Multiple-scale analysis of dynamical systems on the lattice

We propose a new approach to the multiple-scale analysis of difference equations, in the context of the finite operator calculus. We derive the transformation formulae that map any given dynamical system, continuous or discrete, into a rescaled discrete system, by generalizing a classical result due to Jordan. Under suitable analytical hypotheses on the function space we consider, the rescaled equations are of finite order. Our results are applied to the study of multiple-scale reductions of dynamical systems, and in particular to the case of a discrete nonlinear harmonic oscillator.     

Classification of discrete equations linearizable by point transformation on a square lattice

We provide a complete set of linearizability conditions for nonlinear partial difference equations defined on four points and, using them, we classify all linearizable multilinear partial difference equations defined on four points up to a Möbious transformation.     

Effects of Citicoline,Homotaurine, and Vitamin E on Contrast Sensitivity and Visual-Related Quality of Life in Patients with Primary Open-Angle Glaucoma: A Preliminary Study

The aim of the present study was to evaluate the effects of supplementation with a fixed combination of citicoline 500 mg, homotaurine 50 mg, and vitamin E 12 mg (CIT/HOMO/VITE) on contrast sensitivity and visual-related quality of life in patients with primary open-angle glaucoma (POAG) in mild stage. This was a multicenter, observational, cross-over, short-term, pilot study on POAG patients with stable controlled intraocular pressure (IOP). Patients were randomly assigned to Group 1 (current topical therapy for 4 months and then current topical therapy plus CIT/HOMO/VITE for 4 months) or Group 2 (CIT/HOMO/VITE in addition to current topical therapy for 4 months and then topical therapy alone for 4 months). Best-corrected visual acuity, IOP, visual field, and the Spaeth/Richman contrast sensitivity (SPARCS) test score were recorded at baseline and after 4 and 8 months. The Glaucoma Quality of Life-15 (GQL-15) questionnaire was administered at each check time. Forty-four patients were assigned to Group 1 and 65 to Group 2. Over the follow-up period, there were no significant changes in IOP or visual field findings, whereas SPARCS and GQL-15 findings significantly varied from baseline, both being improved in subjects treated with CIT/HOMO/VITE fixed combination. These results demonstrate that a daily intake of a fixed combination of citicoline, homotaurine, and vitamin E in addition to the topical medical treatment significantly increased the total score of the contrast sensitivity test and the quality of life in patients with POAG.     

Medical genetics services in the city of Sao Paulo, Brazil

The city of Sao Paulo is located in the center of a metropolitan area with nearly 18 million inhabitants and 300,000 births/year. The currently existing medical genetics services are unable to meet the demand, due to their insufficient physical and personnel infrastructure. Institutions and experts in medical genetics could give short training and refresher courses to health professionals to enable them to work in the public health network. The city has a reasonably well developed health care network, represented by the Single Health System (Sistema Unico de Saude - SUS) and by the Family Health Program (Programa de Saude da Familia - PSF). The financial resources for such actions originate in the budget of the managing agencies of such systems. The limitations of genetic services provided to the population of the city could be overcome in a short period of time by developing programs within the public health care network. The city has institutions, professionals and financial resources to make this project feasible. To that end, the competent authorities of the Sao Paulo State and City Secretariats of Health should take managerial responsibility for the genetic services in the city.     

Differential Equations Invariant Under Conditional Symmetries

Nonlinear PDE’s having given conditional symmetries are constructed. They are obtained starting from the invariants of the conditional symmetry generator and imposing the extra condition given by the characteristic of the symmetry. Series of examples starting from the Boussinesq and including non-autonomous Korteweg–de Vries like equations are given to show and clarify the methodology introduced.     

Time‐Dependent Free‐Particle Salpeter Equation: Numerical and Asymptotic Analysis in the Light of the Fundamental Solution

A detailed study of the spinless (1+1)D free‐particle Salpeter equation is presented. It involves several aspects of the topic: from the analysis of the behavior of solutions of the equation, both numerically evaluated and asymptotically approximated for definite initial conditions, to the comparison with the behavior of the corresponding solutions of the Schrödinger equation in order to both highlight the differences and to possibly understand how the latter “flow” in the former. Interesting analogies with other fields of physics, in particular with optics, are suggested.     

Clinical genetics in developing countries: the case of Brazil

There are many impediments to the progress of clinical and medical genetics in developing countries. Higher priorities concerning basic health care usually take precedence over genetic diseases and birth defects among medical professionals and public health officials. This is so in spite of the fact that the global prevalence of these conditions seems higher than in the developed world and that limited resources enhance the burden on individuals, families and populations. Furthermore, as a consequence of recent advances in medical genetics, demand for genetic services has increased, reinforcing the need for programs for the management and prevention of genetic diseases and birth defects, especially at primary health care level. An overview of these issues in Brazil is presented here, with information on the health system, the evolution of medical and clinical genetics in the country, and the situation of medical and clinical genetic services. We discuss proposals for implementing appropriate, ethically acceptable and equitable clinical genetic services for the Brazilian population.