Mapping stability : real rational maps of degree zero

In memory of our beloved Professor José Rodrigues Santos de Sousa Ramos (1948-2007), who João Cabral, one of the authors of this paper, had the honor of being his student between 2000 and 2006, we wrote this paper following the research by experimentation, using the new technologies to capture a new insight about a problem, as him so much love to do it. His passion was to create new relations between different fields of mathematics. He was a builder of bridges of knowledge, encouraging the birth of new ways to understand this science. One of the areas that Sousa Ramos researched was the iteration of maps and the description of its behavior, using the symbolic dynamics. So, in this issue of this journal, honoring his memory, we use experimental results to find some stable regions of a specific family of real rational maps, the ones that he worked with João Cabral. In this paper we describe a parameter space (a,b) to the real rational maps fa,b(x) = (x2 −a)/(x2 −b), using some tools of dynamical systems, as the study of the critical point orbit and Lyapunov exponents. We give some results regarding the stability of these family of maps when we iterate it, specially the ones connected to the order 3 of iteration. We hope that our results would help to understand better the behavior of these maps, preparing the ground to a more efficient use of the Kneading Theory on these family of maps, using symbolic dynamics.

Hydrogen peroxide sensing, signaling and regulation of transcription factors

The regulatory mechanisms by which hydrogen peroxide (H2O2) modulates the activity of transcription factors in bacteria (OxyR and PerR), lower eukaryotes (Yap1, Maf1, Hsf1 and Msn2/4) and mammalian cells (AP-1, NRF2, CREB, HSF1, HIF-1, TP53, NF-κB, NOTCH, SP1 and SCREB-1) are reviewed. The complexity of regulatory networks increases throughout the phylogenetic tree, reaching a high level of complexity in mammalians. Multiple H2O2 sensors and pathways are triggered converging in the regulation of transcription factors at several levels: (1) synthesis of the transcription factor by upregulating transcription or increasing both mRNA stability and translation; (ii) stability of the transcription factor by decreasing its association with the ubiquitin E3 ligase complex or by inhibiting this complex; (iii) cytoplasm-nuclear traffic by exposing/masking nuclear localization signals, or by releasing the transcription factor from partners or from membrane anchors; and, (iv) DNA binding and nuclear transactivation by modulating transcription factor affinity towards DNA, co-activators or repressors, and by targeting specific regions of chromatin to activate individual genes. We also discuss how H2O2 biological specificity results from diverse thiol protein sensors, with different reactivity of their sulfhydryl groups towards H2O2, being activated by different concentrations and times of exposure to H2O2. The specific regulation of local H2O2 concentrations is also crucial and results from H2O2 localized production and removal controlled by signals. Finally, we formulate equations to extract from typical experiments quantitative data concerning H2O2 reactivity with sensor molecules. Rate constants of 140 M-1s−1 and ≥ 1.3 × 103 M-1s−1 were estimated, respectively, for the reaction of H2O2 with KEAP1 and with an unknown target that mediates NRF2 protein synthesis. In conclusion, the multitude of H2O2 targets and mechanisms provides an opportunity for highly specific effects on gene regulation that depend on the cell type and on signals received from the cellular microenvironment.

Mathematical education and interdisciplinarity : promoting public awareness of mathematics in the Azores

Mathematical literacy in Portugal is very unsatisfactory in what concerns international standards. Even more disturbingly, the Azores archipelago ranks as one of the worst regions of Portugal in this respect. We reason that the popularisation of Mathematics through interactive exhibitions and activities can contribute actively to disseminate mathematical knowledge, increase awareness of the importance of Mathematics in today’s world and change its negative perception by the majority of the citizens. Although a significant investment has been undertaken by the local regional government in creating several science centres for the popularisation of Science, there is no centre for the popularisation of Mathematics. We present our first steps towards bringing Mathematics to unconventional settings by means of hands-on activities. We describe in some detail three activities. One activity has to do with applying trigonometry to measure distances in Astronomy, which can also be applied to Earth objects. Another activity concerns the presence of numerical patterns in the Azorean flora. The third activity explores geometrical patterns in the Azorean cultural heritage. It is our understanding that the implementation of these and other easy-to-follow and challenging activities will contribute to the awareness of the importance and beauty of Mathematics.

