Máquina-ferramenta CNC para gravação: desenvolvimento de protótipo de baixo-custo

Dissertação de mestrado em Engenharia Mecatrónica

Modelos de simulação de processos por junção de componentes

Dissertação de mestrado integrado em Engenharia e Gestão de Sistemas de Informação

Longitudinal evaluation, acceptability and long-term retention of knowledge on a horizontally integrated organic and functional systems course

Undergraduate medical education is moving from traditional disciplinary basic science courses into more integrated curricula. Integration models based on organ systems originated in the 1950s, but few longitudinal studies have evaluated their effectiveness. This article outlines the development and implementation of the Organic and Functional Systems (OFS) courses at the University of Minho in Portugal, using evidence collected over 10 years. It describes the organization of content, student academic performance and acceptability of the courses, the evaluation of preparedness for future courses and the retention of knowledge on basic sciences. Students consistently rated the OFS courses highly. Physician tutors in subsequent clinical attachments considered that students were appropriately prepared. Performance in the International Foundations of Medicine examination of a self-selected sample of students revealed similar performances in basic science items after the last OFS course and 4 years later, at the moment of graduation. In conclusion, the organizational and pedagogical approaches of the OFS courses achieve high acceptability by students and result in positive outcomes in terms of preparedness for subsequent training and long-term retention of basic science knowledge.

Jornalismo desportivo: entretenimento ou informação

Relatório de estágio de mestrado em Ciências da Comunicação (área de especialização em Informação e Jornalismo)

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

FISHji: new ImageJ macros for the quantification of fluorescence in epifluorescence images

Fluorescence in situ hybridization (FISH) is based on the use of fluorescent staining dyes, however, the signal intensity of the images obtained by microscopy is seldom quantified with accuracy by the researcher. The development of innovative digital image processing programs and tools has been trying to overcome this problem, however, the determination of fluorescent intensity in microscopy images still has issues due to the lack of precision in the results and the complexity of existing software. This work presents FISHji, a set of new ImageJ methods for automated quantification of fluorescence in images obtained by epifluorescence microscopy. To validate the methods, results obtained by FISHji were compared with results obtained by flow cytometry. The mean correlation between FISHji and flow cytometry was high and significant, showing that the imaging methods are able to accurately assess the signal intensity of fluorescence images. FISHji are available for non-commercial use at http://paginas.fe.up.pt/nazevedo/.

Desenvolvimento e validação de um método para a caracterização de vinhos por HPLC-DAD

Dissertação de mestrado em Técnicas de Caracterização e Análise Química

Pervasive decision support to predict football corners and goals by means of data mining

Football is considered nowadays one of the most popular sports. In the betting world, it has acquired an outstanding position, which moves millions of euros during the period of a single football match. The lack of profitability of football betting users has been stressed as a problem. This lack gave origin to this research proposal, which it is going to analyse the possibility of existing a way to support the users to increase their profits on their bets. Data mining models were induced with the purpose of supporting the gamblers to increase their profits in the medium/long term. Being conscience that the models can fail, the results achieved by four of the seven targets in the models are encouraging and suggest that the system can help to increase the profits. All defined targets have two possible classes to predict, for example, if there are more or less than 7.5 corners in a single game. The data mining models of the targets, more or less than 7.5 corners, 8.5 corners, 1.5 goals and 3.5 goals achieved the pre-defined thresholds. The models were implemented in a prototype, which it is a pervasive decision support system. This system was developed with the purpose to be an interface for any user, both for an expert user as to a user who has no knowledge in football games.

