Elétrodo de pasta de carbono molecularmente impresso para deteção voltamétrica de Furazolidona

A furazolidona é uma substância ativa do medicamento Giarlam que contém um espetro anti-bacteriano relativamente amplo e que é frequentemente usado para tratar certas doenças bacterianas e protozoárias no homem. A maioria dos fármacos exige uma dosagem que garanta os níveis de segurança e eficácia de atuação. A necessidade de dosear os medicamentos e os seus metabólitos exige o desenvolvimento constante de métodos analíticos eficientes. Neste trabalho desenvolveu-se um novo sensor eletroquímico para a deteção da furazolidona, baseado num elétrodo de pasta de carbono modificado com um polímero molecularmente impresso. A procura de novos materiais que permitam uma melhor seletividade e sensibilidade aos sistemas de deteção é especialmente importante no desenvolvimento de métodos analíticos. Os polímeros molecularmente impressos enquadram-se nesse perfil e o seu uso tem vindo a ser cada vez mais frequente como ferramenta importante em química analítica. Assim, sintetizou-se um polímero com cavidades seletivas para a Furazolidona. Este polímero foi, misturado com grafite e perafina de modo a produzir uma pasta de carbono. Uma seringa de plástico foi usada como suporte da pasta de carbono. O comportamento eletroquímico do sensor foi avaliado e diversas condições de utilização foram estudadas e otimizadas. O sensor apresenta um comportamento linear entre a intensidade do pico e a concentração numa gama de concentrações entre 1 e 100 μM, um limite de deteção de 1 μM e uma precisão (repetibilidade) inferior a 7%. A aplicabilidade do sensor fabricado em amostras complexas foi avaliada pela deteção do fármaco em amostras de urina.

Molecularly imprinted sensor for voltammetric detection of norfloxacin

In this work, a norfloxacin selective modified glassy carbon electrode (GCE) based on a molecularly imprinted polymer (MIP) as electrochemical sensor was developed. A suspension of multi-walled carbon nanotubes (MWCNTs) was deposited on the electrode surface. Subsequently, a molecularly imprinted film was prepared by electropolymerization, via cyclic voltammetry of pyrrole (PPy) in the presence of norfloxacin (NFX) as the template molecule. A control electrode (NIP) was also prepared. Scanning electron microscopy (SEM) and cyclic voltammetry in a ferrocyanide solution were performed for morphological and electrochemical characterisation, respectively. Several experimental parameters were studied and optimised. For quantification purposes the MIP/MWCNT/GCE was immersed in NFX solutions for 10 min, and the detection was performed in voltammetric cell by square wave voltammetry. The proposed sensor presented a linear behaviour, between peak current intensity and logarithmic concentration of NFX between 1 × 10−7 and 8 × 10−6 M. The obtained results presented good precision, with a repeatability of 4.3% and reproducibility of 9% and the detection limit was 4.6 × 10−8 M (S/N = 3). The developed sensor displayed good selectivity and operational lifetime, is simple to fabricate and easy to operate and was successfully applied to the analysis of NFX in urine samples.

Minimum detection limit of an in-house nested-PCR assay for herpes simplex virus and varicella zoster virus

Introduction Herpes simplex virus (HSV) and varicella zoster virus (VZV) are responsible for a variety of human diseases, including central nervous system diseases. The use of polymerase chain reaction (PCR) techniques on cerebrospinal fluid samples has allowed the detection of viral DNA with high sensitivity and specificity. Methods Serial dilutions of quantified commercial controls of each virus were subjected to an in-house nested-PCR technique. Results The minimum detection limits for HSV and VZV were 5 and 10 copies/µL, respectively. Conclusions The detection limit of nested-PCR for HSV and VZV in this study was similar to the limits found in previous studies.

Evolução, a curto prazo, do perfil do estado de nutrição no transplante hepático, em adultos : contributo para otimização da abordagem clínica e nutricional