Shear-induced lamellar phase of an ionic liquid crystal at room temperature

The phase behaviour of a number of N-alkylimidazolium salts was studied using polarizing optical microscopy, differential scanning calorimetry and X-ray diffraction. Two of these compounds exhibit lamellar mesophases at temperatures above 50 degrees C. In these systems, the liquid crystalline behaviour may be induced at room temperature by shear. Sheared films of these materials, observed between crossed polarisers, have a morphology that is typical of (wet) liquid foams: they partition into dark domains separated by brighter (birefringent) walls, which are approximately arcs of circle and meet at "Plateau borders" with three or more sides. Where walls meet three at a time, they do so at approximately 120 degrees angles. These patterns coarsen with time and both T1 and T2 processes have been observed, as in foams. The time evolution of domains is also consistent with von Neumann's law. We conjecture that the bright walls are regions of high concentration of defects produced by shear, and that the system is dominated by the interfacial tension between these walls and the uniform domains. The control of self-organised monodomains, as observed in these systems, is expected to play an important role in potential applications.

Analysis and visualization of seismic data using mutual information

Seismic data is difficult to analyze and classical mathematical tools reveal strong limitations in exposing hidden relationships between earthquakes. In this paper, we study earthquake phenomena in the perspective of complex systems. Global seismic data, covering the period from 1962 up to 2011 is analyzed. The events, characterized by their magnitude, geographic location and time of occurrence, are divided into groups, either according to the Flinn-Engdahl (F-E) seismic regions of Earth or using a rectangular grid based in latitude and longitude coordinates. Two methods of analysis are considered and compared in this study. In a first method, the distributions of magnitudes are approximated by Gutenberg-Richter (G-R) distributions and the parameters used to reveal the relationships among regions. In the second method, the mutual information is calculated and adopted as a measure of similarity between regions. In both cases, using clustering analysis, visualization maps are generated, providing an intuitive and useful representation of the complex relationships that are present among seismic data. Such relationships might not be perceived on classical geographic maps. Therefore, the generated charts are a valid alternative to other visualization tools, for understanding the global behavior of earthquakes.

Fractional dynamics and MDS visualization of earthquake phenomena

This paper analyses earthquake data in the perspective of dynamical systems and fractional calculus (FC). This new standpoint uses Multidimensional Scaling (MDS) as a powerful clustering and visualization tool. FC extends the concepts of integrals and derivatives to non-integer and complex orders. MDS is a technique that produces spatial or geometric representations of complex objects, such that those objects that are perceived to be similar in some sense are placed on the MDS maps forming clusters. In this study, over three million seismic occurrences, covering the period from January 1, 1904 up to March 14, 2012 are analysed. The events are characterized by their magnitude and spatiotemporal distributions and are divided into fifty groups, according to the Flinn–Engdahl (F–E) seismic regions of Earth. Several correlation indices are proposed to quantify the similarities among regions. MDS maps are proven as an intuitive and useful visual representation of the complex relationships that are present among seismic events, which may not be perceived on traditional geographic maps. Therefore, MDS constitutes a valid alternative to classic visualization tools for understanding the global behaviour of earthquakes.

Water quality in lakes and reservoirs in China

Dissertation elaborated for the partial fulfilment of the requirements of the Master Degree in Civil Engineering in the Speciality Area of Hydarulics

Dynamic analysis of earthquake phenomena by means of pseudo phase plane

This paper analyses earthquake data in the perspective of dynamical systems and its Pseudo Phase Plane representation. The seismic data is collected from the Bulletin of the International Seismological Centre. The geological events are characterised by their magnitude and geographical location and described by means of time series of sequences of Dirac impulses. Fifty groups of data series are considered, according to the Flinn-Engdahl seismic regions of Earth. For each region, Pearson’s correlation coefficient is used to find the optimal time delay for reconstructing the Pseudo Phase Plane. The Pseudo Phase Plane plots are then analysed and characterised.

