Reply to Comment on "Synchronization dynamics in non-normal networks: the trade-off for optimality"

We reply to the recent note "Comment on Synchronization dynamics in non-normal networks: the trade-off for optimality", showing that the authors base their claims mainly on general theoretical arguments that do not necessarily invalidate the adequacy of our previous study. In particular, they do not specifically tackle the correctness of our analysis but instead limit their discussion on the interpretation of our results and conclusions, particularly related to the concept of optimality of network structure related to synchronization dynamics. Nevertheless, their idea of optimal networks is strongly biased towards their previous work and does not necessarily correspond to our framework, making their interpretation subjective and not consistent. We bring here further evidence from the existing and more recent literature, omitted in the Comment note, that the synchronized state of oscillators coupled through optimal networks, as intended by the authors, can indeed be highly fragile to small but finite perturbations, confirming our original results

Analytical study of non Gaussian fluctuations in a stochastic scheme of autocatalytic reactions

A stochastic model of autocatalytic chemical reactions is studied both numerically and analytically. The van Kampen perturbative scheme is implemented, beyond the second order approximation, so to capture the non Gaussianity traits as displayed by the simulations. The method is targeted to the characterization of the third moments of the distribution of fluctuations, originating from a system of four populations in mutual interaction. The theory predictions agree well with the simulations, pointing to the validity of the van Kampen expansion beyond the conventional Gaussian solution.Comment: 15 pages, 8 figures, submitted to Phys. Rev.

Perturbation Theory and Control in Classical or Quantum Mechanics by an Inversion Formula

We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the Lie- algebra of observables. We give a bound for the perturbation in order to solve this inversion. And apply this result to a particular case of the control theory, as a first example, and to the ``quantum adiabatic transformation'', as another example.Comment: Version 8.0. 26 pages, Latex2e, final version published in J. Phys.

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

Isolation and genotyping of Acanthamoeba strains from corneal infections in Italy

Acanthamoeba keratitis (AK) is a corneal disease caused by members of a genus of free-living amoebae and is associated predominantly with contact lens (CL) use. This study reports 16 cases of culture-proven AK diagnosed in northern Italy. Genotype identification was carried out with a PCR assay based on sequence analysis of the 18S rRNA gene, and sensitivity and specificity were evaluated in comparison with traditional parasitological techniques. A 405 bp region of the 18S rRNA gene (ASA.S1) including diagnostic fragment 3 (DF3) was amplified using the genus-specific primers JDP1 and JDP2. Genotype assignment was based on phenetic analysis of the ASA.S1 subset of the nuclear small-subunit rRNA gene sequence excluding the highly variable DF3 region. Phylogenetic analysis was also performed on the sequences obtained. All patients complained of monolateral infection; 11 (68.75%) admitted improper CL disinfection. In 14/16 (87.5 %) subjects, corneal scrapings were stained with calcofluor white and haematoxylin and eosin and, in ten cases (62.5 %), microscopy was positive for Acanthamoeba cysts. In vitro culture on 3 % non-nutrient agar plates was obtained in all cases (100 %), whereas cloning and axenic growth were positive for 14 amoebic stocks (87.5 %). PCR analysis had 100 % sensitivity and specificity compared with in vitro axenic culture, showing positive amplification from 15 isolates. All Acanthamoeba strains belonged to the T4 genotype, the main AK-related genotype worldwide. These results confirmed the importance of a complete diagnostic protocol, including a PCR assay, for the clinical diagnosis of AK on biological samples. Genotyping allowed inclusion of all isolates in the T4 group, thus demonstrating the prevalence of this genotype in northern Italy