Non-classical error bounds in the central limit theorem

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

Hereditariedade da homeose

A preliminary account on the normal development of the imaginai discs in holometabolic Insects is made to serve as an introduction to the study of the hereditary homoeosis. Several facts and experimental data furnished specially by the students of Drosophila are brought here in searching for a more adequate explanation of this highly interesting phenomenon. The results obtained from the investigations of different homoeotic mutants are analysed in order to test Goldschmidt's theory of homoeosis. Critical examination of the basis on which this theory was elaborated are equally made. As a result from an extensive theoretical consideration of the matter and a long discussion of the most recent papers on this subject the present writer concludes that the Goldschmidt explanation of the homoeotic phenomena based on the action of diffusing substances produced by the genes, the "evocators", and on the alteration of the normal speed of maturation of the imaginai discs equally due to the activity of the genes, could not be proved and therefore should be abandoned. In the same situation is any other explanation like that of Waddington or Villee considered as fundamentally identical to that of Goldschmidt. In order to clear the problem of homoeosis in terms which seem to put the phenomenon in complete agreement with the known facts the present writer elaborated a theory first published a few years ago (1941) based entirely on the assumption that the imaginai discs are specifically determined by some kind of substances, probably of chemical nature, contained in the cytoplam of the cells entering in the consti- tution of each individual disc. These substances already present in the blastem of the egg in which they are distributed in a definite order, pass to different cells at the time the blastem is transformed into blastoderm. These substances according to their organogenic potentiality may be called antenal-substance, legsubstance, wing-substance, eye-substance, etc. The hipoderm of the embryo resulting from the multiplication of the blastoderm cells would be constituted by a series of cellular areas differing from each other in their particular organoformative capacity. Thus the hypoderm giving rise to the imaginai discs, it follows that each disc must have the same organogenic power of the hypodermal area it came from. Therefore the discs i*re determinated since their origin by substances enclosed in the cytoplasm of their cells and consequently can no longer alter their potentiality. When an antennal disc develops into a leg one can conclude that this disc in spite of its position in the body of the larva is not, properly speaking, an antennal disc but a true leg disc whose cells instead of having in their cytoplasm the antennal substance derived from the egg blastem have in its place the leg-substance. Now, if a disc produces a tarsus or an antenna or even a compound appendage partly tarsus-like, partly antenna-like, it follows tha,t both tarsal and antennal substances are present in it. The ultimate aspect of the compound structure depends upon the reaction of each kind of substance to the different causes influencing development. For instance, temperature may orient the direction of development either lowards arista or tarsus, stimulating, or opposing to the one or the other of these substances. Confering to the genes the faculty of altering the constitution of the substances containing in the cytoplasm forming the egg blastem or causing transposition of these substances from one area to another or promoting the substitution of a given substance by a different one, the hereditary homoeocis may be easily explained. However, in the opinion of the present writer cytoplasm takes the initiative in all developmental process, provoking the chromosomes to react specifically and proportionally. Accordingly, the mutations causing homoeotic phenomena may arise independently at different rime in the cytoplasm and in the chromosomes. To the part taken by the chromosomes in the manifestation of the homoeotic characters is due the mendalian ratio observed in homoeotic X normal crosses. Expression, in itself, is mainly due to the proportion of the different substances in the cells of the affected discs. Homoeotic phenomena not presenting mendelian ratio may appear as consequence of cytoplasmic mutation not accompanied by chromosomal mutation. The great variability in the morphology of the homoeotic characteres, some individual being changed towards an extreme expression of the mutant phenotype while others in spite of their homozigous constitution cannot be distinguished from the normal ones, strongly supports the interpretation based on the relative proportion of the determining substances in the discs. To the same interpretation point also asymetry and other particularities observed in the exteriorization of the phenomenon. In conformity with this new conception homoeosis should not prove homology of Insect appendages (Villee 1942) since a more replacement of substances may cause legs to develop in substitution of the wings, as it was already observed (requiring confirmation in the opinion of Bateson 1894, p. 184) and no one would conclude for the homology of these organs in the usual meaning of the term.

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.

Análise do tamanho e da forma do ôvo em galinhas das raças Rhode Island Red e Light Sussex e do híbrido entre essas duas raças

Size and shape in eggs of Rhode Island Red and Light Sussex breeds and in the hibrid Rhode x Sussex were studied. These characters are influenced by quantitative genes. Major and minor diameter were used for estimating size of the eggs and the ratio minor/major diameter for shape indice. It was found, in the material analyzed, that: a) the eggs laid by the sa- me chick are pratically uniform; b) the correlation coeficient between major and minor diameter is weak; c) Rhode Island Red has short eggs than Light Sussex; d) short eggs is dominant on long eggs; e) egg shape is the same in Rhode Island Red and Light Sussex breeds and different in the hibrid, which has rounder eggs than the breeds.

