An alternative method for dating unknown tephras based on a segmented regression model

In CoDaWork’05, we presented an application of discriminant function analysis (DFA) to 4 differentcompositional datasets and modelled the first canonical variable using a segmented regression modelsolely based on an observation about the scatter plots. In this paper, multiple linear regressions areapplied to different datasets to confirm the validity of our proposed model. In addition to dating theunknown tephras by calibration as discussed previously, another method of mapping the unknown tephrasinto samples of the reference set or missing samples in between consecutive reference samples isproposed. The application of these methodologies is demonstrated with both simulated and real datasets.This new proposed methodology provides an alternative, more acceptable approach for geologists as theirfocus is on mapping the unknown tephra with relevant eruptive events rather than estimating the age ofunknown tephra.Kew words: Tephrochronology; Segmented regression

An alternative method for dating unknown tephras based on a segmented regression model

In CoDaWork’05, we presented an application of discriminant function analysis (DFA) to 4 different compositional datasets and modelled the first canonical variable using a segmented regression model solely based on an observation about the scatter plots. In this paper, multiple linear regressions are applied to different datasets to confirm the validity of our proposed model. In addition to dating the unknown tephras by calibration as discussed previously, another method of mapping the unknown tephras into samples of the reference set or missing samples in between consecutive reference samples is proposed. The application of these methodologies is demonstrated with both simulated and real datasets. This new proposed methodology provides an alternative, more acceptable approach for geologists as their focus is on mapping the unknown tephra with relevant eruptive events rather than estimating the age of unknown tephra. Kew words: Tephrochronology; Segmented regression

Adaptabilidade e estabilidade de cultivares de milho para diferentes safras, espaçamentos e populações de plantas

Pós-graduação em Agronomia - FEIS

Estabilidade e adaptabilidade de cultivares de soja, incluindo transgênicas, na região dos chapadões

Pós-graduação em Agronomia - FEIS

Genetic parameters and trends of morphometric traits of GIFT tilapia under selection for weight gain

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Ventilation behavior in trained and untrained men during incremental test: evidence of one metabolic transition point

This study aimed to describe and compare the ventilation behavior during an incremental test utilizing three mathematical models and to compare the feature of ventilation curve fitted by the best mathematical model between aerobically trained (TR) and untrained ( UT) men. Thirty five subjects underwent a treadmill test with 1 km.h(-1) increases every minute until exhaustion. Ventilation averages of 20 seconds were plotted against time and fitted by: bi-segmental regression model (2SRM); three-segmental regression model (3SRM); and growth exponential model (GEM). Residual sum of squares (RSS) and mean square error (MSE) were calculated for each model. The correlations between peak VO2 (VO2PEAK), peak speed (Speed(PEAK)), ventilatory threshold identified by the best model (VT2SRM) and the first derivative calculated for workloads below (moderate intensity) and above (heavy intensity) VT2SRM were calculated. The RSS and MSE for GEM were significantly higher (p < 0.01) than for 2SRM and 3SRM in pooled data and in UT, but no significant difference was observed among the mathematical models in TR. In the pooled data, the first derivative of moderate intensities showed significant negative correlations with VT2SRM (r = -0.58; p < 0.01) and Speed(PEAK) (r = -0.46; p < 0.05) while the first derivative of heavy intensities showed significant negative correlation with VT2SRM (r = -0.43; p < 0.05). In UT group the first derivative of moderate intensities showed significant negative correlations with VT2SRM (r = -0.65; p < 0.05) and Speed(PEAK) (r = -0.61; p < 0.05), while the first derivative of heavy intensities showed significant negative correlation with VT2SRM (r= -0.73; p < 0.01), Speed(PEAK) (r = -0.73; p < 0.01) and VO2PEAK (r = -0.61; p < 0.05) in TR group. The ventilation behavior during incremental treadmill test tends to show only one threshold. UT subjects showed a slower ventilation increase during moderate intensities while TR subjects showed a slower ventilation increase during heavy intensities.

