Testes de ajuste a distribuições estatísticas e métodos para estimação dos parâmetros em análises de fiabilidade

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Mecânica

Power law and entropy analysis of catastrophic phenomena

Catastrophic events, such as wars and terrorist attacks, tornadoes and hurricanes, earthquakes, tsunamis, floods and landslides, are always accompanied by a large number of casualties. The size distribution of these casualties has separately been shown to follow approximate power law (PL) distributions. In this paper, we analyze the statistical distributions of the number of victims of catastrophic phenomena, in particular, terrorism, and find double PL behavior. This means that the data sets are better approximated by two PLs instead of a single one. We plot the PL parameters, corresponding to several events, and observe an interesting pattern in the charts, where the lines that connect each pair of points defining the double PLs are almost parallel to each other. A complementary data analysis is performed by means of the computation of the entropy. The results reveal relationships hidden in the data that may trigger a future comprehensive explanation of this type of phenomena.

A Lei de ZIPF ou Regra 80/20 da Internet

As Leis de Potência, LP, (Power Laws, em inglês), Leis de Pareto ou Leis de Zipf são distribuições estatísticas, com inúmeras aplicações práticas, em sistemas naturais e artificiais. Alguns exemplos são a variação dos rendimentos pessoais ou de empresas, a ocorrência de palavras em textos, as repetições de sons ou conjuntos de sons em composições musicais, o número de vítimas em guerras ou outros cataclismos, a magnitude de tremores de terra, o número de vendas de livros ou CD’s na internet, o número de sítios mais acedidos na Internet, entre muitos outros. Vilfredo Pareto (1897-1906) afirma, no manual de economia política “Cours d’Economie Politique”, que grande parte da economia mundial segue uma determinada distribuição, em que 20% da população reúne 80% da riqueza total do país, estando, assim uma pequena fração da sociedade a controlar a maior fatia do dinheiro. Isto resume o comportamento de uma variável que segue uma distribuição de Pareto (ou Lei de Potência). Neste trabalho pretende-se estudar em pormenor a aplicação das leis de potência a fenómenos da internet, como sendo o número de sítios mais visitados, o número de links existentes em determinado sítio, a distribuição de nós numa rede da internet, o número livros vendidos e as vendas em leilões online. Os resultados obtidos permitem-nos concluir que todos os dados estudados são bem aproximados, numa escala logarítmica, por uma reta com declive negativo, seguindo, assim, uma distribuição de Pareto. O desenvolvimento e crescimento da Web, tem proporcionado um aumento do número dos utilizadores, conteúdos e dos sítios. Grande parte dos exemplos presentes neste trabalho serão alvo de novos estudos e de novas conclusões. O fato da internet ter um papel preponderante nas sociedades modernas, faz com que esteja em constante evolução e cada vez mais seja possível apresentar fenómenos na internet associados Lei de Potência.

Leis de Pareto para Guerras e Actos de Terrorismo

Mestrado em Engenharia Eletrotécnica e de Computadores - Área de Especialização de Sistemas e Planeamento Industrial

Leis de potência em economia e finanças

Nesta dissertação aborda-se a aplicação de Leis de Potência (LPs), também designadas de Leis de Pareto ou Leis de Zipf, a dados económicos. As LPs são distribuições estatísticas amplamente usadas na compreensão de sistemas naturais e artificiais. O aparecimento das LPs deve-se a Vilfredo Pareto que, no século XIX, publicou o manual de economia política,“Cours d’Economie Politique”. Nesse manual refere que grande parte da economia mundial segue uma LP, em que 20% da população reúne 80% da riqueza do país. Esta propriedade carateriza uma variável que segue uma distribuição de Pareto (ou LP). Desde então, as LPs foram aplicadas a outros fenómenos, nomeadamente a ocorrência de palavras em textos, os sobrenomes das pessoas, a variação dos rendimentos pessoais ou de empresas, o número de vítimas de inundações ou tremores de terra, os acessos a sítios da internet, etc. Neste trabalho, é estudado um conjunto de dados relativos às fortunas particulares ou coletivas de pessoas ou organizações. Mais concretamente são analisados dados recolhidos sobre as fortunas das mulheres mais ricas do mundo, dos homens mais ricos no ramo da tecnologia, das famílias mais ricas, das 20 mulheres mais ricas da América, dos 400 homens mais ricos da América, dos homens mais ricos do mundo, dos estabelecimentos mais ricos do mundo, das empresas mais ricas do mundo e dos países mais ricos do mundo, bem como o valor de algumas empresas no mercado de ações. Os resultados obtidos revelam uma boa aproximação de parte desses dados a uma LP simples e uma boa aproximação pelos restantes dados a uma LP dupla. Observa-se, assim, diferenciação na forma de crescimento das fortunas nos diferentes casos estudados. Como trabalho futuro, procurar-se-á analisar estes e outros dados, utilizando outras distribuições estatísticas, como a exponencial ou a lognormal, que possuem comportamentos semelhantes à LP, com o intuito de serem comparados os resultados. Um outro aspeto interessante será o de encontrar a explicação analítica para as vantagens da aproximação de dados económicos por uma LP simples vs por uma LP dupla.