Quantifying the legacy of the Chinese Neolithic on the maternal genetic heritage of Taiwan and Island Southeast Asia

There has been a long-standing debate concerning the extent to which the spread of Neolithic ceramics and Malay-Polynesian languages in Island Southeast Asia (ISEA) were coupled to an agriculturally driven demic dispersal out of Taiwan 4000 years ago (4 ka). We previously addressed this question using founder analysis of mitochondrial DNA (mtDNA) control-region sequences to identify major lineage clusters most likely to have dispersed from Taiwan into ISEA, proposing that the dispersal had a relatively minor impact on the extant genetic structure of ISEA, and that the role of agriculture in the expansion of the Austronesian languages was therefore likely to have been correspondingly minor. Here we test these conclusions by sequencing whole mtDNAs from across Taiwan and ISEA, using their higher chronological precision to resolve the overall proportion that participated in the "out-of-Taiwan" mid-Holocene dispersal as opposed to earlier, postglacial expansions in the Early Holocene. We show that, in total, about 20 % of mtDNA lineages in the modern ISEA pool result from the "out-of-Taiwan" dispersal, with most of the remainder signifying earlier processes, mainly due to sea-level rises after the Last Glacial Maximum. Notably, we show that every one of these founder clusters previously entered Taiwan from China, 6-7 ka, where rice-farming originated, and remained distinct from the indigenous Taiwanese population until after the subsequent dispersal into ISEA.

Development of a subject-specific musculoskeletal shoulder model : inverse and forward dynamics applications

A prevalência de pessoas que referem dor no complexo articular do ombro, com concomitante limitação na capacidade para realizar atividades da vida diária, é elevada. Estes níveis de prevalência sobrecarregam quer os utentes, como a própria sociedade. A evidência científica atual indicia a existência de uma relação entre as alterações da articulação escápulo-torácica e as patologias associadas à articulação gleno-umeral. A capacidade de quantificar, cinemática e cineticamente, as disfunções ao nível das articulações escápulo-torácica e gleno-umeral, é algo de enorme importância, quer para a comunidade biomecânica, como para a clínica. No decorrer dos trabalhos desta tese foi desenvolvido, através do software OpenSim, um modelo tridimensional músculo-esquelético do complexo articular do ombro que inclui a representação do tórax/coluna, clavícula, omoplata, úmero, rádio, cúbito e articulações que permitem os movimentos relativos desses segmentos, assim como, 16 músculos e 4 ligamentos. Com um total de 11 graus de liberdade, incluindo um novo modelo articular escápulo-torácico, os resultados demonstram que este é capaz de reconstruir de forma precisa e rápida os movimentos escápulo-torácicos e glenoumerais, recorrendo para tal, à cinemática inversa, e à dinâmica inversa e direta. Conta ainda com um método de transformação inovador para determinar, com base nas especificidades dos sujeitos, os locais de inserção muscular. As principais motivações subjacentes ao desenvolvimento desta tese foram contribuir para o aprofundar do atual conhecimento sobre as disfunções do complexo articular do ombro e, simultaneamente, proporcionar à comunidade clínica uma ferramenta biomecânica de livre acesso com o intuito de melhor suportar as decisões clínicas e dessa forma concorrer para uma prática mais efetiva.

Terapéutica racional, mediante indicadores de eficacia antimicrobiana, de la mastitis caprina utilizando marbofloxacina y cefquinoma. Rational therapeutics, indicators of antimicrobial efficiency in the mastitis goats using marbofloxacine and cefquinome