Changes in prescribing patterns of benzodiazepines after training of general practitioners

RESUMO: Introdução: As benzodiazepinas são os fármacos ansiolíticos e hipnóticos mais utilizados. O elevado consumo destes fármacos tem representado uma preocupação devido aos efeitos secundários do seu uso prolongado e dependência. Portugal tem a maior utilização de benzodiazepinas na Europa. Este estudo pretende analisar a alteração do padrão de prescrição de benzodiazepinas após uma intervenção com clínicos gerais. Métodos: A intervenção consistiu numa sessão educacional a um grupo de clínicos gerais. Foi comparado o padrão de prescrição de benzodiazepinas dos médicos intervencionados com o de um grupo de médicos não intervencionado da mesma região e com o de um grupo de médicos não intervencionados de outra região. Analisaram-­‐se as prescrições de 12 meses antes e depois da intervenção. A análise do padrão de prescrição utilizou como metodologia a Dose Diária Definida (DDD) e a Dose Diária Definida por 1000 pacientes por dia (DHD). A análise estatística recorreu a métodos de regressão segmentada. Resultados: Houve uma diminuição no padrão de prescrição de benzodiazepinas no grupo intervencionado após a intervenção (p=0.005). Houve também uma redução no padrão de prescrição no grupo não intervencionada da mesma região (p=0.037) e no grupo não-intervencionado da região diferente (p=0.010). Analisando por género, prescritores do género feminino prescrevem uma quantidade maior de benzodiazepinas. Os clínicos gerais do género feminino intervencionados tiveram a maior redução na prescrição após a intervenção (p=0.008). Discussão: Os dados demonstraram que a intervenção reduziu a prescrição de benzodiazepinas após a intervenção. A diminuição geral do padrão de prescrição poderá ser explicada pelo efeito de Hawthorne ou pela contaminação entre os três grupos de clínicos gerais. Os dados disponíveis não explicam as diferenças nos padrões de prescrição por género. Conclusão: Este estudo demonstra como uma única intervenção tem um impacto positivo na melhoria dos padrões de prescrição. A replicação desta intervenção poderá representar uma oportunidade para alterar a prescrição de benzodiazepinas em Portugal. -----------------------------ABSTRACT: Introduction: Benzodiazepines are the most utilized anxiolytic and hypnotic drugs. The high consumption of benzodiazepines has been a concern due to the reported side effects of long-­‐term use and dependence. Portugal has the highest benzodiazepine utilisation in Europe. This study aims to analyse the change in General Practitioners’ (GPs) benzodiazepine prescription pattern after na intervention period. Methods: An educational session was delivered to a group of intervened GPs. The benzodiazepine prescription pattern of the intervened group was compared to the pattern of a non-­‐intervened matched group from the same region, and to the pattern of another non-­‐intervened matched group from a diferente region. The research time frame was 12 month before and after intervention. The analysis of the prescription trends used the Defined Daily Dose (DDD) and Defined Daily Dose per 1000 patients per day (DHD) methodology. The statistical methods consisted of segmented regression analysis. Results: There was a decrease in benzodiazepine prescription pattern of intervened GPs after intervention (p=0.005). There was also a decrease in benzodiazepine prescription pattern for the non-­‐intervened group from the same region (p=0.037) and for the non-­‐ intervened group from a diferente region (p=0.010). Concerningthe analysis by gender, female gender prescribed a higher amount of benzodiazepines. The intervened female gender prescribers presented the highest decrease in prescription trend after intervention (p=0.008). Discussion: The data demonstrated that the intervention was effective in reducing benzodiazepine prescription after intervention. The general decrease in prescription trend might be explained by a Hawthorne effect or a contamination effect between the three groups of GPs. The available data couldn´t explain the diferences in prescription patterns by gender. Conclusion: This study demonstrates how a single intervention has a positive impact on improving prescription trends. The replication of this intervention might be an opportunity to changing the worrying benzodiazepine utilisation in Portugal.

Long-Term Control of Endemic Hospital-Wide Methicillin-Resistant Staphylococcus aureus (MRSA): The Impact of Targeted Active Surveillance for MRSA in Patients and Healthcare Workers

