First-class features

Magdeburg, Univ., Fak. für Informatik, Diss., 2011

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.

Interpolatory methods for model reduction of large-scale dynamical systems

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

Attitudes toward corporate sustainability : a multi-item scale and a multi-country empirical analysis

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

Micro scale modeling grain boundary damage under creep conditions

Magdeburg, Univ., Fak. für Maschinenbau, Diss., 2014

Statistical model identification : dynamical processes and large-scale networks in systems biology

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2014

Statistical model identification : dynamical processes and large-scale networks in systems biology

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2014

Computational methods for model reduction of large-scale sparse structured descriptor systems

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

Observations on a collection of Papuan crania / by George A. Dorsey ; with notes on preservation and decorative features by William H. Holmes.

v.2:no.1(1897)

Structural features and phylogenetic relationships among larvae of genera of gyrophaenine staphylinids (Coleoptera: Staphylinidae: Aleocharinae) / James S. Ashe.

n.s. no.30(1986)

Quantitative fidelity of recent freshwater mollusk assemblages from the Touro Passo River, Rio Grande do Sul, Brazil

This study represents one of the first contributions to the knowledge on the quantitative fidelity of the recent freshwater molluscan assemblages in subtropical rivers. Thanatocoenoses and biocoenoses were studied in straight and meandering to braided sectors, in the middle course of the Touro Passo River, a fourth-order tributary of the Uruguay River, located in the westernmost part of the State of Rio Grande do Sul. Samplings were carried out through quadrats of 5 m², five in each sector. A total area of 50 m² was sampled. Samplings were also made in a lentic environment (abandoned meander), with intermittent communication with the Touro Passo River, aiming to record out-of-habitat shell transportation from the lentic communities to the main river channel. The results show that, despite the frequent oscillation of the water level, the biocoenosis of the Touro Passo River shows high ecological fidelity and undergoes little influence from the lentic vicinal environments. The taxonomic composition and some features of the structure of communities, especially the dominant species, also reflect some ecological differences between the two main sectors sampled, such as the complexity of habitats in the meandering-sector. Regarding the quantitative fidelity, 60% of the species found alive were also found dead and 47.3% of the species found dead were also found alive, at river-scale. However, 72% of the dead individuals belong to species also found alive. This value might be related with the good rank order correlation obtained for live/dead assemblages. Consequently, the dominant species of the thanatocoenoses could be used to infer the ecological attributes of the biocoenoses. The values of all the indexes analyzed were very variable in small-scale samplings (quadrat), but were more similar to others registered in previous studies, when they were analyzed in a station and river scale.

Population and reproductive features of the western Atlantic hermit crab Pagurus criniticornis (Anomura, Paguridae) from Anchieta Island, southeastern Brazil

The population of the hermit crab Pagurus criniticornis (Dana, 1852) was studied based on seasonal abundance, size frequency distribution, sex ratio, reproductive period, fecundity and shell relationship. Specimens were collected monthly by SCUBA diving in the infralittoral area of Anchieta Island, Ubatuba. A total of 1,017 individuals was analyzed. Animal size (minimum and maximum shield length, respectively) was 0.7 and 2.9 mm for males, 0.6 and 2.8 mm for non-ovigerous females, and 1.0 and 2.5 mm for ovigerous females. The sex ratio was 1:1.29. Sexual dimorphism was recorded by the presence of males in the largest size classes. Ovigerous females were captured during all months along the year, with percentages varying from 8% (July) to 84.3% (February) in relation to the total females collected. Mean ± SD fecundity was 168 ± 125 eggs and tended to increase with increasing hermit size. Shells of four gastropod species [Cerithium atratum (Born, 1778), Morula nodulosa (Adams, 1845), Anachis lyrata (Sowerby, 1832) and Modulus modulus (Linnaeus, 1758)] were occupied by ovigerous females of P. criniticornis but fecundity was not significantly different in relation to the different shell types. The profile showed continuous and intense reproduction of P. criniticornis probably related to strategies developed to compensate for interspecific competition in the studied insular area.

The swim bladder in the Serrasalminae, with notes on additional morphological features.

v.39:no.56(1961)