Temporal trends and spatial distribution of unsafe abortion in Brazil, 1996-2012

OBJECTIVE To analyze temporal trends and distribution patterns of unsafe abortion in Brazil. METHODS Ecological study based on records of hospital admissions of women due to abortion in Brazil between 1996 and 2012, obtained from the Hospital Information System of the Ministry of Health. We estimated the number of unsafe abortions stratified by place of residence, using indirect estimate techniques. The following indicators were calculated: ratio of unsafe abortions/100 live births and rate of unsafe abortion/1,000 women of childbearing age. We analyzed temporal trends through polynomial regression and spatial distribution using municipalities as the unit of analysis. RESULTS In the study period, a total of 4,007,327 hospital admissions due to abortions were recorded in Brazil. We estimated a total of 16,905,911 unsafe abortions in the country, with an annual mean of 994,465 abortions (mean unsafe abortion rate: 17.0 abortions/1,000 women of childbearing age; ratio of unsafe abortions: 33.2/100 live births). Unsafe abortion presented a declining trend at national level (R2: 94.0%, p < 0.001), with unequal patterns between regions. There was a significant reduction of unsafe abortion in the Northeast (R2: 93.0%, p < 0.001), Southeast (R2: 92.0%, p < 0.001) and Central-West regions (R2: 64.0%, p < 0.001), whereas the North (R2: 39.0%, p = 0.030) presented an increase, and the South (R2: 22.0%, p = 0.340) remained stable. Spatial analysis identified the presence of clusters of municipalities with high values for unsafe abortion, located mainly in states of the North, Northeast and Southeast Regions. CONCLUSIONS Unsafe abortion remains a public health problem in Brazil, with marked regional differences, mainly concentrated in the socioeconomically disadvantaged regions of the country. Qualification of attention to women’s health, especially to reproductive aspects and attention to pre- and post-abortion processes, are necessary and urgent strategies to be implemented in the country.

Evaluation of maternal and neonatal hospital care: quality index of completeness

OBJECTIVE Develop an index to evaluate the maternal and neonatal hospital care of the Brazilian Unified Health System.METHODS This descriptive cross-sectional study of national scope was based on the structure-process-outcome framework proposed by Donabedian and on comprehensive health care. Data from the Hospital Information System and the National Registry of Health Establishments were used. The maternal and neonatal network of Brazilian Unified Health System consisted of 3,400 hospitals that performed at least 12 deliveries in 2009 or whose number of deliveries represented 10.0% or more of the total admissions in 2009. Relevance and reliability were defined as criteria for the selection of variables. Simple and composite indicators and the index of completeness were constructed and evaluated, and the distribution of maternal and neonatal hospital care was assessed in different regions of the country.RESULTS A total of 40 variables were selected, from which 27 single indicators, five composite indicators, and the index of completeness of care were built. Composite indicators were constructed by grouping simple indicators and included the following variables: hospital size, level of complexity, delivery care practice, recommended hospital practice, and epidemiological practice. The index of completeness of care grouped the five variables and classified them in ascending order, thereby yielding five levels of completeness of maternal and neonatal hospital care: very low, low, intermediate, high, and very high. The hospital network was predominantly of small size and low complexity, with inadequate child delivery care and poor development of recommended and epidemiological practices. The index showed that more than 80.0% hospitals had a low index of completeness of care and that most qualified heath care services were concentrated in the more developed regions of the country.CONCLUSIONS The index of completeness proved to be of great value for monitoring the maternal and neonatal hospital care of Brazilian Unified Health System and indicated that the quality of health care was unsatisfactory. However, its application does not replace specific evaluations.

