Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences

Integrability and non-integrability of periodic non-autonomous Lyness recurrences

This paper studies non-autonomous Lyness type recurrences of the form x_{n+2}=(a_n+x_n)/x_{n+1}, where a_n is a k-periodic sequence of positive numbers with prime period k. We show that for the cases k in {1,2,3,6} the behavior of the sequence x_n is simple(integrable) while for the remaining cases satisfying k not a multiple of 5 this behavior can be much more complicated(chaotic). The cases k multiple of 5 are studied separately.

Integrability and non-integrability of periodic non-autonomous Lyness recurrences (revised and enlarged version)

This paper studies non-autonomous Lyness type recurrences of the form xn+2 = (an+xn+1)=xn, where fang is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k 2 f1; 2; 3; 6g the behavior of the sequence fxng is simple (integrable) while for the remaining cases satisfying this behavior can be much more complicated (chaotic). We also show that the cases where k is a multiple of 5 present some di erent features.

Asymptotics of orthogonal polynomials via the Koosis theorem

The main aim of this short paper is to advertize the Koosis theorem in the mathematical community, especially among those who study orthogonal polynomials. We (try to) do this by proving a new theorem about asymptotics of orthogonal polynomi- als for which the Koosis theorem seems to be the most natural tool. Namely, we consider the case when a SzegÄo measure on the unit circumference is perturbed by an arbitrary measure inside the unit disk and an arbitrary Blaschke sequence of point masses outside the unit disk.

El espacio como producto social: variables arqueológicas para un análisis de la organización social en prehistoria

El espacio social es un concepto ambiguo cuyo componente material está determinado por el carácter del componente social, puesto que la organización de los objetos en el espacio y el espacio mismo, responden a las normas sociales del comportamiento humano. Partimos de la premisa que los residuos generados durante el proceso de producción y del consumo tienden a tener una distribución relativamente regular en el espacio físico. La ausencia de la aleatoriedad en la dispersión de estos restos solo significa que habían sido acumulados y depositados como restos de acciones previamente planificadas no-aleatoriamente. En este trabajo planteamos estudiar la organización y la producción del espacio social de una sociedad cazadora-recolectora concreta – la sociedad yámana - a través del análisis de las actividades cotidianas que figuran en las fuentes etnográficas y en el registro arqueológico. Con este fin creamos una metodología de trabajo interdisciplinaria, basada en un enfoque etnoarqueológico, y a través del estudio de las fuentes etnográficas, los trabajos etnoarqueológicos previos y el registro arquelógico concreto, descubrimos cuáles son las posibilidades y limitaciones de este tipo de estudios. Pudimos reconocer la regularidad espacial de los procesos de producción y reproducción social y a resolver algunas preguntas acerca del estudio de la organización social en prehistoria trabajando con los datos etnoarqueológicos obtenidos en los yacimientos Lanashuaia y Túnel VII (Tierra del Fuego, Argentina), analizando el registro extraido y trabajado en varias campañas de excavaciones arqueológicas en ultimos 25 años. El presente trabajo al fondo es un experimento etnoarqueológico estándar: partiendo de la observación etnográfica registramos unas recurrencias específicas entre algunas variables (por ejemplo: mujer/lugar/tipo de trabajo), intentamos extraer las variables definitorias de esas recurrencias, y finalmente las buscamos en el espacio definido arqueológicamente.  

Predictors of death among patients who completed tuberculosis treatment: a population-based cohort study.