To evaluate the long-term impact of successive interventions on rates of methicillin-resistant Staphylococcus aureus (MRSA) colonization or infection and MRSA bacteremia in an endemic hospital-wide situation. DESIGN:Quasi-experimental, interrupted time-series analysis. The impact of the interventions was analyzed by use of segmented regression. Representative MRSA isolates were typed by use of pulsed-field gel electrophoresis. SETTING:A 950-bed teaching hospital in Seville, Spain. PATIENTS:All patients admitted to the hospital during the period from 1995 through 2008. METHODS:Three successive interventions were studied: (1) contact precautions, with no active surveillance for MRSA; (2) targeted active surveillance for MRSA in patients and healthcare workers in specific wards, prioritized according to clinical epidemiology data; and (3) targeted active surveillance for MRSA in patients admitted from other medical centers. RESULTS:Neither the preintervention rate of MRSA colonization or infection (0.56 cases per 1,000 patient-days [95% confidence interval {CI}, 0.49-0.62 cases per 1,000 patient-days]) nor the slope for the rate of MRSA colonization or infection changed significantly after the first intervention. The rate decreased significantly to 0.28 cases per 1,000 patient-days (95% CI, 0.17-0.40 cases per 1,000 patient-days) after the second intervention and to 0.07 cases per 1,000 patient-days (95% CI, 0.06-0.08 cases per 1,000 patient-days) after the third intervention, and the rate remained at a similar level for 8 years. The MRSA bacteremia rate decreased by 80%, whereas the rate of bacteremia due to methicillin-susceptible S. aureus did not change. Eighty-three percent of the MRSA isolates identified were clonally related. All MRSA isolates obtained from healthcare workers were clonally related to those recovered from patients who were in their care. CONCLUSION:Our data indicate that long-term control of endemic MRSA is feasible in tertiary care centers. The use of targeted active surveillance for MRSA in patients and healthcare workers in specific wards (identified by means of analysis of clinical epidemiology data) and the use of decolonization were key to the success of the program.

Application of discriminant function analysis and change-point problem in dating volcanic ashes

The application of Discriminant function analysis (DFA) is not a new idea in the studyof tephrochrology. In this paper, DFA is applied to compositional datasets of twodifferent types of tephras from Mountain Ruapehu in New Zealand and MountainRainier in USA. The canonical variables from the analysis are further investigated witha statistical methodology of change-point problems in order to gain a betterunderstanding of the change in compositional pattern over time. Finally, a special caseof segmented regression has been proposed to model both the time of change and thechange in pattern. This model can be used to estimate the age for the unknown tephrasusing Bayesian statistical calibration