Prescription, dispensation and marketing patterns of methylphenidate

OBJECTIVE To analyze the patterns and legal requirements of methylphenidate consumption. METHODS We conducted a cross-sectional study of the data from prescription notification forms and balance lists of drugs sales – psychoactive and others – subject to special control in the fifth largest city of Brazil, in 2006. We determined the defined and prescribed daily doses, the average prescription and dispensation periods, and the regional sales distribution in the municipality. In addition, we estimated the costs of drug acquisition and analyzed the individual drug consumption profile using the Lorenz curve. RESULTS The balance lists data covered all notified sales of the drug while data from prescription notification forms covered 50.6% of the pharmacies that sold it, including those with the highest sales volumes. Total methylphenidate consumption was 0.37 DDD/1,000 inhabitants/day. Sales were concentrated in more developed areas, and regular-release tablets were the most commonly prescribed pharmaceutical formulation. In some regions of the city, approximately 20.0% of the prescriptions and dispensation exceeded 30 mg/day and 30 days of treatment. CONCLUSIONS Methylphenidate was widely consumed in the municipality and mainly in the most developed areas. Of note, the consumption of formulations with the higher abuse risk was the most predominant. Both its prescription and dispensation contrasted with current pharmacotherapeutic recommendations and legal requirements. Therefore, the commercialization of methylphenidate should be monitored more closely, and its use in the treatment of behavioral changes of psychological disorders needs to be discussed in detail, in line with the concepts of the quality use of medicines.

Hospitalization flow in the public and private systems in the state of Sao Paulo, Brazil

OBJECTIVE To describe the migration flows of demand for public and private hospital care among the health regions of the state of Sao Paulo, Brazil. METHODS Study based on a database of hospitalizations in the public and private systems of the state of Sao Paulo, Southeastern Brazil, in 2006. We analyzed data from 17 health regions of the state, considering people hospitalized in their own health region and those who migrated outwards (emigration) or came from other regions (immigration). The index of migration effectiveness of patients from both systems was estimated. The coverage (hospitalization coefficient) was analyzed in relation to the number of inpatient beds per population and the indexes of migration effectiveness. RESULTS The index of migration effectiveness applied to the hospital care demand flow allowed characterizing health regions with flow balance, with high emigration of public and private patients, and with high attraction of public and private patients. CONCLUSIONS There are differences in hospital care access and opportunities among health regions in the state of Sao Paulo, Brazil.

Spatial patterns of leprosy in a hyperendemic state in Northern Brazil, 2001-2012

ABSTRACT OBJECTIVE To describe the spatial patterns of leprosy in the Brazilian state of Tocantins. METHODS This study was based on morbidity data obtained from the Sistema de Informações de Agravos de Notificação (SINAN – Brazilian Notifiable Diseases Information System), of the Ministry of Health. All new leprosy cases in individuals residing in the state of Tocantins, between 2001 and 2012, were included. In addition to the description of general disease indicators, a descriptive spatial analysis, empirical Bayesian analysis and spatial dependence analysis were performed by means of global and local Moran’s indexes. RESULTS A total of 14,542 new cases were recorded during the period under study. Based on the annual case detection rate, 77.0% of the municipalities were classified as hyperendemic (> 40 cases/100,000 inhabitants). Regarding the annual case detection rate in < 15 years-olds, 65.4% of the municipalities were hyperendemic (10.0 to 19.9 cases/100,000 inhabitants); 26.6% had a detection rate of grade 2 disability cases between 5.0 and 9.9 cases/100,000 inhabitants. There was a geographical overlap of clusters of municipalities with high detection rates in hyperendemic areas. Clusters with high disease risk (global Moran’s index: 0.51; p < 0.001), ongoing transmission (0.47; p < 0.001) and late diagnosis (0.44; p < 0.001) were identified mainly in the central-north and southwestern regions of Tocantins. CONCLUSIONS We identified high-risk clusters for transmission and late diagnosis of leprosy in the Brazilian state of Tocantins. Surveillance and control measures should be prioritized in these high-risk municipalities.