RESUMO:Contexto: A avaliação do estado de nutrição do doente com indicação para transplante hepático (TH) deve ser abrangente, considerando o amplo espetro de situações clínicas e metabólicas. As alterações metabólicas relacionadas com a doença hepática podem limitar a aplicação de métodos de avaliação nutricional, subestimando a desnutrição. Após o TH, é expectável a reversão dos distúrbios metabólicos da doença hepática, pela melhoria da função do fígado. No entanto, algumas complicações metabólicas podem surgir após o TH, relacionadas com a má-nutrição, a desnervação hepática e o uso prolongado de imunossupressão, comprometendo os resultados clínicos a longo-prazo. A medição longitudinal e confiável do metabolismo energético e dos compartimentos corporais após o TH, avaliada em conjunto com fatores influentes no estado de nutrição, pode identificar precocemente situações de risco e otimizar e individualizar estratégias clínicas e nutricionais com vantagens no prognóstico. Objetivo: Avaliar longitudinalmente, a curto prazo, o estado de nutrição após o TH em doentes com insuficiência hepática por doença crónica e identificar os fatores, para além da cirurgia, que determinam diferentes evoluções do metabolismo energético e da composição corporal. Métodos: Foi estudada uma coorte de indivíduos com indicação para TH por doença hepática crónica, admitidos consecutivamente para TH ortotópico eletivo, durante 2 anos. Foram programados 3 momentos de avaliação: na última consulta pré-TH (T0), logo que adquirida autonomia respiratória e funcional após o TH (T1) e um mês após o TH (T2). Nesses momentos, foram medidos no mesmo dia: o suprimento nutricional por recordatório das últimas 24 horas, o estado de nutrição por Avaliação Subjetiva Global (ASG), o gasto energético em repouso (GER) por calorimetria indireta, a antropometria, a composição corporal por bioimpedância elétrica tetrapolar multifrequências e a força muscular por dinamometria de preensão palmar. O índice de massa magra (IMM) e a massa celular corporal (MCC) foram usados como indicadores do músculo esquelético e a percentagem de massa gorda (%MG) e o índice de massa gorda (IMG) como indicadores de adiposidade. O GER foi comparado com o estimado pelas fórmulas de Harris-Benedict para classificação do estado metabólico em:hipermetabolismo (GER medido >120% do GER estimado), normometabolismo (GER medido entre 80 e 120% do GER estimado) e hipometabolismo (GER medido <80% do GER estimado). Foi utilizada análise multivariável: por regressão logística, para identificar variáveis associadas à possibilidade (odds ratio – OR) de pertencer a cada grupo metabólico pré-TH; por regressão linear múltipla, para identificar variáveis associadas à variação dos compartimentos corporais no período pós-TH; e por modelos de efeitos mistos generalizados, para identificar variáveis associadas à evolução do GER e dos compartimentos corporais entre o período pré- e pós-TH. Resultados: Foram incluídos 56 indivíduos com idade, média (DP), 53,7 (8,5) anos, 87,5% do sexo masculino, 23,2% com doença hepática crónica de etiologia etanólica. Após o TH, em 60,7% indivíduos foi administrado regime imunossupressor baseado no tacrolimus. Os indivíduos foram avaliados [mediana (AIQ)] 90,5 (P25: 44,2; P75: 134,5) dias antes do TH (T0), 9,0 (P25: 7,0; P75: 12,0) dias após o TH (T1) e 36,0 (P25: 31,0; P75: 43,0) dias após o TH (T2). Após o TH houve melhoria significativa do estado de nutrição, com diminuição da prevalência de desnutrição classificada pela ASG (37,5% em T0, 16,1% em T2, p<0,001). Antes do TH, 41,1% dos indivíduos eram normometabólicos, 37,5% hipometabólicos e 21,4% hipermetabólicos. A possibilidade de pertencer a cada grupo metabólico pré-TH associou-se à: idade (OR=0,899, p=0,010) e desnutrição pela ASG (OR=5,038, p=0,015) para o grupo normometabólico; e índice de massa magra (IMM, OR=1,264, p=0,049) e etiologia viral da doença hepática (OR=8,297, p=0,019) para o grupo hipermetabólico. Não se obteve modelo múltiplo para o grupo de hipometabólico pré-TH, mas foram identificadas associações univariáveis com a história de toxicodependência (OR=0,282, p=0,047) e com a sarcopénia pré- TH (OR=8,000, p=0,040). Após o TH, houve normalização significativa e progressiva do estado metabólico, indicada pelo aumento da prevalência de normometabolismo (41,1% em T0, 57,1% em T2, p=0,040). Foram identificados diferentes perfis de evolução do GER após o TH, estratificado pelo estado metabólico pré-TH: no grupo hipometabólico pré-TH, o GER (Kcal) aumentou significativa e progressivamente (1030,6 em T0; 1436,1 em T1, p=0,001; 1659,2 em T2, p<0,001); no grupo hipermetabólico pré-TH o GER diminuiu significativa e progressivamente (2097,1 em T0; 1662,5 em T1, p=0,024; 1493,0 em T2, p<0.001); no grupo normometabólico não houve variações significativas. Os perfis de evolução do GER associaram-se com: peso corporal (β=9,6, p<0,001) e suprimento energético (β=13,6, p=0,005) na amostra total; com peso corporal (β=7,1, p=0,018) e contributo energético dos lípidos (β=18,9, p=0,003) no grupo hipometabólico pré-TH; e com peso corporal (β=14,1, p<0,001) e desnutrição pela ASG (β=-171,0, p=0,007) no grupo normometabólico pré-TH.Houve redução transitória dos compartimentos corporais entre T0 e T1, mas a maioria destes recuperou para valores semelhantes aos pré-TH. As exceções foram a água extracelular, que diminuiu entre T0 e T2 (média 18,2 L e 17,8 L, p=0,042), a massa gorda (média 25,1 Kg e 21,7 Kg, p<0,001) e o IMG (média 10,6 Kg.m-2 e 9,3 Kg.m-2, p<0,001) que diminuíram entre T1 e T2. Relativamente à evolução dos indicadores de músculo esquelético e adiposidade ao longo do estudo: a evolução do IMM associou-se com força de preensão palmar (β=0,06, p<0,001), creatininémia (β=2,28, p<0,001) e número total de fármacos administrados (β=-0,21, p<0,001); a evolução da MCC associou-se com força de preensão palmar (β=0,16, p<0,001), creatininémia (β=4,17, p=0,008) e número total de fármacos administrados (β=-0,46, p<0,001); a evolução da %MG associou-se com força de preensão palmar (β=-0,11, p=0,028), história de toxicodependência (β=-5,75, p=0,024), creatininémia (β=-5,91, p=0,004) e suprimento proteico (β=-0,06, p=0,001); a evolução do IMG associou-se com história de toxicodependência (β=- 2,64, p=0,019), creatininémia (β=-2,86, p<0,001) e suprimento proteico (β=-0,02, p<0,001). A variação relativa (%Δ) desses compartimentos corporais entre T1 e T2 indicou o impacto da terapêutica imunossupressora na composição corporal: o regime baseado na ciclosporina associou-se positivamente com a %Δ do IMM (β=23,76, p<0,001) e %Δ da MCC (β=26,58, p<0,001) e negativamente com a %Δ MG (β=-25,64, p<0,001) e %Δ do IMG (β=-25,62, p<0,001), relativamente ao regime baseado no tacrolimus. Os esteróides não influenciaram a evolução do GER nem com a dos compartimentos corporais. Conclusões: O estado de nutrição, avaliado por ASG, melhorou significativamente após o TH, traduzida pela diminuição da prevalência de desnutrição. O normometabolismo pré-TH foi prevalente e associou-se à menor idade e à desnutrição pré- TH. O hipometabolismo pré-TH associou-se à história de toxicodependência e à sarcopénia pré-TH. O hipermetabolismo pré-TH associou-se ao maior IMM e à etiologia viral da doença hepática. Após o TH, houve normalização progressiva do estado metabólico. Foram identificados três perfis de evolução do GER, associando-se com: peso corporal e suprimento energético na amostra total; peso corporal e contributo energético dos lípidos no grupo hipometabólico pré- TH; e peso corporal e desnutrição pela ASG no grupo normometabólico pré-TH. Foram identificados diferentes perfis de evolução da composição corporal após TH. A evolução do músculo esquelético associou-se positivamente com a força de preensão palmar e a creatininémia e negativamente com o número total de fármacos administrados. A evolução da adiposidade (%MG e IMG) associou-se inversamente com a história de toxicodependência, a creatininémia e o suprimento proteico; adicionalmente, a %MG associou-se inversamente com a força de preensão palmar. O regime baseado na ciclosporina associou-se independentemente com diminuição da adiposidade e aumento do músculo esquelético, comparativamente ao regime baseado no tacrolimus.