Distribuições de eventos extremos e telecomunicações

As distribuições de Lei de Potência (PL Power Laws), tais como a lei de Pareto e a lei de Zipf são distribuições estatísticas cujos tamanhos dos eventos são inversamente proporcionais à sua frequência. Estas leis de potência são caracterizadas pelas suas longas caudas. Segundo Vilfredo Pareto (1896), engenheiro, cientista, sociólogo e economista italiano, autor da Lei de Pareto, 80% das consequências advêm de 20% das causas. Segundo o mesmo, grande parte da economia mundial segue uma determinada distribuição, onde 80% da riqueza mundial é detida por 20% da população ou 80% da poluição mundial é feita por 20% dos países. Estas percentagens podem oscilar nos intervalos [75-85] e [15-25]. A mesma percentagem poderá ser aplicada à gestão de tempo, onde apenas 20% do tempo dedicado a determinado assunto produzirá cerca de 80% dos resultados obtidos. A lei de Pareto, também designada de regra 80/20, tem aplicações nas várias ciências e no mundo físico, nomeadamente na biodiversidade. O número de ocorrências de fenómenos extremos, aliados ao impacto nas redes de telecomunicações nas situações de catástrofe, no apoio imediato às populações e numa fase posterior de reconstrução, têm preocupado cada vez mais as autoridades oficiais de protecção civil e as operadoras de telecomunicações. O objectivo é o de preparar e adaptarem as suas estruturas para proporcionar uma resposta eficaz a estes episódios. Neste trabalho estuda-se o comportamento de vários fenómenos extremos (eventos críticos) e aproximam-se os dados por uma distribuição de Pareto (Lei de Pareto) ou lei de potência. No final, especula-se sobre a influência dos eventos críticos na utilização das redes móveis. É fundamental que as redes móveis estejam preparadas para lidar com as repercussões de fenómenos deste tipo.

Power Law Behavior and Self-similarity in Modern Industrial Accidents

Advances in technology have produced more and more intricate industrial systems, such as nuclear power plants, chemical centers and petroleum platforms. Such complex plants exhibit multiple interactions among smaller units and human operators, rising potentially disastrous failure, which can propagate across subsystem boundaries. This paper analyzes industrial accident data-series in the perspective of statistical physics and dynamical systems. Global data is collected from the Emergency Events Database (EM-DAT) during the time period from year 1903 up to 2012. The statistical distributions of the number of fatalities caused by industrial accidents reveal Power Law (PL) behavior. We analyze the evolution of the PL parameters over time and observe a remarkable increment in the PL exponent during the last years. PL behavior allows prediction by extrapolation over a wide range of scales. In a complementary line of thought, we compare the data using appropriate indices and use different visualization techniques to correlate and to extract relationships among industrial accident events. This study contributes to better understand the complexity of modern industrial accidents and their ruling principles.

Integer and Fractional Order Entropy Analysis of Earthquake Data-series

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions.