La producción de leche de cabra es considerada en nuestro país, y en la provincia de Córdoba, una alternativa productiva para el desarrollo sustentable y socio – económico de la población. Por otra parte, existe una mayor demanda del mercado nacional e internacional de esta leche, por lo que los productores deben garantizar la seguridad y calidad de la misma de acuerdo a las normas vigentes. Es por ello que el control y tratamiento de las diferentes enfermedades es de vital importancia tanto para maximizar la producción del hato como para cumplir con los cánones de seguridad exigidos. En este contexto la mastitis caprina es una de las enfermedades que afecta la productividad del sector, y para controlarla una de las medidas a emplear es la terapéutica con antimicrobianos. Se trabajará en este proyecto con marbofloxacina y cefquinoma, estableciendo pautas racionales (eficaces y seguras) para su empleo en la afección a nivel regional. Los indicadores de eficacia estarán fijados de acuerdo a los parámetros integrados de farmacocinética (FC) y farmacodinamia (FD). Estos últimos (FD) serán calculados a través de la determinación concentraciones inhibitorias mínimas de cepas bacterianas aisladas de mastitis caprinas en Córdoba. Se establecerán los parámetros farmacocinéticos a dosis únicas y múltiples para la marbofloxacina (5 mg/kg IV, IM) y cefquinoma (2 mg/kg IV, IM e IMM) a partir de muestras de suero y leche de cabras Anglo Nubian (n = 6 por antimicrobiano; diseño cruzado en función de la ruta de administración). Se determinarán sus concentraciones en dichos fluidos, por cromatografía líquida de alta precisión. Los resultados FC/FD para ambos medicamentos se compararán con parámetros recomendados por expertos para cada tipo de antimicrobiano y se utilizarán como medida para recomendar una terapéutica racional, fundamental para optimizar la posología, garantizar la eficacia clínica, y reducir al mínimo la selección y propagación de cepas resistentes de agentes patógenos. The production of milk of goat is considered the province of Cordoba, a productive alternative for the sustainable development and partner - economically of the population. There is a major demand of the domestic and international market of this milk, for what the producers must guarantee the safety and quality of the same one of agreement to the in force procedure. It is for it that the control and treatment of the different diseases performs vital importance so much to maximize the production of the herd as to expire with the safety demanded. In this context the mastitis goat is one of the diseases that affect the productivity of the sector, and to control her one of the measures to using is the therapeutics with antimicrobial. One will be employed at this project with marbofloxacine and cefquinome, establishing rational guidelines (effective and sure) for his employment in the affection to regional level. The indicators of efficiency will be fixed in agreement to the integrated parameters of pharmacokinetics (PK) and pharmacodinamics (PD). The latter (PK) will be calculated across the determination inhibitory minimal concentrations of bacterial strains isolated of mastitis goat in Córdoba. The parameters will be established pharmacokinetics to the only and multiple doses for the marbofloxacine (5 mg/kg the IV, IM) and cefquinome (2 mg/kg the IVth, IM and IMM), From samples of whey and milk of goats Anglo Nubian (n = 6 for antimicrobial; design crossed depending on the route of administration). Its concentrations will decide in the above mentioned fluids, for liquid chromatography of high precision. The results PK/PD for both antimicrobial will be compared with parameters recommended by experts for every type of antimicrobial and will be in use as measure for recommending a rational, fundamental therapeutics for optimizing the dosage, for guaranteeing the clinical efficiency, and to reduce to the minimum the selection and spread of resistant of pathogenic agents.

Caracterización, procesamiento e industrialización del grano de quinoa, cultivado en la provincia de Córdoba - Argentina. Characterization, processing and industrialization of quinoa seed harvested in the province of Córdoba - Argentina