---------------------------ABSTRACT:Background: The assessment of nutritional status in patients undergoing liver transplantation (LTx) should be comprehensive, accounting for the wide spectrum of the clinical and metabolic conditions. The metabolic disturbances related to liver disease may limit the precision and accuracy of traditional nutritional assessment methods underestimating the undernourishment. After LTx, it is expected that many metabolic derangements improve with the recovery of liver function. However, some metabolic complications arising after LTx, related to nutritional status, hepatic denervation, and prolonged immunosuppression, may compromise the longterm outcome. A reliable longitudinal assessment of both energy metabolism and body compartments after LTx, combined with assessments of other factors potentially affecting the nutritional status, may enable a better interpretation on the relationship between the metabolic and the nutritional status. These reliable assessments may precociously identify nutritional risk conditions and optimize and customize clinical and nutritional strategies improving the prognosis. Objective: To assess longitudinally the nutritional status shortly after orthotopic LTx in patients with chronic liver disease, and identify factors, beyond surgery, determining different energy metabolism and body composition profiles.Methods: A cohort of consecutive patients who underwent LTx due to chronic liver disease was studied within a period of two years. The assessments were performed in three occasions: at the last visit before LTx (T0), after surgery as soon as respiratory and functional autonomy was established (T1), and approximately one month after surgery (T2). On each occasion all assessments were performed on the same day, and included: the dietary assessment by 24- hour dietary recall, nutritional status by the Subjective Global Assessment (SGA), the resting energy expenditure (REE) by indirect calorimetry, anthropometry, body composition by multifrequency bioelectrical impedance analysis, and muscle strength by handgrip strength. Both the lean mass index (LMI) and body cell mass (BCM) were used as surrogates of skeletal muscle, and both the percentage of fat mass (%FM) and fat mass index (FMI) of adiposity. The REE was predicted according to the Harris and Benedict equation. Hypermetabolism was defined as a measured REE more than 120% of the predicted value; normometabolism as a measured REE within 80-120% of the predicted value; and hypometabolism as a measured REE less than 80% of the predicted value. Multiple regression analysis was used: by logistic regression to identify variables associated with odds of belong each pre-LTx metabolic groups; by linear multiple regression analysis to identify variables associated with body compartments relative variations (%Δ) in the post-LTx period; and by mixed effects models to identify variables associated with the REE and body compartments profiles pre- and post-LTx. Results: Fifty six patients with a mean (SD) of 53.7 (8.5) years of age were included, 87.5% were men and 23.2% with alcoholic liver disease. After LTx 60.7% individuals were assigned to tacrolimus-based immunosuppressive regimen. The patients were assessed at a median time (inter-quartil range) of 90.5 (P25 44.2; P75 134.5) days before LTx (T0), at a median time of 9.0 (P25 7.0; P75 12.0) (T1) and 36 (P25 31.0; P75 43.0) (T2) days after LTx. After LTx the nutritional status significantly improved: the SGA-undernourishment decreased from 37.5% (T0) to 16.1% (T2) (p<0.001). Before LTx, 41.1% patients were normometabolic, 37.5% hypometabolic, and 21.4% hypermetabolic. The predictors of each pre-LTx metabolic group were: age (OR=0.899, p=0.010) and SGA-undernourishment (OR=5.038, p=0.015) for the normometabolic group; and LMI (OR=1.264, p=0.049) and viral etiology of liver disease (OR=8.297, p=0.019) for the hypermetabolic group. No multiple model was found for the pre-LTx hypometabolic group, but univariate association was found with history of drug addiction (OR=0.282, p=0.047) and pre- LTx sarcopenia (OR=8.000, p=0.040). After