A comparative study of dyslipidaemia in men and woman with androgenic alopecia

Several studies have analyzed the relationship between androgenetic alopecia and cardiovascular disease (mainly heart disease). However few studies have analyzed lipid values in men and women separately. This case-control study included 300 patients consecutively admitted to an outpatient clinic, 150 with early onset androgenetic alopecia (80 males and 70 females) and 150 controls (80 males and 70 females) with other skin diseases. Female patients with androgenic alopecia showed significant higher triglycerides values (123.8 vs 89.43 mg/dl, p = 0.006), total cholesterol values (196.1 vs 182.3 mg/dl, p = 0.014), LDL-C values (114.1 vs 98.8 mg/dl, p = 0.0006) and lower HDL-C values (56.8 vs 67.7 mg/dl, p <0.0001) versus controls respectively. Men with androgenic alopecia showed significant higher triglycerides values (159.7 vs 128.7 mg/dl, p = 0.04) total cholesterol values (198.3 vs 181.4 mg/dl, p = 0.006) and LDL-C values (124.3 vs 106.2, p = 0.0013) versus non-alopecic men. A higher prevalence of dyslipidemia in women and men with androgenic alopecia has been found. The elevated lipid values in these patients may contribute, alongside other mechanisms, to the development of cardiovascular disease in patient with androgenic alopecia.

CD209 in inflammatory bowel disease: a case-control study in the Spanish population

BACKGROUND The etiology of Ulcerative Colitis (UC) and Crohn's Disease (CD), considered together as Inflammatory Bowel Diseases (IBD), involves environmental and genetic factors. Although some genes are already known, the genetics underlying these diseases is complex and new candidates are continuously emerging. The CD209 gene is located in a region linked previously to IBD and a CD209 functional polymorphism (rs4804803) has been associated to other inflammatory conditions. Our aim was to study the potential involvement of this CD209 variant in IBD susceptibility. METHODS We performed a case-control study with 515 CD patients, 497 UC patients and 731 healthy controls, all of them white Spaniards. Samples were typed for the CD209 single nucleotide polymorphism (SNP) rs4804803 by TaqMan technology. Frequency comparisons were performed using chi2 tests. RESULTS No association between CD209 and UC or CD was observed initially. However, stratification of UC patients by HLA-DR3 status, a strong protective allele, showed that carriage of the CD209_G allele could increase susceptibility in the subgroup of HLA-DR3-positive individuals (p = 0.03 OR = 1.77 95% CI 1.04-3.02, vs. controls). CONCLUSION A functional variant in the CD209 gene, rs4804803, does not seem to be influencing Crohn's disease susceptibility. However, it could be involved in the etiology or pathology of Ulcerative Colitis in HLA-DR3-positive individuals but further studies are necessary.

Influencia de la temperatura en la ingesta de pacientes hospitalizados.

BACKGROUND AND OBJECTIVES Prevalence of hyponutrition in hospitalized patients is very high and it has been shown to be an important prognostic factor. Most of admitted patients depend on hospital food to cover their nutritional demands being important to assess the factors influencing their intake, which may be modified in order to improve it and prevent the consequences of inadequate feeding. In previous works, it has been shown that one of the worst scored characteristics of dishes was the temperature. The aim of this study was to assess the influence of temperature on patient's satisfaction and amount eaten depending on whether the food was served in isothermal trolleys keeping proper food temperature or not. MATERIAL AND METHODS We carried out satisfaction surveys to hospitalized patients having regular diets, served with or without isothermal trolleys. The following data were gathered: age, gender, weight, number of visits, mobility, autonomy, amount of orally taken medication, intake of out-of-hospital foods, qualification of food temperature, presentation and smokiness, amount of food eaten, and reasons for not eating all the content of the tray. RESULTS Of the 363 surveys, 134 (37.96%) were done to patients with isothermal trays and 229 (62.04%) to patients without them. Sixty percent of the patients referred having eaten less than the normal amount within the last week, the most frequent reason being decreased appetite. During lunch and dinner, 69.3% and 67.7%, respectively, ate half or less of the tray content, the main reasons being as follows: lack of appetite (42% at lunch time and 40% at dinner), do not like the food (24.3 and 26.2%) or taste (15.3 and 16.8%). Other less common reasons were the odor, the amount of food, having nausea or vomiting, fatigue, and lack of autonomy. There were no significant differences in the amount eaten by gender, weight, number of visits, amount of medication, and level of physical activity. The food temperature was classified as adequate by 62% of the patients, the presentation by 95%, and smokiness by 85%. When comparing the patients served with or without isothermal trays, there were no differences with regards to baseline characteristics analyzed that might have had an influence on amount eaten. Ninety percent of the patients with isothermal trolley rated the food temperature as good, as compared with 57.2% of the patients with conventional trolley, the difference being statistically significant (P = 0.000). Besides, there were differences in the amount of food eaten between patients with and without isothermal trolley, so that 41% and 27.7% ate all the tray content, respectively, difference being statistically significant (P = 0.007). There were no differences in smokiness or presentation rating. CONCLUSIONS Most of the patients (60%) had decreased appetite during hospital admission. The percentage of hospitalized patients rating the food temperature as being good is higher among patients served with isothermal trolleys. The amount of food eaten by the patients served with isothermal trolleys is significantly higher that in those without them.