Raça em formação de galinhas de plumagem azul e ovos azuis - II. Teste de cruzamento

The data reported in this paper are in accordance with the hypothesis previously established (2) of the interaction of a main pair of alleles as controlling the inheritance of black, blue and blue-splashed plumage in chickens received from the State of Goias, Brazil. The black plumage is relatively uniform but the blue and blue splashed plumages indicate the action of other genes regulating the lack of uniformity.

Nota preliminar sôbre a absorção e a translocação do radiozinco no cafeeiro [Coffea arabica] cultivado em solução nutritiva

Two water-culture experiments were carried out to study the absorption and the translocation of radiozinc in young coffee plants as influenced by two factors, namely, concentration of heavy metals (iron, manganese, copper and molybdenum) and method of application. Inert zinc was furnished at a uniform rate of 0.05 p.p.m.; the levels of iron supply were 0, 1.0 and 10 p.p.m.; manganese was supplied in three doses 0, 0.5, and 5 p.p.m.; copper - 0, 0.02, and 0.2 p.p.m.; molybdenum - 0, 0.01 and 0.1 p.p.m. When applied to the nutrient solution the activity of the radiozinc was 0.15 microcuries per plant. In the study of the leaf absorption, the radiozinc was supplied at the level of 0.10 microcuries per plant; in this case the material was brushed either on the lower or in the upper surface or both of two pairs of mature leaves. In both experiments the absorption period was 8 weeks. The following conclusions can be drawn: 1. Among the heavy metals herein investigated the iron concentration did not affecc the uptake of the radiozinc; by raising the level of Mn, Cu and Mo ten times, the absorption dropped to 50 per cent and even more whe compared with the control plant; however, when these micronutrients were omitted from the nutrient solution an increase in the uptake of zinc was registered only in the minus - Cu treatment. The effects of high leveds of Mn, Cu and Mo probably indicate an interionic competition for a same site on a common binding substance in the cell surface. 2. The absorption of the radiozinc directly applied to the leaf surface reached levels as high as 8 times that registered when the root uptake took place. Among the three methods of application which have been tried, brushing the lower surface of the leaves proved to be the most effective; this result is easily understood since the stomatal openings of the coffee leaves are preferentially located in the lower surface. In this treatment, about 40 per cent of the activity was absorbed and around 12 per cent were translocated either to the old or to the newer organs. 3. Data herein presented suggest that leaf sprays should be preferred - rather than soil applications - to control zinc deficiency in coffee plants when growing in field conditions.

Estudos sôbre alimentação mineral do cafeeiro: VIII. Estudo da absorção e da translocação do radiozinco no cafeeiro (Coffea arabica L.)

