. A parallel study with gold and ferromagnetic NPs is detailed, concluding that the Au coating of FexOy NP does not affect their performance and that they are suitable as complex biosensors. These results prove the high detection potency of Au-coated SPIONs for biomedical applications especially for DNA repair detection.The Communities MULTIFUN (contract NMP4-LA-2011-262943) and by “Ministerio Ciencia e Innovación” (grants CTQ-2010-20541-C03-03 and CTQ2014-52588-R) are acknowledged for financial support. Maria Tintoré was supported by a pre-doctoral fellowship (FPI) and a short stay grant (EEBB) from MINECO. Carme Fàbrega is grateful to Fundació La Marató de TV3 (20132032) for a research contract. We thank Dr. Susana Vilchez from the Surface Chemistry group at IQAC-CSIC for her help with the DLS experiments. Laura Polito thanks RSPPTECH—Convenzione Operativa inserita nella Raccolta Convenzioni e Contratti della Regione Lombardia (grant number 18095/RU) and the Italian Ministero dell’Università e della Ricerca (MIUR) (PRIN 2010–2011, contract number 2010JMAZML_003). We acknowledge support by the CSIC Open Access Publication Initiative through its Unit of Information Resources for Research (URICI)Peer reviewe

Eucalyptus cinerea and E. nicholii by-Products as Source of Bioactive Compounds for Agricultural Applications

The cultivation of different species of Eucalyptus has recently expanded in Liguria (Italy) due to the growing demand of the North European floricultural market. Eucalyptus tree branches are cut and selected for their quality, resulting in large amounts of waste biomass to be disposed of. The aim of our study was to evaluate the phytotoxic and antimicrobial activities of essential oils (EOs) from pruning wastes of E. cinerea (EC) and E. nicholii (EN), for potential applications in agriculture. Phytochemical analyses showed eucalyptol (1,8-cineole) as the major component in both EOs, but the EO yield of EN was higher than that of EC, in agreement with a significantly higher oil gland density on EN leaves. EOs from both species showed phytotoxicity on both weeds tested, but no significant inhibition on horticultural crop seed germination, except for Raphanus sativus. The EO from EC showed the strongest antibacterial activity, while the EO from EN showed the strongest antifungal activity. Concluding, EOs from Eucalyptus pruning may be used as possible alternatives to synthetic herbicides and pesticides, acting as antimicrobial and antifungal agents, thus representing a safe strategy for crop management programs