LTx a significant normalization of the metabolic status occurred, indicated by the increase in the prevalence of normometabolic patients (from T0: 41.1% to T2: 57.1%, p=0.040). Different REE profiles were found with REE stratified by preoperative metabolic status: in the hypometabolic group a significant progressive increase in mean REE (Kcal) was observed (T0: 1030.6; T1: 1436.1, p=0.001; T2: 1659.2, p<0.001); in the hypermetabolic group, a significant progressive decrease in mean REE (Kcal) was observed (T0: 2097.1; T1: 1662.5, p=0.024; T2: 1493.0, p<0.001); and in the normometabolic group, no significant differences were found. The REE profiles were associated with: body weight (β- estimate=9.6, p<0.001) and energy intake (β-estimate=13.6, p=0.005) in the whole sample; with body weight (β-estimate=7.1, p=0.018) and %TEV from lipids (β-estimate=18.9, p=0.003) in the hypometabolic group; and with body weight (β-estimate=14.1, p<0.001), and SGAundernourishment (β-estimate=-171, p=0.007) in the normometabolic group. A transient decrease in most body compartments occurred from T0 to T1, with subsequent catch-up to similar preoperative values. Exceptions were the extracellular water, decreasing from T0 to T2 (mean 18.2 L to 17.8 L, p=0.042), the fat mass (mean 25.1 Kg to 21.7 Kg, p<0.001) and FMI (mean 10.6 Kg.m-2 to 9.3 Kg.m-2, p<0.001), decreasing from T1 to T2. Significant predictors of skeletal muscle and adiposity profiles were found: LMI evolution was associated with handgrip strength (β-estimate=0.06, p<0.001), serum creatinine (β- estimate=2.28, p<0.001) and number of medications (β-estimate=-0.21, p<0.001); BCM evolution was associated with handgrip strength (β-estimate=0.16, p<0.001), serum creatinine (β-estimate=4.17, p<0.001) and number of medications (β-estimate=-0.46, p<0.001); the %FM evolution was associated with handgrip strength (β-estimate=-0.11, p=0.028), history of drug addiction (β-estimate=-5.75, p=0.024), serum creatinine (β-estimate=-5.91, p=0.004) and protein intake (β-estimate=-0.06, p=0.001); and FMI evolution was associated with history of drug addiction (β-estimate=-2.64, p=0.019), serum creatinine (β-estimate=-2.86, p<0.001) and protein intake (β-estimate=-0.02, p<0.001). The %Δ of the aforementioned body compartments from T1 to T2 indicated the influence of immunosuppressive agents on body composition: the cyclosporine-based regimen, compared with tacrolimus-based regimen, was positively associated with %Δ LMI (β-estimate=23.76, p<0.001) and %Δ BCM (β- estimate=26.58, p<0.001), and inversely associated with %Δ FM (β-estimate=-25.64, p<0.001) and %Δ FMI (β-estimate=-25.62, p<0.001). No significant changes in REE or body composition were observed associated with dose or duration of steroid therapy. Conclusions: The SGA-assessed nutritional status improved shortly after LTx, with significant decrease in prevalence undernourished individuals. XXI Preoperative normometabolism was prevalent and was associated with younger age and SGAundernourishment before LTx. Preoperative hypometabolism was associated with history of drug addiction and pre-LTx sarcopenia. Preoperative hypermetabolism was associated with higher LMI and viral etiology of liver disease. A significant normalization of the metabolic status was observed after LTx. The REE profiles were positively predicted by body weight and energy intake in the whole sample, by body weight and percentage of energy intake from lipids in the preoperative hypometabolic patients, and by body weight and SGA–undernourishment in the preoperative normometabolic patients. Different body composition profiles were found after LTx. Skeletal muscle profile was positively associated with handgrip strength and serum creatinine, and inversely with the number of medications. The adiposity profile was inversely associated with history of drug addiction, serum creatinine and protein intake. Additionally, the %FM evolution was inversely associated with handgrip strength. The cyclosporine-based regimen, compared with tacrolimus-based regimen, was independently associated with skeletal muscle increase and adiposity decrease.