Discovery of novel arenavirus receptors and entry factors

Arenaviruses are enveloped negative-strand RNA viruses that contain a bi-segmented genome. They are rodent-borne pathogens endemic to the Americas and Africa, with the exception of lymphocytic choriomeningitis virus (LCMV) that is world-wide distributed. The arenaviruses include numerous important human pathogens including the Old World arenavirus Lassa virus (LASV), the causative agent of a severe viral hemorrhagic fever in humans with several hundred thousand infections per year in Africa and thousands of deaths. Viruses are obligatory intracellular parasites, strictly depending on cellular processes and factors to complete their replication cycle. The binding of a virus to target cells is the first step of every viral infection, and is mainly mediated by viral proteins that can directly engage cellular receptors, providing a key determinant for viral tropism. This early step of infection represents a promising target to block the pathogen before it can take control over the host cell. Old World arenaviruses, such as LASV and LCMV, bind to host cells via attachment to their main receptor, dystroglycan (DG), an ubiquitous receptor for extracellular matrix proteins. The engagement of DG by LASV results in a fast internalization and transfer the virus to late endosomal compartment suggesting that the virus binding to DG causes marked changes in the dynamics of the receptor. These events could result in the clustering of the receptor and subsequent induction of signaling that could be modulated by the virus. Recently, numerous findings also suggest the presence of alternative receptor(s) for LASV in absence of the main DG receptor. In my first project, I was interested to investigate the effects of virus-receptor binding on the tyrosine phosphorylation of the cytoplasmic domain of DG and to test if this post-translational modification was crucial for the internalization of the LASV-receptor complex. We found that engagement of cellular DG by a recombinant LCMV expressing the envelope GP of LASV in human epithelial cells induced tyrosine phosphorylation of the cytoplasmic domain of DG. LASV GP binding to DG further resulted in dissociation of the adapter protein utrophin from virus-bound DG. Virus-induced dissociation of utrophin and consequent virus internalization were affected by the broadly specific tyrosine kinase inhibitor genistein. We speculate that the detachment of virus- bound DG from the actin-based cytoskeleton following DG phosphorylation may facilitate subsequent endocytosis of the virus-receptor complex. In the second project, I was interested to characterize the newly indentified LASV alternative receptor Axl in the context of productive arenavirus infection. In a first step, we demonstrated that Axl supports productive infection by rLCMV-LASVGP in a DG-independent manner. In line with previous studies, cell entry of rLCMV-LASVGP via Axl was less efficient when compared to functional DG. Interestingly, Axl-mediated infection showed rapid kinetics similar to DG-dependent entry. Using a panel of inhibitors, we found that Axl-mediated cell entry of rLCMV-LASVGP involved a clathrin-independent pathway that critically depended on actin and dynamin and was sensitive to EIPA but not to PAK inhibitors, compatible with a macropinocytosis-like mechanism of entry. In a next step, we aimed to investigate the molecular mechanism by which rLCMV-LASVGP recognizes Axl. Phosphatidylserine (PS) is the natural ligand of Axl via the adaptor protein Gas6. We detected the presence of PS in the envelope of Old World arenaviruses, suggesting that PS could mediate Axl-virus binding, in a mechanism of apoptotic mimicry already described for other viruses. Whether envelope PS and/or the GP of LASV plays any role in virus entry via Axl is still an open question. The molecular mechanisms underlying host cell-virus interaction are of particular interest to answer basic scientific questions as well as to apply key findings to translational research. Understanding pathogen induced-signaling and its link to invasion of the host cell is of great importance to develop drugs for therapeutic intervention against highly pathogenic viruses like LASV. - Les Arenavirus sont des virus enveloppés à ARN négatifs organisés sous forme de génome bisegmenté. Ils sont véhiculés par les rongeurs et se retrouvent de manière endémique aux Amériques et en Afrique avec l'exception du virus de la chorioméningite lymphocytaire (LCMV) qui lui est distribué mondialement. De nombreux pathogènes humains font parti de la famille des Arenavirus dont le virus de l'Ancien Monde Lassa (LASV), un agent responsable de fièvres hémorragiques sévères chez les humains. Le virus de Lassa cause plusieurs centaines de milliers d'infections par année en Afrique ainsi que des milliers de morts. De manière générale, les virus sont des parasites intracellulaires obligatoires qui dépendent strictement de processus et facteurs cellulaires pour clore leur cycle de réplication. L'attachement d'un virus à sa cellule cible représente la première étape de chaque infection virale et est principalement dirigée par des protéines virales qui interagissent directement avec leur récepteurs cellulaires respectifs fournissant ainsi un indicateur déterminant pour le tropisme d'un virus. Cette première étape de l'infection représente aussi une cible prometteuse pour bloquer le pathogène avant qu'il ne puisse prendre le contrôle de la cellule. Les Arenavirus de l'Ancien Monde comme LASV et LCMV s'attachent à la cellule hôte en se liant à leur récepteur principal, le dystroglycan (DG), un récepteur ubiquitaire pour les protéines de la matrice extracellulaire. La liaison du DG par LASV résulte en une rapide internalisation transférant le virus aux endosomes tardifs suggérant ainsi que l'attachement du virus au DG peut provoquer des changements marqués dans la dynamique moléculaire du récepteur. Ces événements sont susceptibles d'induire un regroupement du récepteur à la surface cellulaire, ainsi qu'une induction subséquente qui pourrait être, par la suite, modulée par le virus. Récemment, plusieurs découvertes suggèrent aussi la présence d'un récepteur alternatif pour LASV en l'absence du récepteur principal, le DG. Concernant mon premier projet, j'étais intéressée à étudier les effets de la liaison virus- récepteur sur la phosphorylation des acides aminés tyrosines se trouvant dans la partie cytoplasmique du DG, le but étant de tester si cette modification post-translationnelle était cruciale pour Γ internalisation du complexe LASV-DG récepteur. Nous avons découvert que l'engagement du récepteur DG par le virus recombinant LCMV, exprimant la glycoprotéine de LASV, dans des cellules épithéliales humaines induit une phosphorylation de résidu(s) tyrosine se situant dans le domaine cytoplasmique du DG. La liaison de la glycoprotéine de LASV au DG induit par la suite la dissociation de la protéine adaptatrice utrophine du complexe virus-DG récepteur. Nous avons observé que cette dissociation de l'utrophine, induite par le virus, ainsi que son internalisation, sont affectées par l'inhibiteur à large spectre des tyrosines kinases, la génistéine. Nous avons donc supposé que le détachement du virus, lié au récepteur DG, du cytosquelette d'actine suite à la phosphorylation du DG faciliterait l'endocytose subséquente du complexe virus-récepteur. Dans le second projet, j'étais intéressée à caractériser le récepteur alternatif Axl qui a été récemment identifié dans le contexte de l'infection productive des Arenavirus. Dans un premier temps, nous avons démontré que le récepteur alternatif Axl permet l'infection des cellules par le virus LCMV recombinant LASV indépendamment du récepteur DG. Conformément aux études publiées précédemment, nous avons pu observer que l'entrée du virus recombinant LASV via Axl est moins efficace que via le récepteur principal DG. De façon intéressante, nous avons aussi remarqué que l'infection autorisée par Axl manifeste une cinétique virale d'entrée similaire à celle observée avec le récepteur DG. Utilisant un éventail de différents inhibiteurs, nous avons trouvé que l'entrée du virus recombinant rLCMV-LASVGP via Axl implique une voie d'entrée indépendante de la clathrine et dépendant de manière critique de l'actine et de la dynamine. Cette nouvelle voie d'entrée est aussi sensible à l'EIPA contrairement aux inhibiteurs PAK indiquant un mécanisme d'entrée compatible avec un mécanisme de macropinocytose. L'étape suivante du projet a été d'investiguer le mécanisme moléculaire par lequel le virus recombinant rLCMV-LASVGP reconnaît le récepteur alternatif Axl. La phosphatidylsérine (PS) se trouve être un ligand naturel pour Axl via la protéine adaptatrice Gas6. Nous avons détecté la présence de PS dans l'enveloppe des Arenavirus du Vieux Monde suggérant que la PS pourrait médier la liaison du virus à Axl dans un mécanisme de mimétisme apoptotique déjà observé et décrit pour d'autres virus. Cependant, il reste encore à déterminer qui de la PS ou de la glycoprotéine de l'enveloppe virale intervient dans le processus d'entrée de LASV via le récepteur alternatif Axl. Les mécanismes moléculaires à la base de l'interaction entre virus et cellule hôte sont d'intérêts particuliers pour répondre aux questions scientifiques de base ainsi que dans l'application de découvertes clés pour la recherche translationnelle. La compréhension de la signalisation induite par les pathogènes ainsi que son lien à l'invasion de la cellule hôte est d'une importance considérable pour le développement de drogues pour l'intervention thérapeutique contre les virus hautement pathogènes comme LASV.