Background: Mortality among patients who complete tuberculosis (TB) treatment is still high among vulnerable populations. The objective of the study was to identify the probability of death and its predictive factors in a cohort of successfully treated TB patients. Methods: A population-based retrospective longitudinal study was performed in Barcelona, Spain. All patients who successfully completed TB treatment with culture-confirmation and available drug susceptibility testing between 1995 1997 were retrospectively followed-up until December 31, 2005 by the Barcelona TB Control Program. Socio-demographic, clinical, microbiological and treatment variables were examined. Mortality, TB Program and AIDS registries were reviewed. Kaplan-Meier and a Cox regression methods with time-dependent covariates were used for the survival analysis, calculating the hazard ratio (HR) with 95% confidence intervals (CI). Results: Among the 762 included patients, the median age was 36 years, 520 (68.2%) were male, 178 (23.4%) HIV-infected, and 208 (27.3%) were alcohol abusers. Of the 134 (17.6%) injecting drug users (IDU), 123 (91.8%) were HIV-infected. A total of 30 (3.9%) recurrences and 173 deaths (22.7%) occurred (mortality rate: 3.4/100 person-years of follow-up). The predictors of death were: age between 4160 years old (HR: 3.5; CI:2.15.7), age greater than 60 years (HR: 14.6; CI:8.924), alcohol abuse (HR: 1.7; CI:1.22.4) and HIV-infected IDU (HR: 7.9; CI:4.713.3). Conclusions: The mortality rate among TB patients who completed treatment is associated with vulnerable populations such as the elderly, alcohol abusers, and HIV-infected IDU. We therefore need to fight against poverty, and promote and develop interventions and social policies directed towards these populations to improve their survival.

On periodic solutions of 2-periodic Lyness difference equations

We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) different from (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is not equal to b, then any odd period, except 1, appears.

Treatment of oral mucocele - scalpel versus C02 laser

Objective: To compare the results obtained after oral mucocele resection with the scalpel versus the CO2 laser, based on the complications and recurrences after surgery Patients and Methods: Of the 68 patients we studied who have mucocele, 38 were resected with a scalpel and the remaining 30 with the CO2 laser (5-7 W). Patient sex and age were documented, along with location of the lesion as well as size, symptoms, duration, etiological factors, type of treatment, complications and recurrences after surgical removal. Results: The sample comprised 40 males and 28 females, aged between 6-65 years. The histological diagnosis was extravasation mucocele in 95% of the cases. The most frequent location was the lower lip (73.5%). The mean lesion diameter was 9 mm , and in most cases no evident etiological factor was recorded. The mean duration of the lesion was 4 months. Among the cases of conventional surgical removal of mucocele, recurrence was recorded in 8.8% of the cases, and 13.2% of the patients suffered postoperative complications - the most frequent being the presence of fibrous scars. There were no complications or relapses after a minimum follow-up of 12 months in the cases subjected to CO2 laser treatment. Conclusions: Oral mucocele ablation with the CO2 laser offers more predictable results and fewer complications and recurrences than conventional resection with the scalpel

Some pneumococcal serotypes are more frequently associated with relapses of acute exacerbations in COPD patients

Objectives: To analyze the role of the capsular type in pneumococci causing relapse and reinfection episodes of acute exacerbation in COPD patients. Methods: A total of 79 patients with 116 recurrent episodes of acute exacerbations caused by S. pneumoniae were included into this study (1995–2010). A relapse episode was considered when two consecutive episodes were caused by the same strain (identical serotype and genotype); otherwise it was considered reinfection. Antimicrobial susceptibility testing (microdilution), serotyping (PCR, Quellung) and molecular typing (PFGE/MLST) were performed. Results: Among 116 recurrent episodes, 81 (69.8%) were reinfections, caused by the acquisition of a new pneumococcus,and 35 (30.2%) were relapses, caused by a pre-existing strain. Four serotypes (9V, 19F, 15A and 11A) caused the majority (60.0%) of relapses. When serotypes causing relapses and reinfection were compared, only two serotypes were associatedwith relapses: 9V (OR 8.0; 95% CI, 1.34–85.59) and 19F (OR 16.1; 95% CI, 1.84–767.20). Pneumococci isolated from relapses were more resistant to antimicrobials than those isolated from the reinfection episodes: penicillin (74.3% vs. 34.6%, p,0.001), ciprofloxacin (25.7% vs. 9.9%, p,0.027), levofloxacin (22.9% vs. 7.4%, p = 0.029), and co-trimoxazole (54.3% vs. 25.9%, p,0.001). Conclusions: Although the acquisition of a new S. pneumoniae strain was the most frequent cause of recurrences, a third ofthe recurrent episodes were caused by a pre-existing strain. These relapse episodes were mainly caused by serotypes 9V and 19F, suggesting an important role for capsular type

Empirical study of correlated survival times for recurrent events with proportional hazards margins and the effect of correlation and censoring.