La quinoa (Chenopodium quinoa Willd), es un pseudocereal originario de la región Andina. Fue utilizada como alimento básico por los pueblos nativos. La quinoa, la papa y el maíz constituyeron el trinomio base de la alimentación indígena de este continente. La colonización española fue desplazando su cultivo a favor del trigo europeo y otros cereales, quedando reducida a las zonas altas de la región andina. La Quínoa ha adquirido una considerable atención en los últimos tiempos, principalmente por la calidad de sus proteínas y la ausencia de gluten en ella. Su empleo está ampliamente difundido en los países andinos, especialmente Bolivia y Perú, con un notable crecimiento de la superficie sembrada. En nuestro país la explotación de este cultivo se ubica principalmente en las provincias norteñas de Salta y Jujuy. En estos últimos años se ha reivindicado su cultivo y los granos privados de saponinas son considerados como un excelente alimento, reconocido por la OMS, la FAO y la NASA. Además de la calidad de sus lípidos y vitaminas, y al elevado contenido en almidón, la quinoa posee una proteína de excelente calidad nutricional y libre de gluten, lo que hace a este grano especialmente indicado para la alimentación de personas que sufren de la enfermedad celíaca o del síndrome de intestino irritado. El presente proyecto está orientado al aprovechamiento integral del grano de quinoa. Es nuestra intensión aquí, demostrar que dicho grano, cultivado en la provincia de Córdoba, permitirá elaborar productos alimenticios asi como también derivados de su industrialización. Para este objetivo se cuenta con las instalaciones de la Planta Piloto del Instituto de Ciencia y Tecnología de los Alimentos (ICTA), de la UNC, así como de intrumental moderno y acorde, como HPLC, GC, Espectrofotómetro UV-Vis, rotavapores de laboratorio e industrial, cámara fría, balanzas analíticas y de precisión, muflas, estufas, molinos y tamices, así como también, contamos con profesionales, algunos de ellos realizando su tesis doctoral en este tema. En cuanto a los objetivos que se persiguen, se espera obtener productos tales como sopas, papillas, productos para panadería y galletería y salsas. En el plano industrial, se pretende elaborar concentrados proteicos, almidón y saponinas. Como se dijo más arriba, a nivel internacional la quinoa ha comenzado a extender sus fronteras, y es así que hoy el principal productor mundial de este grano, Bolivia, destina un porcentaje importante de su producción a la exportación. La creciente demanda mundial de quinoa a hecho que se constituya en un cultivo estratégico y de alto valor, con precios internacionales que rondan los U$S 1200 la tonelada. Si a esto unimos que la planta presenta una gran resistencia a la sequía, que se adapta bien a terrenos salitrosos, arenosos y pobres, podemos comprender la importancia que adquiere para nuestra provincia, toda vez que en la misma existen zonas geográficas potencialmente aptas para su cultivo. Quinoa (Chenopodium quinoa Willd) is a pseudocereal originating in the Andean region. It was used as a staple food by native peoples. Quinoa, potatoes and corn were the tree most important indigenous staple food to this part of South America. Spanish colonization was marginalized cultivation in favor of European wheat and other grains, displacing it to the highlands of the Andean region. Quinoa has recently gained considerable attention, mainly by its protein quality and lack of gluten. Its use is widespread in the Andean countries, especially Bolivia and Peru, with a notable increase in plantings. In our country, the exploitation of this crop is located mainly in the northern provinces of Salta and Jujuy. In recent years its cultivation has been promoted, and the grains once free of saponins are considered an excellent food, recognized by WHO, FAO and NASA. In addition to its lipid and vitamins, and high starch contain, quinoa protein has an excellent nutritional value and it is free of gluten, making it particularly suitable for this grain to feed people with celiac disease or irritable bowel syndrome. This project aims at an integral development of quinoa grain. It is our intention here to demonstrate that this grain grown in the province of Córdoba, can produce food products resulting from local industrialization. This team has access to the facilities of the Pilot Plant of the Institute of Science and Food Technology (ICTA) of the UNC, and the modern equipments in it, as HPLC, GC, UV-Vis spectrophotometer, laboratory and industrial rotary evaporators, cold storage, analytical and precision balances, flasks, ovens, grinders and screens. Also, we have an important professional staff, some of them doing their thesis on this subject. With regard to the objectives pursued, we expect to obtain products such as soups, baby food, bakery products and biscuits and sauces. At the industrial level, it aims at producing protein concentrates, starch and saponins.