WATER-CULTURE EXPERIMENTS. Two water-culture experiments were carried out to study the absorption and the translocation of radiozinc in young coffee plants as influenced by two factors, namely, concentration of heavy metals (iron, man ganese, copper and molybdenum) and method of application. Inert zinc was supplied at an uniform rate of 0. 05 p. p. m.; the levels of iron supply were 0, 1.0, and 10.0 p. p.m.; manganese was supplied in three doses 0, 0.5, and 5.0 p. p.m.; copper- 0, 0. 02, and 0. 2 p. p. m.; molybdenum- 0, 0. 01, and 0. 1 p. p. m. When applied to the nutrient solution the activity os the radiozinc (as zinc chloride) was 0. 15 microcuries per plant. In the study of the leaf absorption, Zn65 was supplied at the level of 0. 10 microcuries per plant; in this case the radioative material was brushed either on the lower or on the upper surface or both two pairs of mature leaves. The absorption period was 8 weeks. The radioactivity assay showed the following results: 1 - Among the heavy metals herein investigated the iron concentration did not affect the uptake of the radiozinc; by raising the level of Mn, Cu and Mo ten times, the absorption dropped to 50 per cent and even more when compared with the control plants; when, however, these micronutrients were omitted from the nutrient solution, an increase in the uptake of zinc was registered in the minus Cu treatment only. The effects of high levels of Mn, Cu and Mo probably indicate an interionic competition for a same site on a common binding substance in the cell surface. 2 - The absorption of the radiozinc directly applied to the leaf surface reached levels as high as 8 times that registered when the root uptake took place. Among the three methods of application which have been tried, brushing the lower surface of the leaves proved to be the most effective; this result is easily understood since the stomatal openings of the coffee leaves an preferentially located in the lower surface - in this treatment, about 40 per cent of the activity was absorved and around 12 per cent were translocated either to the old or to the newer organs. Chemical analyses for heavy metals, were carried out only in the plants received Zn65Cl2 in the nutrient solution; the results were as follows; 1 - Control plants had, per 1,000 gm, of dry weight the following amounts in mg.: Zn- 48 in the roots and 29 in the tops; Fe- 165 in the roots and 9 in the tops; Mn- 58 in the roots and 15 in the tops, Cu- 15 in the roots and 1. 2 in the tops; Mo- 2. 8 in the roots and 0. 45 in the tops. 2 - The effect of different levels of micronutrients in the composition of the plants can be summarized as follows: Fe and Zn- when omitted from the nutrient solution, the iron and zinc contents in the roots decreased, no variation being noted in the tops; the higher dosis caused an accumulation in the roots but no apparent effect in the tops; Mn- by omitting this micronutrient a decrease in its content in the roots was noted, where as the concentration in the tops was the same; Mo- no variation in roots and tops contents when molybdenum was omitted; higher dosis of manganese and molybdenum increased the amounts formed both in the roots and in the tops. 3 - The influence of the different concentrations of micronutrients heavy metals on the zinc content of the coffee plants can be described by saying that: Fe and Mo- no marked variation; Mn- no effect when omitted, reduced amount when the high dosis was supplied; Mn- when the plants did not receive manganese the zinc content in roots and tops was the same as in the control plants; a decrease in the zinc content of the total plant occurred when the high dosis was employed; Cu -the situation is similar to that described for manganese. Hence, results showed by the chemical analyses roughly correspond to those of the radioactivity assay; the use of the tracer technique, however, gave best informations along this line. SOIL-POTS EXPERIMENTS. The two types of soils which when selected support the most extensive coffee plantations in the State of São Paulo, Brazil: "arenito de Bauru", a light sandy soil and "terra roxa legitima", a red soil derived from basalt. Besides NPK containing salts, the coffee plants were given two doses of inert zinc (65 and 130 mg ZnCl2 per pot) and radiozinc at a total activity of 10(6) counts/minute. The results of the countings can be summarized as follows: 1 - When plants were grown in "arenito de Bauru" the activity absorbed as per cent of the total activity supplied was not affected by the dosis of inert zinc. The highest value found was around 0. 1 per cent. 2 - For the "terra roxa" plants, the situation is almost the same; there was, however, a slight increase in the absorption of the radiozinc when 130 mgm of ZnClg2 was given: a little above 0. 2 per cent of the activity supplied was absorbed. The results clearly show that the young coffee plants practically did not absorb none of the zinc supplied; two reasons at least could be pointed out to explain such a fact: 1 - Zinc fixation by an exchange with magnesium or by filling holes in the octahedral layer of aluminosilicates, probably kaolinite; 2 - No need for fertilizer zinc in the particular stage of life cycle under which the experiment was set up. The data from chemical analysis are roughly parallel to the above mentioned. When one attempts to compare - by taking data herein reported zinc uptake from nutrient solution, leaf brushing or from fertilizers in the soil, a practical conclusion can be drawn: the control of zinc deficiency in coffee plants should not be done by adding the zinc salts to the soil; in other words: the soil applications used so extensively in other countries seem not to be suitable for our conditions; hence zinc sprays should be used wherever necessary.

Estudos sobre a alimentação mineral do cafeeiro: XII. efeito da adubação na composição mineral das fôlhas

Leaf samples from coffee plants under three different fertilizations, namely NPK, NP and PK, were collected for chemical analysis. It was found that the contents of N, K, Ca, Mg and S in the first, second, third and fourth pair of leaves were the same from the statistical point of view. On the onder hand, there was a significant effect of the position of the leaf in the branch on the P content, which was higher in the first pair. With the exception of the P level ,the four pairs of leaves are chemically uniform. Nevertheless it is not considered as convenient to mix all kinds of leaves into one sample, since the composition may vary a great deal when sampling is done some other time, such as the period of fruit growing. It is recommended therefore that either the third or the fourth pair leaves should be collected for routine work in foliar diagnosis.