Application of discriminant function analysis and change-point problem in dating volcanic ashes

The application of Discriminant function analysis (DFA) is not a new idea in the study of tephrochrology. In this paper, DFA is applied to compositional datasets of two different types of tephras from Mountain Ruapehu in New Zealand and Mountain Rainier in USA. The canonical variables from the analysis are further investigated with a statistical methodology of change-point problems in order to gain a better understanding of the change in compositional pattern over time. Finally, a special case of segmented regression has been proposed to model both the time of change and the change in pattern. This model can be used to estimate the age for the unknown tephras using Bayesian statistical calibration

Modelos matemáticos para estimar as exigências de lisina digestível para aves de corte ISA Label

O objetivo neste estudo foi avaliar diferentes modelos ajustados às respostas de ganho de peso obtidas em experimento com aves da linhagem ISA Label no período de 1 a 28 dias de idade. Foram utilizados 480 pintos de ambos os sexos, distribuídos em delineamento inteiramente casualizado, em arranjo fatorial 4 X 2 (níveis de lisina X sexo), com três repetições, com 20 aves por unidade experimental. Uma ração basal foi formulada para atender às exigências das aves, exceto em lisina. Essa ração foi suplementada com L-lisina HCl em substituição ao ácido L-glutâmico, resultando em rações experimentais isonitrogênicas e isoenergéticas contendo 0,85; 0,97; 1,09 e 1,21% de lisina digestível. As respostas de ganho de peso foram ajustadas de acordo com os níveis de lisina da ração pelos modelos Linear Reponse Plateau (LRP), segmentado de duas inclinações, polinomial quadrático e exponencial. A primeira intersecção da equação quadrática com o platô do LRP também foi utilizado para estimar o nível ótimo. Os níveis de lisina digestível estimados pelos modelos LRP, segmentado e quadrático, foram 0,999; 1,010 e 1,116%, respectivamente. Na combinação do modelo quadrático com o LRP, a estimativa da exigência de lisina digestível foi de 1,041%. O modelo exponencial proporcionou estimativa de 1,066%, considerando 95% da resposta assintótica. Com base nos custos com alimentação, esse mesmo modelo gerou estimativas de 1,000 e 1,030% quando o custo do quilograma de L-lisina HCl foi R$ 8,50 e R$ 6,50, respectivamente. Considerando as limitações de cada um dos modelos propostos, o procedimento para estimar as exigências de lisina digestível pela primeira intersecção da equação quadrática com o platô do LRP foi o mais adequado para melhorar o ganho de peso das aves quando variáveis econômicas não foram consideradas.

