Linearization of analytic and non--analytic germs of diffeomorphisms of (C,0)({\mathbb C},0)

We study Siegel's center problem on the linearization of germs of diffeomorphisms in one variable. In addition of the classical problems of formal and analytic linearization, we give sufficient conditions for the linearization to belong to some algebras of ultradifferentiable germs closed under composition and derivation, including Gevrey classes. In the analytic case we give a positive answer to a question of J.-C. Yoccoz on the optimality of the estimates obtained by the classical majorant series method. In the ultradifferentiable case we prove that the Brjuno condition is sufficient for the linearization to belong to the same class of the germ. If one allows the linearization to be less regular than the germ one finds new arithmetical conditions, weaker than the Brjuno condition. We briefly discuss the optimality of our results.Comment: AMS-Latex2e, 11 pages, in press Bulletin Societe Mathematique de Franc

Clinical significance of epithelial-to-mesenchymal transition in laryngeal carcinoma: Its role in the different subsites

Background: During epithelial-to-mesenchymal transition, cancer cells lose adhesion capacity gaining migratory properties. The role of the process on prognosis has been evaluated in 50 cases of laryngeal carcinoma. Methods: E-cadherin, N-cadherin, β-catenin, α-catenin, γ-catenin, caveolin-1, and vimentin immunohistochemical expression were evaluated using a double score based on staining intensity and cellular localization. Results: Cytoplasmic E-cadherin and α/γ catenin staining were associated with a decrease in survival, cytoplasmic β-catenin was associated with advanced stage, and N-cadherin and vimentin expression were associated with poor differentiation and tumor relapse. On the basis of cancer cells, epithelial or mesenchymal morphological and immunophenotypic similarity we identified 4 main subgroups correlated with a transition to a more undifferentiated phenotype, which have a different pattern of relapse and survival. Conclusion: The negative prognostic role of epithelial-to-mesenchymal transition has been confirmed and a predictive role in glottic tumors has been suggested, leading us to propose epithelial-to-mesenchymal transition as an additional adverse feature in laryngeal carcinoma

A new regression model for the forecasting of COVID-19 outbreak evolution: an application to Italian data

none5noThe novel coronavirus SARS-CoV-2 was first identified in China in December 2019. In just over five months, the virus affected over 4 million people and caused about 300,000 deaths. This study aimed to model new COVID-19 cases in Italian regions using a new curve. A new empirical curve is proposed to model the number of new cases of COVID-19. It resembles a known exponential growth curve, which has a straight line as an exponent, but in the growth curve proposed, the exponent is a logistic curve multiplied for a straight line. This curve shows an initial phase, the expected exponential growth, then rises to the maximum value and finally reaches zero. We characterized the epidemic growth patterns for the entire Italian nation and each of the 20 Italian regions. The estimated growth curve has been used to calculate the expected time of the beginning, the time related to peak, and the end of the epidemics. Our analysis explores the development of the outbreaks in Italy and the impact of the containment measures. Data obtained are useful to forecast future scenarios and the possible end of the epidemic.openD. Sisti, S. Amatori, E. Rocchi, S. Peluso, M. CarlettiSisti, D.; Amatori, S.; Rocchi, E.; Peluso, S.; Carletti, M

Digital humanities and crowdsourcing: an exploration

publication-status: Published‘Crowdsourcing’ is a recent and evolving phenomenon, and the term has been broadly adopted to define different shades of public participation and contribution. Cultural institutions are progressively exploring crowdsourcing, and projects’ related research is increasing. Nonetheless, few studies in the digital humanities have investigated crowdsourcing as a whole. The aim of this paper is to shed light on crowdsourcing practices in the digital humanities, thus providing insights to design new paths of collaboration between cultural organisations and their audiences. A web survey was carried out on 36 crowdsourcing projects promoted by galleries, libraries, archives, museums, and education institutions. A variety of practices emerged from the research. Even though, it seems that there is no ‘one-solution-fits-all’ for crowdsourcing in the cultural domain, few reflections are presented to support the development of crowdsourcing initiatives.Horizon Digital Economy Research Hu

Noisy continuous--opinion dynamics

We study the Deffuant et al. model for continuous--opinion dynamics under the influence of noise. In the original version of this model, individuals meet in random pairwise encounters after which they compromise or not depending of a confidence parameter. Free will is introduced in the form of noisy perturbations: individuals are given the opportunity to change their opinion, with a given probability, to a randomly selected opinion inside the whole opinion space. We derive the master equation of this process. One of the main effects of noise is to induce an order-disorder transition. In the disordered state the opinion distribution tends to be uniform, while for the ordered state a set of well defined opinion groups are formed, although with some opinion spread inside them. Using a linear stability analysis we can derive approximate conditions for the transition between opinion groups and the disordered state. The master equation analysis is compared with direct Monte-Carlo simulations. We find that the master equation and the Monte-Carlo simulations do not always agree due to finite-size induced fluctuations that we analyze in some detail

Emerging structures in social networks guided by opinions’ exchanges

n this paper, we show that the small world and weak ties phenomena can spontaneously emerge in a social network of interacting agents. This dynamics is simulated in the framework of a simplified model of opinion diffusion in an evolving social network where agents are made to interact, possibly update their beliefs and modify the social relationships according to the opinion exchange

Scaling of the Critical Function for the Standard Map: Some Numerical Results

The behavior of the critical function for the breakdown of the homotopically non-trivial invariant (KAM) curves for the standard map, as the rotation number tends to a rational number, is investigated using a version of Greene's residue criterion. The results are compared to the analogous ones for the radius of convergence of the Lindstedt series, in which case rigorous theorems have been proved. The conjectured interpolation of the critical function in terms of the Bryuno function is discussed.Comment: 26 pages, 3 figures, 13 table