Iteration of holomorphic functions in the complex plane

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Núria Fagella RabionetWhen a holomorphic function is iterated, it generates a dynamic system on the complex plane. In this project, we describe both the local and global behavior of the different orbits of a rational map on the complex plane (or the Riemann sphere). We mainly concentrate in the study of the dynamical plane (where initial conditions and orbits live) although we briefly discuss one parameter families of polynomials and their bifurcation loci, like the well known Mandelbrot set. Towards the end, we experiment with a singular perturbation of a family of cubic polynomials and explore the drastic changes that occur in the topology of their Julia sets

Pensamiento arbitrista y estructuras institucionales en la carrera de Indias (siglo XVII): entre la desincentivación y la represión

The Castilian arbitrism of the 17th century demonstrated great concern about the colonial trade; however, the Spanish Treasure Fleets are only moderately present in arbitrista culture. How can this paradox be explained? This paper proposes an argument based on three ideas: 1) there was a contradictory relationship between the arbitrista culture and the institutional system of the Fleets; 2) this relationship changed throughout the 17th century: during the first decades of the century the institutions disincentivized arbitrismo and, during the last ones, they tended to repress it; 3) this evolution is largely due to the transfer of the Fleets from Seville to Cadiz.El arbitrismo castellano del siglo XVII mostró una gran preocupación por el comercio colonial y, sin embargo, la carrera de Indias participó en la cultura arbitrista de forma moderada. ¿Cómo puede explicarse esta paradoja? Este artículo ofrece como respuesta una argumentación basada en tres ideas: 1) existió una relación contradictoria entre la cultura arbitrista y el aparato institucional de la carrera; 2) esa relación varió a lo largo del siglo XVII: durante las primeras décadas las instituciones desincentivaron el arbitrismo y, durante las últimas, tendieron más a reprimirlo; 3) tal evolución se debe en gran medida al desplazamiento del centro de la Carrera desde Sevilla hasta Cádiz

Kinetics of humoral immune response over 17 months of COVID-19 pandemic in a large cohort of healthcare workers in Spain : the ProHEpiC-19 study

Understanding the immune response to the SARS-CoV-2 virus is critical for efficient monitoring and control strategies. The ProHEpic-19 cohort provides a fine-grained description of the kinetics of antibodies after SARS-CoV-2 infection with an exceptional resolution over 17 months. We established a cohort of 769 healthcare workers including healthy and infected with SARS-CoV-2 in northern Barcelona to determine the kinetics of the IgM against the nucleocapsid (N) and the IgG against the N and spike (S) of SARS-CoV-2 in infected healthcare workers. The study period was from 5 May 2020 to 11 November 2021.We used non-linear mixed models to investigate the kinetics of IgG and IgM measured at nine time points over 17 months from the date of diagnosis. The model included factors of time, gender, and disease severity (asymptomatic, mild-moderate, severe-critical) to assess their effects and their interactions. 474 of the 769 participants (61.6%) became infected with SARS-CoV-2. Significant effects of gender and disease severity were found for the levels of all three antibodies. Median IgM(N) levels were already below the positivity threshold in patients with asymptomatic and mild-moderate disease at day 270 after the diagnosis, while IgG(N and S) levels remained positive at least until days 450 and 270, respectively. Kinetic modelling showed a general rise in both IgM(N) and IgG(N) levels up to day 30, followed by a decay with a rate depending on disease severity. IgG(S) levels remained relatively constant from day 15 over time. IgM(N) and IgG(N, S) SARS-CoV-2 antibodies showed a heterogeneous kinetics over the 17 months. Only the IgG(S) showed a stable increase, and the levels and the kinetics of antibodies varied according to disease severity. The kinetics of IgM and IgG observed over a year also varied by clinical spectrum can be very useful for public health policies around vaccination criteria in adult population. Regional Ministry of Health of the Generalitat de Catalunya (Call COVID19-PoC SLT16_04; NCT04885478). The online version contains supplementary material available at 10.1186/s12879-022-07696-6

Mortality from gastrointestinal congenital anomalies at 264 hospitals in 74 low-income, middle-income, and high-income countries: a multicentre, international, prospective cohort study

Summary Background Congenital anomalies are the fifth leading cause of mortality in children younger than 5 years globally. Many gastrointestinal congenital anomalies are fatal without timely access to neonatal surgical care, but few studies have been done on these conditions in low-income and middle-income countries (LMICs). We compared outcomes of the seven most common gastrointestinal congenital anomalies in low-income, middle-income, and high-income countries globally, and identified factors associated with mortality. Methods We did a multicentre, international prospective cohort study of patients younger than 16 years, presenting to hospital for the first time with oesophageal atresia, congenital diaphragmatic hernia, intestinal atresia, gastroschisis, exomphalos, anorectal malformation, and Hirschsprung’s disease. Recruitment was of consecutive patients for a minimum of 1 month between October, 2018, and April, 2019. We collected data on patient demographics, clinical status, interventions, and outcomes using the REDCap platform. Patients were followed up for 30 days after primary intervention, or 30 days after admission if they did not receive an intervention. The primary outcome was all-cause, in-hospital mortality for all conditions combined and each condition individually, stratified by country income status. We did a complete case analysis. Findings We included 3849 patients with 3975 study conditions (560 with oesophageal atresia, 448 with congenital diaphragmatic hernia, 681 with intestinal atresia, 453 with gastroschisis, 325 with exomphalos, 991 with anorectal malformation, and 517 with Hirschsprung’s disease) from 264 hospitals (89 in high-income countries, 166 in middleincome countries, and nine in low-income countries) in 74 countries. Of the 3849 patients, 2231 (58·0%) were male. Median gestational age at birth was 38 weeks (IQR 36–39) and median bodyweight at presentation was 2·8 kg (2·3–3·3). Mortality among all patients was 37 (39·8%) of 93 in low-income countries, 583 (20·4%) of 2860 in middle-income countries, and 50 (5·6%) of 896 in high-income countries (p<0·0001 between all country income groups). Gastroschisis had the greatest difference in mortality between country income strata (nine [90·0%] of ten in lowincome countries, 97 [31·9%] of 304 in middle-income countries, and two [1·4%] of 139 in high-income countries; p≤0·0001 between all country income groups). Factors significantly associated with higher mortality for all patients combined included country income status (low-income vs high-income countries, risk ratio 2·78 [95% CI 1·88–4·11], p<0·0001; middle-income vs high-income countries, 2·11 [1·59–2·79], p<0·0001), sepsis at presentation (1·20 [1·04–1·40], p=0·016), higher American Society of Anesthesiologists (ASA) score at primary intervention (ASA 4–5 vs ASA 1–2, 1·82 [1·40–2·35], p<0·0001; ASA 3 vs ASA 1–2, 1·58, [1·30–1·92], p<0·0001]), surgical safety checklist not used (1·39 [1·02–1·90], p=0·035), and ventilation or parenteral nutrition unavailable when needed (ventilation 1·96, [1·41–2·71], p=0·0001; parenteral nutrition 1·35, [1·05–1·74], p=0·018). Administration of parenteral nutrition (0·61, [0·47–0·79], p=0·0002) and use of a peripherally inserted central catheter (0·65 [0·50–0·86], p=0·0024) or percutaneous central line (0·69 [0·48–1·00], p=0·049) were associated with lower mortality. Interpretation Unacceptable differences in mortality exist for gastrointestinal congenital anomalies between lowincome, middle-income, and high-income countries. Improving access to quality neonatal surgical care in LMICs will be vital to achieve Sustainable Development Goal 3.2 of ending preventable deaths in neonates and children younger than 5 years by 2030