The global radar applied to the precision farming sector

The case describes the development of MyFARM’s internationalization plan, a service of Deimos Engenharia, under the GloCal Radar. This space engineering company hired Lisbon Consulting Company to undertake the project to overcome its lack of market orientation. The consultants’ analysis revealed Stevens County, Kansas, as the market with the highest potential for MyFARM. A suitable entry strategy and adaptation of the service for the local market was proposed. The case culminates with the Board of Directors discussing the viability of implementing the consultants’ recommendations to start diversifying their sources of revenue streams.

Determinação de psicofármacos em cabelo humano por técnicas cromatográficas hifenadas: um método alternativo não-invasivo

Dissertação de mestrado em Técnicas de Caracterização e Análise Química

DESARROLLO DE APLICACIONES ESTADÍSTICAS PARA LA AGRICULTURA DE PRECISIÓN. STATISTICAL APPLICATIONS FOR PRECISION AGRICULTURE

A partir de las últimas décadas se ha impulsado el desarrollo y la utilización de los Sistemas de Información Geográficos (SIG) y los Sistemas de Posicionamiento Satelital (GPS) orientados a mejorar la eficiencia productiva de distintos sistemas de cultivos extensivos en términos agronómicos, económicos y ambientales. Estas nuevas tecnologías permiten medir variabilidad espacial de propiedades del sitio como conductividad eléctrica aparente y otros atributos del terreno así como el efecto de las mismas sobre la distribución espacial de los rendimientos. Luego, es posible aplicar el manejo sitio-específico en los lotes para mejorar la eficiencia en el uso de los insumos agroquímicos, la protección del medio ambiente y la sustentabilidad de la vida rural. En la actualidad, existe una oferta amplia de recursos tecnológicos propios de la agricultura de precisión para capturar variación espacial a través de los sitios dentro del terreno. El óptimo uso del gran volumen de datos derivado de maquinarias de agricultura de precisión depende fuertemente de las capacidades para explorar la información relativa a las complejas interacciones que subyacen los resultados productivos. La covariación espacial de las propiedades del sitio y el rendimiento de los cultivos ha sido estudiada a través de modelos geoestadísticos clásicos que se basan en la teoría de variables regionalizadas. Nuevos desarrollos de modelos estadísticos contemporáneos, entre los que se destacan los modelos lineales mixtos, constituyen herramientas prometedoras para el tratamiento de datos correlacionados espacialmente. Más aún, debido a la naturaleza multivariada de las múltiples variables registradas en cada sitio, las técnicas de análisis multivariado podrían aportar valiosa información para la visualización y explotación de datos georreferenciados. La comprensión de las bases agronómicas de las complejas interacciones que se producen a la escala de lotes en producción, es hoy posible con el uso de éstas nuevas tecnologías. Los objetivos del presente proyecto son: (l) desarrollar estrategias metodológicas basadas en la complementación de técnicas de análisis multivariados y geoestadísticas, para la clasificación de sitios intralotes y el estudio de interdependencias entre variables de sitio y rendimiento; (ll) proponer modelos mixtos alternativos, basados en funciones de correlación espacial de los términos de error que permitan explorar patrones de correlación espacial de los rendimientos intralotes y las propiedades del suelo en los sitios delimitados. From the last decades the use and development of Geographical Information Systems (GIS) and Satellite Positioning Systems (GPS) is highly promoted in cropping systems. Such technologies allow measuring spatial variability of site properties including electrical conductivity and others soil features as well as their impact on the spatial variability of yields. Therefore, site-specific management could be applied to improve the efficiency in the use of agrochemicals, the environmental protection, and the sustainability of the rural life. Currently, there is a wide offer of technological resources to capture spatial variation across sites within field. However, the optimum use of data coming from the precision agriculture machineries strongly depends on the capabilities to explore the information about the complex interactions underlying the productive outputs. The covariation between spatial soil properties and yields from georeferenced data has been treated in a graphical manner or with standard geostatistical approaches. New statistical modeling capabilities from the Mixed Linear Model framework are promising to deal with correlated data such those produced by the precision agriculture. Moreover, rescuing the multivariate nature of the multiple data collected at each site, several multivariate statistical approaches could be crucial tools for data analysis with georeferenced data. Understanding the basis of complex interactions at the scale of production field is now within reach the use of these new techniques. Our main objectives are: (1) to develop new statistical strategies, based on the complementarities of geostatistics and multivariate methods, useful to classify sites within field grown with grain crops and analyze the interrelationships of several soil and yield variables, (2) to propose mixed linear models to predict yield according spatial soil variability and to build contour maps to promote a more sustainable agriculture.

Spatial data mining in precision agriculture

Magdeburg, Univ., Fak. für Informatik, Diss., 2012

Non-classical error bounds in the central limit theorem

The classical central limit theorem states the uniform convergence of the distribution functions of the standardized sums of independent and identically distributed square integrable real-valued random variables to the standard normal distribution function. While first versions of the central limit theorem are already due to Moivre (1730) and Laplace (1812), a systematic study of this topic started at the beginning of the last century with the fundamental work of Lyapunov (1900, 1901). Meanwhile, extensions of the central limit theorem are available for a multitude of settings. This includes, e.g., Banach space valued random variables as well as substantial relaxations of the assumptions of independence and identical distributions. Furthermore, explicit error bounds are established and asymptotic expansions are employed to obtain better approximations. Classical error estimates like the famous bound of Berry and Esseen are stated in terms of absolute moments of the random summands and therefore do not reflect a potential closeness of the distributions of the single random summands to a normal distribution. Non-classical approaches take this issue into account by providing error estimates based on, e.g., pseudomoments. The latter field of investigation was initiated by work of Zolotarev in the 1960's and is still in its infancy compared to the development of the classical theory. For example, non-classical error bounds for asymptotic expansions seem not to be available up to now ...

A determinação dos números de indivíduos mínimos necessários na experimentação genética