Background: In longitudinal studies where subjects experience recurrent incidents over a period of time, such as respiratory infections, fever or diarrhea, statistical methods are required to take into account the within-subject correlation. Methods: For repeated events data with censored failure, the independent increment (AG), marginal (WLW) and conditional (PWP) models are three multiple failure models that generalize Cox"s proportional hazard model. In this paper, we revise the efficiency, accuracy and robustness of all three models under simulated scenarios with varying degrees of within-subject correlation, censoring levels, maximum number of possible recurrences and sample size. We also study the methods performance on a real dataset from a cohort study with bronchial obstruction. Results: We find substantial differences between methods and there is not an optimal method. AG and PWP seem to be preferable to WLW for low correlation levels but the situation reverts for high correlations. Conclusions: All methods are stable in front of censoring, worsen with increasing recurrence levels and share a bias problem which, among other consequences, makes asymptotic normal confidence intervals not fully reliable, although they are well developed theoretically.

Empirical study of correlated survival times for recurrent events with proportional hazards margins and the effect of correlation and censoring.

Background: In longitudinal studies where subjects experience recurrent incidents over a period of time, such as respiratory infections, fever or diarrhea, statistical methods are required to take into account the within-subject correlation. Methods: For repeated events data with censored failure, the independent increment (AG), marginal (WLW) and conditional (PWP) models are three multiple failure models that generalize Cox"s proportional hazard model. In this paper, we revise the efficiency, accuracy and robustness of all three models under simulated scenarios with varying degrees of within-subject correlation, censoring levels, maximum number of possible recurrences and sample size. We also study the methods performance on a real dataset from a cohort study with bronchial obstruction. Results: We find substantial differences between methods and there is not an optimal method. AG and PWP seem to be preferable to WLW for low correlation levels but the situation reverts for high correlations. Conclusions: All methods are stable in front of censoring, worsen with increasing recurrence levels and share a bias problem which, among other consequences, makes asymptotic normal confidence intervals not fully reliable, although they are well developed theoretically.

Some pneumococcal serotypes are more frequently associated with relapses of acute exacerbations in COPD patients

Objectives: To analyze the role of the capsular type in pneumococci causing relapse and reinfection episodes of acute exacerbation in COPD patients. Methods: A total of 79 patients with 116 recurrent episodes of acute exacerbations caused by S. pneumoniae were included into this study (1995–2010). A relapse episode was considered when two consecutive episodes were caused by the same strain (identical serotype and genotype); otherwise it was considered reinfection. Antimicrobial susceptibility testing (microdilution), serotyping (PCR, Quellung) and molecular typing (PFGE/MLST) were performed. Results: Among 116 recurrent episodes, 81 (69.8%) were reinfections, caused by the acquisition of a new pneumococcus,and 35 (30.2%) were relapses, caused by a pre-existing strain. Four serotypes (9V, 19F, 15A and 11A) caused the majority (60.0%) of relapses. When serotypes causing relapses and reinfection were compared, only two serotypes were associatedwith relapses: 9V (OR 8.0; 95% CI, 1.34–85.59) and 19F (OR 16.1; 95% CI, 1.84–767.20). Pneumococci isolated from relapses were more resistant to antimicrobials than those isolated from the reinfection episodes: penicillin (74.3% vs. 34.6%, p,0.001), ciprofloxacin (25.7% vs. 9.9%, p,0.027), levofloxacin (22.9% vs. 7.4%, p = 0.029), and co-trimoxazole (54.3% vs. 25.9%, p,0.001). Conclusions: Although the acquisition of a new S. pneumoniae strain was the most frequent cause of recurrences, a third ofthe recurrent episodes were caused by a pre-existing strain. These relapse episodes were mainly caused by serotypes 9V and 19F, suggesting an important role for capsular type