Assessment of Severe Apnoea through Voice Analysis, Automatic Speech, and Speaker Recognition Techniques

This study is part of an ongoing collaborative effort between the medical and the signal processing communities to promote research on applying standard Automatic Speech Recognition (ASR) techniques for the automatic diagnosis of patients with severe obstructive sleep apnoea (OSA). Early detection of severe apnoea cases is important so that patients can receive early treatment. Effective ASR-based detection could dramatically cut medical testing time. Working with a carefully designed speech database of healthy and apnoea subjects, we describe an acoustic search for distinctive apnoea voice characteristics. We also study abnormal nasalization in OSA patients by modelling vowels in nasal and nonnasal phonetic contexts using Gaussian Mixture Model (GMM) pattern recognition on speech spectra. Finally, we present experimental findings regarding the discriminative power of GMMs applied to severe apnoea detection. We have achieved an 81% correct classification rate, which is very promising and underpins the interest in this line of inquiry.

Proceso INFORNUT: validación de la fase de filtro-FILNUT--y comparación con otros métodos de detección precoz de desnutrición hospitalaria.

INTRODUCTION According to several series, hospital hyponutrition involves 30-50% of hospitalized patients. The high prevalence justifies the need for early detection from admission. There several classical screening tools that show important limitations in their systematic application in daily clinical practice. OBJECTIVES To analyze the relationship between hyponutrition, detected by our screening method, and mortality, hospital stay, or re-admissions. To analyze, as well, the relationship between hyponutrition and prescription of nutritional support. To compare different nutritional screening methods at admission on a random sample of hospitalized patients. Validation of the INFORNUT method for nutritional screening. MATERIAL AND METHODS In a previous phase from the study design, a retrospective analysis with data from the year 2003 was carried out in order to know the situation of hyponutrition in Virgen de la Victoria Hospital, at Malaga, gathering data from the MBDS (Minimal Basic Data Set), laboratory analysis of nutritional risk (FILNUT filter), and prescription of nutritional support. In the experimental phase, a cross-sectional cohort study was done with a random sample of 255 patients, on May of 2004. Anthropometrical study, Subjective Global Assessment (SGA), Mini-Nutritional Assessment (MNA), Nutritional Risk Screening (NRS), Gassull's method, CONUT and INFORNUT were done. The settings of the INFORNUT filter were: albumin < 3.5 g/dL, and/or total proteins <5 g/dL, and/or prealbumin <18 mg/dL, with or without total lymphocyte count < 1.600 cells/mm3 and/or total cholesterol <180 mg/dL. In order to compare the different methods, a gold standard is created based on the recommendations of the SENPE on anthropometrical and laboratory data. The statistical association analysis was done by the chi-squared test (a: 0.05) and agreement by the k index. RESULTS In the study performed in the previous phase, it is observed that the prevalence of hospital hyponutrition is 53.9%. One thousand six hundred and forty four patients received nutritional support, of which 66.9% suffered from hyponutrition. We also observed that hyponutrition is one of the factors favoring the increase in mortality (hyponourished patients 15.19% vs. non-hyponourished 2.58%), hospital stay (hyponourished patients 20.95 days vs. non-hyponourished 8.75 days), and re-admissions (hyponourished patients 14.30% vs. non-hyponourished 6%). The results from the experimental study are as follows: the prevalence of hyponutrition obtained by the gold standard was 61%, INFORNUT 60%. Agreement levels between INFORNUT, CONUT, and GASSULL are good or very good between them (k: 0.67 INFORNUT with CONUT, and k: 0.94 INFORNUT and GASSULL) and wit the gold standard (k: 0.83; k: 0.64 CONUT; k: 0.89 GASSULL). However, structured tests (SGA, MNA, NRS) show low agreement indexes with the gold standard and laboratory or mixed tests (Gassull), although they show a low to intermediate level of agreement when compared one to each other (k: 0.489 NRS with SGA). INFORNUT shows sensitivity of 92.3%, a positive predictive value of 94.1%, and specificity of 91.2%. After the filer phase, a preliminary report is sent, on which anthropometrical and intake data are added and a Nutritional Risk Report is done. CONCLUSIONS Hyponutrition prevalence in our study (60%) is similar to that found by other authors. Hyponutrition is associated to increased mortality, hospital stay, and re-admission rate. There are no tools that have proven to be effective to show early hyponutrition at the hospital setting without important applicability limitations. FILNUT, as the first phase of the filter process of INFORNUT represents a valid tool: it has sensitivity and specificity for nutritional screening at admission. The main advantages of the process would be early detection of patients with risk for hyponutrition, having a teaching and sensitization function to health care staff implicating them in nutritional assessment of their patients, and doing a hyponutrition diagnosis and nutritional support need in the discharge report that would be registered by the Clinical Documentation Department. Therefore, INFORNUT would be a universal screening method with a good cost-effectiveness ratio.