The relation of the concentration of macronutrients in the substrate and in the foliage to cell wall thickness and cellulose concentration in the xylem of slash pine (Pinus elliotti)

Sand culture experiments, using a sub-irrigation technique, were installed in order to find out the effects of the macronutrients N, P, K, Ca, Mg and S on growth, aspect, mineral composition, length of fibers, thickness of cell wall and cellulose concentration in slash pine. The aim was to obtain, under controlled conditions, basic information which could eventually lead to practical means designed to increase the rate of growth and to make of slash pine a richer source of cellulose. Nitrogen, Phosphorus, Potassium Experiment A 3 x 3 x 3 factorial design with two replicates was used. Nitrogen was supplied initially at the levels of 25, 50 and 100 ppm; phosphorus was given at the rates of 5, 10 and 20 ppm; potassium was supplied at the rates of 25, 50 and 100 ppm; six months after the experiment was started the first level for each element was dropped to zero. Others macro and all micronutrients were supplied at uniform rates. Fifteen hours of illumination per day were provided. The experimental technique for growing the slash pine seedlings proved quite satisfactory. Symptoms of deficiency of nitrogen, phosphorus and potassium were observed, described and recorded in photographs and water colors. These informations will help to identify abnormalities which may appear under field conditions. Chemical analysis of the several plant parts, on the other hand, give a valuable means to assess the nutritional status of slash pine, thus confirming when needed, the visual diagnosis. The correctness of manurial pratices, on the other hand, can be judged with the help of the analytical data tabulated. Under the experimental conditions nitrogen caused the highest increases on growth, as measured by increments in height and dry weights, whereas the effects of phosphorus and potassium were less marked. Cellulose concentration was not significantly affected by the treatments used. Higher levels of N seemed to decrease both length of fiber elements and the thickness of cell wall. The effects of P and K were not well defined. Calcium, Magnesium, Sulfur Experiment A 3 x 3 x 3 factorial design with two replicates was used. Calcium was supplied initially at the levels of 12.5, 25 and 50 ppm; magnesium and sulfur were given at the rates of 6, 12.5 and 25 ppm. Other macro and micronutrients were supplied at uniform rates, common to all treatments. Three months after starting the experiment the first level for each element was dropped to zero. Symptoms of deficiency of calcium, magnesium and sulfur were observed, described and recorded as in the case of the previous experiment. Chemical analysis were made, both for mineral content and cellulose concentration. Length of fibers and thickness of cell wall were measured. Both calcium and magnesium increase height, sulfur failing to give significant response. Dry weight was beneficially affected by calcium and sulfur. The levels of calcium, magnesium and sulfur in the needles associated with deficiency and maximum growth are comparable with those found in the literature. Cellulose concentration increased when the level of sulfur in the substrate was raised. The thickness of cell wall was negatively affected by the treatments; no effect was observed with regards to length of fibers.

Erstellung einer Blitzschutzrichtlinie für die Produktpalette der FAM im Auftrag der "Gesellschaft für Prozeßautomation mbH" (GPA)"

On the basis of the global use of the FAM installations and systems, their location, type and height, a lightning protection system is required, which protects humans and machines from danger of a lightning. At the beginning the development, the threat and the potential for destruction of lightning are described. Besides the resulting solid normative calculation models and tables are presented. Then, the product portfolio of the FAM is characterized. From this demonstration models are selected; on the one hand a model for the totality of all portable devices and the other hand a model which defines the power plants. Subsequently, the risk management and a strengths and weaknesses analysis are performed. After that, with graphical and mathematical models, these weaknesses as well as the functional equipotential bonding and grounding system and its dimensioning are investigated and solutions are demonstrated. The following is a coordination of lightning protection standard with other directives and standards in order to classify the resulting internal lightning protection and protective measures against electromagnetic pulse and to generate a uniform protection and application platform. Furthermore, problems of the economy of protective circuit is shown and a solution is given. Finally, the indicated possible solutions are replaced by definitions. The main classification and structure of lightning protection directive are shown and exemplarily applied.

Reproductive biology of Hyla goiana (Anura, Hylidae)

Male-male and male-female interactions, reproductive habitat, and vocalizations of Hyla goiana B. Lutz, 1968 a member of H. polytaenia species group, are described. Three groups of calling males were surveyed along a small stream, at the Estação de Pesquisa e Desenvolvimento Ambiental de Galheiro, Perdizes municipality, State of Minas Gerais, Brazil. The mean distance between the nearest calling neighbors was 2.7 m, in accordance with an uniform distribution. Clutches (mean 180 eggs) were deposited in the stream, submerged and attached to plants. In two observed courtships the female moved towards a calling male that rapidly clasped her. In the male-male interaction, the males emitted advertisement and encounter calls and then engaged in physical combat. The males have a prepollical fang-like spine on each hand and several of them were observed with scratches on dorsum. The advertisement call consists of alternating harsh notes and a trilled of brief notes. The frequency of the call is lower than that of H. aff. polytaenia and H. cipoensis B. Lutz, 1968. The clutch characteristics of H. goiana are similar to those described for H. polytaenia Cope, 1870 and H. cipoensis.