Ireland’s understudied flatfish: reproduction, age and growth of the dab Limanda limanda (L.) in Irish coastal waters

In Ireland, although flatfish form a valuable fishery, little is known about the smallest, the dab Limanda limanda. In this study, a variety of parameters of reproductive development, including ovarian phase description, gonadosomatic index (GSI), hepatosomatic index (HSI), relative condition (Kn) and oocyte size were analysed to provide information on the dab’s reproductive cycle and spawning periods. Sampling were collected monthly over an 18-month period using bottom trawls of the Irish coastline. A six phase macroscopic guide was developed for both sexes of dab, and verified using histology. In comparisons of macroscopic and microscopic phases, there was high agreement in the proposed female guide (86%), with males demonstratively lower (62%). No significant bias was observed between the the two reproductive methods. When the male macroscopic guide was examined, misclassification was high in phase 5 and phase 5 (41%), with 96% of misclassification occurring in adjacent phases. The sampled population was primarily composed of females, with ratios of females to males 1:0.6, although the predominance of females was less noticeable during the reproductive season. Oocyte growth in dab follows asynchronous development, and spawn over a protracted period indicating a batch spawning strategy. Spawning occurred mainly in early spring, with total regeneration of gonads by May. The length at which 50% of the population was reproductively mature was identified as 14cm and 17cm, for male and female dab, respectively. Precision and bias in age determinations using whole otoliths to age dab was investigated using six age readers from various institutions. Low levels of precision were obtained (CV: 10-23%) inferring the need for an alternative methodology. Precision and bias was influence by the level of experience of the reader, with ageing error attributed to interpretative differences and difficulty in edge determination. Sectioned otolith age determinations were subsequently compared to whole otolith age determinations using two age readers experienced in dab ageing. Although increased precision was observed in whole otoliths from previous estimates (CV=0%, 0% APE), sectioned otoliths were used for growth models. This was based on multinominal logistic regression on age length keys developed using both ageing methods. Biological data (length and age) for both sexes was applied to four growth models, where the Akaike criterion and Multi model Inference indicated the logistic model as having the best fit to the collected data. In general, female dab attained a longer length then males, with growth rates significantly different between the two sexes. Length weight relationships between the two sexes were also significantly different.

Comportamento dos cromossômios na meiose de Euryophthalmus rufipennis Laporte (Hemiptera Pyrrhocoridae)

