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.

Simulation of lime calcination in normal shaft an parallel flow regenerative kilns

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2012

Lagrangian methods for visualization and analysis of time-dependent vector fields

Magdeburg, Univ., Fak. für Informatik, Diss., 2013

Shapes in vector fields : methods for continuous deformations and surface-based flow visualizations

Magdeburg, Univ., Fak. für Informatik, Diss., 2013

Extração de diversos íons do solo com solução normal de KCl

O presente trabalho tem por objetivo extrair e determinar diversos íons, como o alumínio, hidrogênio, cálcio e magnésio que se acham ligados aos colóides do solo por eletrovalência, em alguns solos do Município de Piracicaba. Além disso, constitui também finalidade dêste trabalho relacionar as diversas características dos solos estudados a fim de esclarecer vários aspectos considerados importantes na química do solo. Trinta e seis amostras de solos, correspondentes aos horizontes superficiais e subsuperficiais de dez séries do citado Município, foram submetidas à extração com solução 1 N de KCl e no extrato foram determinados os cátions já mencionados, além de determinar o pH em suspensão da solução 1 N em KCl. Nas mesmas amostras foram determinados: pH em suspensão aquosa, carbono total, cálcio, magnésio e potássio extraídos com solução 0,05 N de HNO3 e hidrogênio extraído com solução 1 N de acetato de cálcio com pH = 7,0. Os dados obtidos permitem concluir que a carga negativa permanente dos colóides dos solos estudados é muito baixa e que uma fração elevada da mesma é neutralizada pelo alumínio, em muitas das amostras analisadas. Verificou-se, também, que o teor de alumínio trocável correlaciona-se tanto com o pH determinado em suspensão aquosa, como com o determinado em suspensão de solução 1 N de CKl e com o hidrogênio, extraído com solução de acetato de cálcio 1 N com pH = 7,0. A porcentagem de saturação de bases, calculada em função da carga permanente e a calculada em função da extração das bases com solução de HNO3 0,05 N e da extração do hidrogênio com solução de acetato de cálcio 1N, pH = 7,0, correlacionam-se com o pH do solo. Finalmente, constatou-se que o teor de cálcio mais magnésio extraído com solução 1 N de KCl é equivalente ao extraído com solução 0,05 N de HNO3, indicando que, provàvelmente, os solos estudados não apresentam minerais silicatados ou carbonatados dos mencionados cátions.

Verification of system properties of polynomial systems using discrete-time approximations and set-based analysis

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2015

Topology of vector fields with uncertainty

Magdeburg, Univ., Fak. für Informatik, Diss., 2015

Aplicação de reguladores de crescimento em figos produzidos fora da época normal

Fez-se a aplicação de giberelinas (50 e 100 ppm) e de clorofenoxipropionamida (250, 500 e 1000 ppm) sobre figos em vários estádios de desenvolvimento, de plantas podadas em dezembro, visando-se à produção de figos fora da época normal. Os resultados demostraram que as giberelinas a 50 ppm provocaram alongamento no comprimento dos figos. O tratamento com clorofenoxipropionamida (Fruitone CPA) a 1000 ppm resultou em frutos mais pesados, porém, estes valores não diferiram estatisticamente daqueles do tratamento controle. O peso médio dos figos foi de 50,0 gramas, para as primeiras oito semanas de colheita, período considerado no experimento.

Contribuição para a determinação do nível normal de componentes do sangue bovino canchim

Conduziu-se um experimento na Fazenda Canchim, em São Carlos, SP, para se verificar se determinados componentes do sangue de bovinos jovens refletiriam diferentes estados nutricionais. 0 delineamento estatístico foi o de blocos casualizados. Empregaram - se 36 bovinos canchim desmamados, inteiros, em regime de pasto exclusivo (T1), ou confinados, recebendo feno de soja e rolão de milho (T2), torta de algodão e cana-de-açúcar (T3), ou ração completa (T4), de março a setembro de 1973, e em seguida somente pasto, até março de 1974. No período de confinamento, as pesagens e coletas de sangue foram a cada 2 semanas, passando para 4no período seguinte. Embora os tratamentos houvessem proporcionado diferentes níveis de consumo, de ganho de peso e de conversão, não houve variação correspondente nos diversos componentes de sangue analisados, talvez porque os intervalos de coleta e de pesagens deveriam ter sido mais curtos, para que se relacionassem melhor, pois os primeiros dados corresponderam às médias diárias do intervalo entre pesagens, enquanto que as dosagens correspondiam a uma única determinação do dia da coleta. A utilização de "kits" para análise do sangue comprovou-se plenamente satisfatória, mais simples e rápida em relação ao sistema convencional. Foram assumidos como normais os níveis médios para os seguintes parâmetros do sangue: uréia, 11,1 a 16,1 mg;proteínas totais, 5,92 a 6,32 g; fósforo, 6,24 a 7,11 mg; Ca, 11,01 a 12,66 mg; e hemoglobina, 10,14 a 10,55 g por decilitro.