Burden of physical inactivity and hospitalization costs due to chronic diseases

OBJECTIVE To evaluate the physical inactivity-related inpatient costs of chronic non-communicable diseases. METHODS This study used data from 2013, from Brazilian Unified Health System, regarding inpatient numbers and costs due to malignant colon and breast neoplasms, cerebrovascular diseases, ischemic heart diseases, hypertension, diabetes, and osteoporosis. In order to calculate the share physical inactivity represents in that, the physical inactivity-related risks, which apply to each disease, were considered, and physical inactivity prevalence during leisure activities was obtained from Pesquisa Nacional por Amostra de Domicílio (Brazil's National Household Sample Survey). The analysis was stratified by genders and residing country regions of subjects who were 40 years or older. The physical inactivity-related hospitalization cost regarding each cause was multiplied by the respective share it regarded to. RESULTS In 2013, 974,641 patients were admitted due to seven different causes in Brazil, which represented a high cost. South region was found to have the highest patient admission rate in most studied causes. The highest prevalences for physical inactivity were observed in North and Northeast regions. The highest inactivity-related share in men was found for osteoporosis in all regions (≈ 35.0%), whereas diabetes was found to have a higher share regarding inactivity in women (33.0% to 37.0% variation in the regions). Ischemic heart diseases accounted for the highest total costs that could be linked to physical inactivity in all regions and for both genders, being followed by cerebrovascular diseases. Approximately 15.0% of inpatient costs from Brazilian Unified Health System were connected to physical inactivity. CONCLUSIONS Physical inactivity significantly impacts the number of patient admissions due to the evaluated causes and through their resulting costs, with different genders and country regions representing different shares.

Spatial analysis of avoidable hospitalizations due to tuberculosis in Ribeirao Preto, SP, Brazil (2006-2012)

ABSTRACT OBJECTIVE To describe the spatial distribution of avoidable hospitalizations due to tuberculosis in the municipality of Ribeirao Preto, SP, Brazil, and to identify spatial and space-time clusters for the risk of occurrence of these events. METHODS This is a descriptive, ecological study that considered the hospitalizations records of the Hospital Information System of residents of Ribeirao Preto, SP, Southeastern Brazil, from 2006 to 2012. Only the cases with recorded addresses were considered for the spatial analyses, and they were also geocoded. We resorted to Kernel density estimation to identify the densest areas, local empirical Bayes rate as the method for smoothing the incidence rates of hospital admissions, and scan statistic for identifying clusters of risk. Softwares ArcGis 10.2, TerraView 4.2.2, and SaTScanTM were used in the analysis. RESULTS We identified 169 hospitalizations due to tuberculosis. Most were of men (n = 134; 79.2%), averagely aged 48 years (SD = 16.2). The predominant clinical form was the pulmonary one, which was confirmed through a microscopic examination of expectorated sputum (n = 66; 39.0%). We geocoded 159 cases (94.0%). We observed a non-random spatial distribution of avoidable hospitalizations due to tuberculosis concentrated in the northern and western regions of the municipality. Through the scan statistic, three spatial clusters for risk of hospitalizations due to tuberculosis were identified, one of them in the northern region of the municipality (relative risk [RR] = 3.4; 95%CI 2.7–4,4); the second in the central region, where there is a prison unit (RR = 28.6; 95%CI 22.4–36.6); and the last one in the southern region, and area of protection for hospitalizations (RR = 0.2; 95%CI 0.2–0.3). We did not identify any space-time clusters. CONCLUSIONS The investigation showed priority areas for the control and surveillance of tuberculosis, as well as the profile of the affected population, which shows important aspects to be considered in terms of management and organization of health care services targeting effectiveness in primary health care.