The main object of the present paper consists in giving formulas and methods which enable us to determine the minimum number of repetitions or of individuals necessary to garantee some extent the success of an experiment. The theoretical basis of all processes consists essentially in the following. Knowing the frequency of the desired p and of the non desired ovents q we may calculate the frequency of all possi- ble combinations, to be expected in n repetitions, by expanding the binomium (p-+q)n. Determining which of these combinations we want to avoid we calculate their total frequency, selecting the value of the exponent n of the binomium in such a way that this total frequency is equal or smaller than the accepted limit of precision n/pª{ 1/n1 (q/p)n + 1/(n-1)| (q/p)n-1 + 1/ 2!(n-2)| (q/p)n-2 + 1/3(n-3) (q/p)n-3... < Plim - -(1b) There does not exist an absolute limit of precision since its value depends not only upon psychological factors in our judgement, but is at the same sime a function of the number of repetitions For this reasen y have proposed (1,56) two relative values, one equal to 1-5n as the lowest value of probability and the other equal to 1-10n as the highest value of improbability, leaving between them what may be called the "region of doubt However these formulas cannot be applied in our case since this number n is just the unknown quantity. Thus we have to use, instead of the more exact values of these two formulas, the conventional limits of P.lim equal to 0,05 (Precision 5%), equal to 0,01 (Precision 1%, and to 0,001 (Precision P, 1%). The binominal formula as explained above (cf. formula 1, pg. 85), however is of rather limited applicability owing to the excessive calculus necessary, and we have thus to procure approximations as substitutes. We may use, without loss of precision, the following approximations: a) The normal or Gaussean distribution when the expected frequency p has any value between 0,1 and 0,9, and when n is at least superior to ten. b) The Poisson distribution when the expected frequecy p is smaller than 0,1. Tables V to VII show for some special cases that these approximations are very satisfactory. The praticai solution of the following problems, stated in the introduction can now be given: A) What is the minimum number of repititions necessary in order to avoid that any one of a treatments, varieties etc. may be accidentally always the best, on the best and second best, or the first, second, and third best or finally one of the n beat treatments, varieties etc. Using the first term of the binomium, we have the following equation for n: n = log Riim / log (m:) = log Riim / log.m - log a --------------(5) B) What is the minimun number of individuals necessary in 01der that a ceratin type, expected with the frequency p, may appaer at least in one, two, three or a=m+1 individuals. 1) For p between 0,1 and 0,9 and using the Gaussean approximation we have: on - ó. p (1-p) n - a -1.m b= δ. 1-p /p e c = m/p } -------------------(7) n = b + b² + 4 c/ 2 n´ = 1/p n cor = n + n' ---------- (8) We have to use the correction n' when p has a value between 0,25 and 0,75. The greek letters delta represents in the present esse the unilateral limits of the Gaussean distribution for the three conventional limits of precision : 1,64; 2,33; and 3,09 respectively. h we are only interested in having at least one individual, and m becomes equal to zero, the formula reduces to : c= m/p o para a = 1 a = { b + b²}² = b² = δ2 1- p /p }-----------------(9) n = 1/p n (cor) = n + n´ 2) If p is smaller than 0,1 we may use table 1 in order to find the mean m of a Poisson distribution and determine. n = m: p C) Which is the minimun number of individuals necessary for distinguishing two frequencies p1 and p2? 1) When pl and p2 are values between 0,1 and 0,9 we have: n = { δ p1 ( 1-pi) + p2) / p2 (1 - p2) n= 1/p1-p2 }------------ (13) n (cor) We have again to use the unilateral limits of the Gaussean distribution. The correction n' should be used if at least one of the valors pl or p2 has a value between 0,25 and 0,75. A more complicated formula may be used in cases where whe want to increase the precision : n (p1 - p2) δ { p1 (1- p2 ) / n= m δ = δ p1 ( 1 - p1) + p2 ( 1 - p2) c= m / p1 - p2 n = { b2 + 4 4 c }2 }--------- (14) n = 1/ p1 - p2 2) When both pl and p2 are smaller than 0,1 we determine the quocient (pl-r-p2) and procure the corresponding number m2 of a Poisson distribution in table 2. The value n is found by the equation : n = mg /p2 ------------- (15) D) What is the minimun number necessary for distinguishing three or more frequencies, p2 p1 p3. If the frequecies pl p2 p3 are values between 0,1 e 0,9 we have to solve the individual equations and sue the higest value of n thus determined : n 1.2 = {δ p1 (1 - p1) / p1 - p2 }² = Fiim n 1.2 = { δ p1 ( 1 - p1) + p1 ( 1 - p1) }² } -- (16) Delta represents now the bilateral limits of the : Gaussean distrioution : 1,96-2,58-3,29. 2) No table was prepared for the relatively rare cases of a comparison of threes or more frequencies below 0,1 and in such cases extremely high numbers would be required. E) A process is given which serves to solve two problemr of informatory nature : a) if a special type appears in n individuals with a frequency p(obs), what may be the corresponding ideal value of p(esp), or; b) if we study samples of n in diviuals and expect a certain type with a frequency p(esp) what may be the extreme limits of p(obs) in individual farmlies ? I.) If we are dealing with values between 0,1 and 0,9 we may use table 3. To solve the first question we select the respective horizontal line for p(obs) and determine which column corresponds to our value of n and find the respective value of p(esp) by interpolating between columns. In order to solve the second problem we start with the respective column for p(esp) and find the horizontal line for the given value of n either diretly or by approximation and by interpolation. 2) For frequencies smaller than 0,1 we have to use table 4 and transform the fractions p(esp) and p(obs) in numbers of Poisson series by multiplication with n. Tn order to solve the first broblem, we verify in which line the lower Poisson limit is equal to m(obs) and transform the corresponding value of m into frequecy p(esp) by dividing through n. The observed frequency may thus be a chance deviate of any value between 0,0... and the values given by dividing the value of m in the table by n. In the second case we transform first the expectation p(esp) into a value of m and procure in the horizontal line, corresponding to m(esp) the extreme values om m which than must be transformed, by dividing through n into values of p(obs). F) Partial and progressive tests may be recomended in all cases where there is lack of material or where the loss of time is less importent than the cost of large scale experiments since in many cases the minimun number necessary to garantee the results within the limits of precision is rather large. One should not forget that the minimun number really represents at the same time a maximun number, necessary only if one takes into consideration essentially the disfavorable variations, but smaller numbers may frequently already satisfactory results. For instance, by definition, we know that a frequecy of p means that we expect one individual in every total o(f1-p). If there were no chance variations, this number (1- p) will be suficient. and if there were favorable variations a smaller number still may yield one individual of the desired type. r.nus trusting to luck, one may start the experiment with numbers, smaller than the minimun calculated according to the formulas given above, and increase the total untill the desired result is obtained and this may well b ebefore the "minimum number" is reached. Some concrete examples of this partial or progressive procedure are given from our genetical experiments with maize.