Daily activity and microhabitat use of sympatric lizards from Serra do Cipó, southeastern Brazil

We studied the influence of seasonality on the daily activity pattern and microhabitat use of three sympatric lizard species, Cnemidophorus ocellifer Spix, 1825 (Teiidae), Tropidurus montanus Rodrigues, 1987 and Eurolophosaurus nanuzae (Rodrigues, 1981) (Tropiduridae), in an area of campos rupestres (rocky fields) habitat in state of Minas Gerais, Brazil. Cnemidophorus ocellifer exhibited low density and activity concentrated within the hottest hours of the day, and was observed mainly on shaded rocks. Tropidurus montanus and E. nanuzae had similar activity patterns that did not vary between seasons. Activity of T. montanus was related to environmental temperatures. However, we did not find such relationships for E. nanuzae during the dry season. Both T. montanus and E. nanuzae were sighted mainly on exposed rocks. Extension of activity varied between seasons, shorter for C. ocellifer and longer for T. montanus and E. nanuzae during the rainy season.

Lipoides do plasma normal

1. In a series of 21 normal cases we found for fatty acids per 100 cc. of plasma an average of 332 mgm., being 314 mgm. for the male sex and 350 mgm. for the female sex. 2.- For lecithin, in four normal cases we found per 100 cc. of plasma 182 mgm. estimated by the contents is phosphorus which ranged from 6.12 to 9.0 mgrs. 3.- Cholesterol in 20 normal cases showed 172 mgm. per 100 cc. of plasma. The averages were 151 mgm. for men and 194 mgm. for women. 4.- The readings of the fractions were 2.01 for the ratio fatty acids divided by lecithins 0.90 for lecithin divided by cholesterol and 1.93 for fatty acids divided by cholesterol. 5.- On comparing the results obtained by us with those reported in foreign literature an absolute conformity is noted chiefly with the values supplied by Bloor and Horiuchi for the ratios among the various lipoid fractions. The average for Cholesterol is comparable with that obtained by Myers but is slightly under that of Bloor's. The lecithin contents found by us did not reach such high values as those supplied by foreign authors.

Glutathion no sangue humano normal

1.) - Woodward-Fry's and Okuda-Hess technics were employed in the determination of blood glutathione in normal healthy adults of both sexes. 2.) - It was found more accurately results with the technic of Woodward and Fry than of any others for the dosage of G. S. H. of blood. 3.) - When the process of Okuda-Hess is modified by the use of an intern indicator (starch) the readings of the end-point are much more easy and therefore the results more exacts. 4.) - The averages of the data obtained for normal blood by the technic of Woodward and Fry were for men per hundred cubic cent. 27 mgrs (G.S.H); 6.6 mgrs. (G.S.S) and 33.6 mges. (G. T) and for women: 28.4 mgrs. (G.S.H), 7.8 mgrs. (G.S.S) and 36,2 mgrs. (G.T). 5.) - Autoxidation in the blood filtrate is only apreciated after 24 hs. In the first eight hours autoxidation is never observed. 6.) - The increase of glutathione in hyperglobulia is a function of the amount of red corpuscles. In acrocyanosis arterial blood is richest in these component than venous blood and this fact is in accordance with the observation of Blanchetière, Mélon and Binet for the experimental asphyxia of dogs.

The human genetic mutant cell repository : list of genetic variants, chromosomal aberrations and normal cell cultures submitted to the repository / Institute for Medical Research, Camden, New Jersey.

4th ed.

Global eriodicity and complete integrability of discrete dynamical systems

Vegeu el resum a l'inici del document del fitxer adjunt