Proposta de teste incremental baseado na percepção subjetiva de esforço para determinação de limiares metabólicos e parâmetros mecânicos do nado livre

A percepção subjetiva de esforço (PSE) é determinada de forma não invasiva e utilizada juntamente com a resposta lactacidêmica como indicadores de intensidade durante teste incremental. em campo, especialmente na natação, há dificuldades nas coletas sanguíneas; por isso, utilizam-se protocolos alternativos para estimar o limiar anaeróbio. Assim, os objetivos do estudo foram: prescrever um teste incremental baseado na PSE (Borg 6-20) visando estimar os limiares metabólicos determinados por métodos lactacidêmicos [ajuste bi-segmentado (V LL), concentração fixa-3,5mM (V3,5mM) e distância máxima (V Dmáx)]; relacionar a PSE atribuída em cada estágio com a freqüência cardíaca (FC) e com parâmetros mecânicos de nado [freqüência (FB) e amplitude de braçada (AB)], analisar a utilização da escala 6-20 na regularidade do incremento das velocidades no teste e correlacionar os limiares metabólicos com a velocidade crítica (VC). Para isso, 12 nadadores (16,4 ± 1,3 anos) realizaram dois esforços máximos (200 e 400m); os dados foram utilizados para determinar a VC, velocidade de 400m (V400m) e a freqüência crítica de braçada (FCb); e um teste incremental com intensidade inicial baseada na PSE, respectivamente, 9, 11, 13, 15 e 17; sendo monitorados em todos os estágios a FC, lactacidêmia e os tempos de quatro ciclos de braçadas e das distâncias de 20m (parte central da piscina) e 50m. Posteriormente, foram calculadas as velocidades dos estágios, FB, AB, V LL, V3,5mM e V Dmáx. Utilizaram-se ANOVA e correlação de Pearson para análise dos resultados. Não foram encontradas diferenças entre VC, V Dmáx e V LL, porém a V3,5mM foi inferior às demais velocidades (P < 0,05). Correlações significativas (P < 0,05) foram observadas entre VC versus V400m, V Dmáx e V3,5mM; V400m versus V3,5mM e V Dmáx; V Dmáx versus V LL; e no teste incremental entre PSE versus velocidade, [Lac], FC, FB e AB (P < 0,05). Concluímos que a PSE é uma ferramenta confiável no controle da velocidade dos estágios durante teste incremental na natação.

Critical points in logistic growth curves and treatment comparisons

Several biological phenomena have a behavior over time mathematically characterized by a strong increasing function in the early stages of development, then by a less pronounced growth, sometimes showing stability. The separation between these phases is very important to the researcher, since the maintenance of a less productive phase results in uneconomical activity. In this report we present methods of determining critical points in logistic functions that separate the early stages of growth from the asymptotic phase, with the aim of establishing a stopping critical point in the growth and on this basis determine differences in treatments. The logistic growth model is fitted to experimental data of imbibition of arariba seeds (Centrolobium tomentosum). To determine stopping critical points the following methods were used: i) accelerating growth function, ii) tangent at the inflection point, iii) segmented regression; iv) modified segmented regression; v) non-significant difference; and vi) non-significant difference by simulation. The analysis of variance of the abscissas and ordinates of the breakpoints was performed with the objective of comparing treatments and methods used to determine the critical points. The methods of segmented regression and of the tangent at the inflection point lead to early stopping points, in comparison with other methods, with proportions ordinate/asymptote lower than 0.90. The non-significant difference method by simulation had higher values of abscissas for stopping point, with an average proportion ordinate/asymptote equal to 0.986. An intermediate proportion of 0.908 was observed for the acceleration function method.