Estudo comparativo entre métodos de contrôle quantitativo da produção leiteira

This paper deals with the estimation of milk production by means of weekly, biweekly, bimonthly observations and also by method known as 6-5-8, where one observation is taken at the 6th week of lactation, another at 5th month and a third one at the 8th month. The data studied were obtained from 72 lactations of the Holstein Friesian breed of the "Escola Superior de Agricultura "Luiz de Queiroz" (Piracicaba), S. Paulo, Brazil), being 6 calvings on each month of year and also 12 first calvings, 12 second calvings, and so on, up to the sixth. The authors criticize the use of "maximum error" to be found in papers dealing with this subject, and also the use of mean deviation. The former is completely supersed and unadvisable and latter, although equivalent, to a certain extent, to the usual standard deviation, has only 87,6% of its efficiency, according to KENDALL (9, pp. 130-131, 10, pp. 6-7). The data obtained were compared with the actual production, obtained by daily control and the deviations observed were studied. Their means and standard deviations are given on the table IV. Inspite of BOX's recent results (11) showing that with equal numbers in all classes a certain inequality of varinces is not important, the autors separated the methods, before carrying out the analysis of variance, thus avoiding to put together methods with too different standard deviations. We compared the three first methods, to begin with (Table VI). Then we carried out the analysis with the four first methods. (Table VII). Finally we compared the two last methods. (Table VIII). These analysis of variance compare the arithmetic means of the deviations by the methods studied, and this is equivalent to compare their biases. So we conclude tht season of calving and order of calving do not effect the biases, and the methods themselves do not differ from this view point, with the exception of method 6-5-8. Another method of attack, maybe preferrable, would be to compare the estimates of the biases with their expected mean under the null hypothesis (zero) by the t-test. We have: 1) Weekley control: t = x - 0/c(x) = 8,59 - 0/ = 1,56 2) Biweekly control: t = 11,20 - 0/6,21= 1,80 3) Monthly control: t = 7,17 - 0/9,48 = 0,76 4) Bimonthly control: t = - 4,66 - 0/17,56 = -0,26 5) Method 6-5-8 t = 144,89 - 0/22,41 = 6,46*** We denote above by three asterisks, significance the 0,1% level of probability. In this way we should conclude that the weekly, biweekly, monthly and bimonthly methods of control may be assumed to be unbiased. The 6-5-8 method is proved to be positively biased, and here the bias equals 5,9% of the mean milk production. The precision of the methods studied may be judged by their standard deviations, or by intervals covering, with a certain probability (95% for example), the deviation x corresponding to an estimate obtained by cne of the methods studied. Since the difference x - x, where x is the mean of the 72 deviations obtained for each method, has a t distribution with mean zero and estimate of standard deviation. s(x - x) = √1+ 1/72 . s = 1.007. s , and the limit of t for the 5% probability, level with 71 degrees of freedom is 1.99, then the interval to be considered is given by x ± 1.99 x 1.007 s = x ± 2.00. s The intervals thus calculated are given on the table IX.

On the number of limit cycles bifurcating from a non-global degenerated center

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Lower bounds for the number of limit cycles of trigonometric Abel equations

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Limit cycles for cubic systems with a symmetry of order 4 and without in nite critical points

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Limit Cycles for a class of three dimensional polynomial differential systems

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