In this paper an account is given of the principal facts observer in the meiosis of Euryophthalmus rufipennis Laporte which afford some evidence in favour of the view held by the present writer in earlier publications regarding the existence of two terminal kinetochores in Hem ip ter an chromosomes as well as the transverse division of the chromosomes. Spermatogonial mitosis - From the beginning of prophase until metaphase nothing worthy of special reference was observed. At anaphase, on the contrary, the behavior of the chromosomes deserves our best attention. Indeed, the chromoso- mes, as soon as they begin to move, they show both ends pronouncedly turned toward the poles to which they are connected by chromosomal fibres. So a premature and remarkable bending of the chromosomes not yet found in any other species of Hemiptera and even of Homoptera points strongly to terminally localized kinetochores. The explanation proposed by HUGHES-SCHRADER and RIS for Nautococcus and by RIS for Tamalia, whose chromosomes first become bent late in anaphase do not apply to chromosomes which initiate anaphase movement already turned toward the corresponding pole. In the other hand, the variety of positions assumed by the anaphase chromosomes of Euryophthalmus with regard to one another speaks conclusively against the idea of diffuse spindle attachments. First meiotic division - Corresponding to the beginning of the story of the primary spermatocytes cells are found with the nucleus entirelly filled with leptonema threads. Nuclei with thin and thick threads have been considered as being in the zygotente phase. At the pachytene stage the bivalents are formed by two parallel strands clearly separated by a narrow space. The preceding phases differ in nothing from the corresponding orthodox ones, pairing being undoubtedly of the parasynaptic type. Formation of tetrads - When the nuclei coming from the diffuse stage can be again understood the chromosomes reappear as thick threads formed by two filaments intimately united except for a short median segment. Becoming progressively shorter and thicker the bivalents sometimes unite their extremities forming ring-shaped figures. Generally, however, this does not happen and the bivalents give origin to more or less condensed characteristic Hemipteran tetrads, bent at the weak median region. The lateral duplicity of the tetrads is evident. At metaphase the tetrads are still bent and are connected with both poles by their ends. The ring-shaped diakinesis tetrads open themselves out before metaphase, showing in this way that were not chiasmata that held their ends together. Anaphase proceeds as expected. If we consider the median region of the tetrads as being terminalized chiasmata, then the chromosomes are provided with a single terminal kinetochore. But this it not the case. A critical analysis of the story of the bivalents before and after the diffuse stage points to the conclusion that they are continuous throughout their whole length. Thence the chromosomes are considered as having a kinetochore at each end. Orientation - There are some evidences that Hemipteran chromosomes are connected by chiasmata. If this is true, the orientation of the tetrads may be understood in the following manner: Chiasmata being hindered to scape by the terminal kinetochores accumulate at the ends of the tetrads, where condensation begins. Repulsion at the centric ends being prevented by chiasmata the tetrads orient themselves as if they were provided with a single kinetochore at each extremity, taking a position parallelly to the spindle axis. Anaphase separation - Anaphase separation is consequently due to a transverse division of the chromosomes. Telophase and secund meiotic division - At telophase the kinetochore repeli one another following the moving apart of the centosomes, the chiasmata slip toward the acentric extremities and the chromosomes rotate in order to arrange themselves parallelly to the axis of the new spindle. Separation is therefore throughout the pairing plane. Origin of the dicentricity of the chromosomes - Dicentricity of the chromosomes is ascribed to the division of the kinetochore of the chromosomes reaching the poles followed by separation and distension of the chromatids which remain fused at the acentric ends giving thus origin to terminally dicentric iso-chromosomes. Thence, the transverse division of the chromosomes, that is, a division through a plane perpendicular to the plane of pairing, actually corresponds to a longitudinal division realized in the preceding generation. Inactive and active kinetochores - Chromosomes carrying inactive kinetochore is not capable of orientation and active anaphasic movements. The heterochromosome of Diactor bilineatus in the division of the secondary spermatocytes is justly in this case, standing without fibrilar connection with the poles anywhere in the cell, while the autosomes are moving regularly. The heterochromosome of Euryophthalmus, on the contrary, having its kinetochores perfectly active ,is correctly oriented in the plane of the equator together with the autosomes and shows terminal chromosomal connection with both poles. Being attracted with equal strength by two opposite poles it cannot decide to the one way or the other remaining motionless in the equator until some secondary causes (as for instances a slight functional difference between the kinetochores) intervene to break the state of equilibrium. When Yiothing interferes to aide the heterochromosome in choosing its way it distends itself between the autosomal plates forming a fusiform bridge which sometimes finishes by being broken. Ordinarily, however, the bulky part of the heterochromosome passes to one pole. Spindle fibers and kinetic activity of chromosomal fragments - The kinetochore is considered as the unique part of the chromosome capable of being influenced by other kinetochore or by the poles. Under such influence the kinetochore would be stimulated or activited and would elaborate a sort of impulse which would run toward the ends. In this respect the chromosome may be compared to a neüròn, the cell being represented by the kinetochore and the axon by the body of the chromosome. Due to the action of the kinetochore the entire chromosome becomes also activated for performing its kinetic function. Nothing is known at present about the nature of this activation. We can however assume that some active chemical substance like those produced by the neuron and transferred to the effector passes from the kinetochore to the body of the chromosome runing down to the ends. And, like an axon which continues to transmit an impulse after the stimulating agent has suspended its action, so may the chromosome show some residual kinetic activity even after having lost its kinetochore. This is another explanation for the kinetic behavior of acentric chromosomal fragmehs. In the orthodox monocentric chromosomes the kinetic activity is greater at the kinetochore, that is, at the place of origin of the active substance than at any other place. In chromosomes provided with a kinetochore at each end the entire body may become active enough to produce chromosomal fibers. This is probably due to a more or less uniform distribution and concentration of the active substance coming simultaneously from both extremities of the chromosome.

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.