Caracterització estadística dels pics de correlació a GPS

Aquest projecte es centra a donar una caracterització estadística del valor que tenen els pics de correlació sota diferents escenaris d’adquisició a un receptor GPS. En primer lloc, s’ha volgut donar una visió general de tots els fonaments del sistema GPS per tal de poder entendre el seu funcionament. A continuació, s’ha passat a analitzar el bloc d’adquisició d’un receptor GPS. Primer, hem estudiat quines operacions es realitzen en aquest bloc i quines són les diferents formes d’implementar-lo. Seguidament, sota un escenari d’adquisició per cerca de fase de codi en paral·lel i utilitzant integracions coherents, s’han estudiat les distribucions estadístiques de les pdf’s obtingudes pels pics de correlació de senyal+soroll i pels pics de correlació de només soroll, i s’ha vist com aquestes fan modificar la corba ROC del receptor . Les simulacions s’han realitzat amb MATLAB i en diferents escenaris d’adquisició per tal de poder comparar com varien les estadístiques obtingudes en casos diferents.

Macronutrient composition of the diet and prospective weight change in participants of the EPIC-PANACEA study.

BACKGROUND The effect of the macronutrient composition of the usual diet on long term weight maintenance remains controversial. METHODS 373,803 subjects aged 25-70 years were recruited in 10 European countries (1992-2000) in the PANACEA project of the EPIC cohort. Diet was assessed at baseline using country-specific validated questionnaires and weight and height were measured at baseline and self-reported at follow-up in most centers. The association between weight change after 5 years of follow-up and the iso-energetic replacement of 5% of energy from one macronutrient by 5% of energy from another macronutrient was assessed using multivariate linear mixed-models. The risk of becoming overweight or obese after 5 years was investigated using multivariate Poisson regressions stratified according to initial Body Mass Index. RESULTS A higher proportion of energy from fat at the expense of carbohydrates was not significantly associated with weight change after 5 years. However, a higher proportion of energy from protein at the expense of fat was positively associated with weight gain. A higher proportion of energy from protein at the expense of carbohydrates was also positively associated with weight gain, especially when carbohydrates were rich in fibre. The association between percentage of energy from protein and weight change was slightly stronger in overweight participants, former smokers, participants ≥60 years old, participants underreporting their energy intake and participants with a prudent dietary pattern. Compared to diets with no more than 14% of energy from protein, diets with more than 22% of energy from protein were associated with a 23-24% higher risk of becoming overweight or obese in normal weight and overweight subjects at baseline. CONCLUSION Our results show that participants consuming an amount of protein above the protein intake recommended by the American Diabetes Association may experience a higher risk of becoming overweight or obese during adult life.