Improving Post-Discharge Medication Adherence in Patients with CVD: A Pilot Randomized Trial

Background:Effective interventions to improve medication adherence are usually complex and expensive.Objective:To assess the impact of a low-cost intervention designed to improve medication adherence and clinical outcomes in post-discharge patients with CVD.Method:A pilot RCT was conducted at a teaching hospital. Intervention was based on the four-item Morisky Medication Adherence Scale (MMAS-4). The primary outcome measure was medication adherence assessed using the eight-item MMAS at baseline, at 1 month post hospital discharge and re-assessed 1 year after hospital discharge. Other outcomes included readmission and mortality rates.Results:61 patients were randomized to intervention (n = 30) and control (n = 31) groups. The mean age of the patients was 61 years (SD 12.73), 52.5% were males, and 57.4% were married or living with a partner. Mean number of prescribed medications per patient was 4.5 (SD 3.3). Medication adherence was correlated to intervention (p = 0.04) and after 1 month, 48.4% of patients in the control group and 83.3% in the intervention group were considered adherent. However, this difference decreased after 1 year, when adherence was 34.8% and 60.9%, respectively. Readmission and mortality rates were related to low adherence in both groups.Conclusion:The intervention based on a validated patient self-report instrument for assessing adherence is a potentially effective method to improve adherent behavior and can be successfully used as a tool to guide adherence counseling in the clinical visit. However, a larger study is required to assess the real impact of intervention on these outcomes.

Progression of Blood Pressure and Cardiovascular Outcomes in Hypertensive Patients in a Reference Center

Background: Hypertension is a public health problem, considering its high prevalence, low control rate and cardiovascular complications. Objective: Evaluate the control of blood pressure (BP) and cardiovascular outcomes in patients enrolled at the Reference Center for Hypertension and Diabetes, located in a medium-sized city in the Midwest Region of Brazil. Methods: Population-based study comparing patients enrolled in the service at the time of their admission and after an average follow-up of five years. Participants were aged ≥18 years and were regularly monitored at the Center up to 6 months before data collection. We assessed demographic variables, BP, body mass index, risk factors, and cardiovascular outcomes. Results: We studied 1,298 individuals, predominantly women (60.9%), and with mean age of 56.7±13.1 years. Over time, there was a significant increase in physical inactivity, alcohol consumption, diabetes, dyslipidemia, and excessive weight. As for cardiovascular outcomes, we observed an increase in stroke and myocardial revascularization, and a lower frequency of chronic renal failure. During follow-up, there was significant improvement in the rate of BP control (from 29.6% to 39.6%; p = 0.001) and 72 deaths, 91.7% of which were due to cardiovascular diseases. Conclusion: Despite considerable improvements in the rate of BP control during follow-up, risk factors worsened and cardiovascular outcomes increased.

Effects of One Resistance Exercise Session on Vascular Smooth Muscle of Hypertensive Rats

AbstractBackground:Hypertension is a public health problem and increases the incidence of cardiovascular diseases.Objective:To evaluate the effects of a resistance exercise session on the contractile and relaxing mechanisms of vascular smooth muscle in mesenteric arteries of NG-nitro L-arginine methyl ester (L-NAME)-induced hypertensive rats.Methods:Wistar rats were divided into three groups: control (C), hypertensive (H), and exercised hypertensive (EH). Hypertension was induced by administration of 20 mg/kg of L-NAME for 7 days prior to experimental protocols. The resistance exercise protocol consisted of 10 sets of 10 repetitions and intensity of 40% of one repetition maximum. The reactivity of vascular smooth muscle was evaluated by concentration‑response curves to phenylephrine (PHEN), potassium chloride (KCl) and sodium nitroprusside (SNP).Results:Rats treated with L-NAME showed an increase (p < 0.001) in systolic blood pressure (SBP), diastolic blood pressure (DBP) and mean arterial pressure (MAP) compared to the initial period of induction. No difference in PHEN sensitivity was observed between groups H and EH. Acute resistance exercise reduced (p < 0.001) the contractile response induced by KCl at concentrations of 40 and 60 mM in group EH. Greater (p < 0.01) smooth muscle sensitivity to NPS was observed in group EH as compared to group H.Conclusion:One resistance exercise session reduces the contractile response induced by KCl in addition to increasing the sensitivity of smooth muscle to NO in mesenteric arteries of hypertensive rats.

Dissecando o GEN

In thee present paper the classical concept of the corpuscular gene is dissected out in order to show the inconsistency of some genetical and cytological explanations based on it. The author begins by asking how do the genes perform their specific functions. Genetists say that colour in plants is sometimes due to the presence in the cytoplam of epidermal cells of an organic complex belonging to the anthocyanins and that this complex is produced by genes. The author then asks how can a gene produce an anthocyanin ? In accordance to Haldane's view the first product of a gene may be a free copy of the gene itself which is abandoned to the nucleus and then to the cytoplasm where it enters into reaction with other gene products. If, thus, the different substances which react in the cell for preparing the characters of the organism are copies of the genes then the chromosome must be very extravagant a thing : chain of the most diverse and heterogeneous substances (the genes) like agglutinins, precipitins, antibodies, hormones, erzyms, coenzyms, proteins, hydrocarbons, acids, bases, salts, water soluble and insoluble substances ! It would be very extrange that so a lot of chemical genes should not react with each other. remaining on the contrary, indefinitely the same in spite of the possibility of approaching and touching due to the stato of extreme distension of the chromosomes mouving within the fluid medium of the resting nucleus. If a given medium becomes acid in virtue of the presence of a free copy of an acid gene, then gene and character must be essentially the same thing and the difference between genotype and phenotype disappears, epigenesis gives up its place to preformation, and genetics goes back to its most remote beginnings. The author discusses the complete lack of arguments in support of the view that genes are corpuscular entities. To show the emharracing situation of the genetist who defends the idea of corpuscular genes, Dobzhansky's (1944) assertions that "Discrete entities like genes may be integrated into systems, the chromosomes, functioning as such. The existence of organs and tissues does not preclude their cellular organization" are discussed. In the opinion of the present writer, affirmations as such abrogate one of the most important characteristics of the genes, that is, their functional independence. Indeed, if the genes are independent, each one being capable of passing through mutational alterations or separating from its neighbours without changing them as Dobzhansky says, then the chromosome, genetically speaking, does not constitute a system. If on the other hand, theh chromosome be really a system it will suffer, as such, the influence of the alteration or suppression of the elements integrating it, and in this case the genes cannot be independent. We have therefore to decide : either the chromosome is. a system and th genes are not independent, or the genes are independent and the chromosome is not a syntem. What cannot surely exist is a system (the chromosome) formed by independent organs (the genes), as Dobzhansky admits. The parallel made by Dobzhansky between chromosomes and tissues seems to the author to be inadequate because we cannot compare heterogeneous things like a chromosome considered as a system made up by different organs (the genes), with a tissue formed, as we know, by the same organs (the cells) represented many times. The writer considers the chromosome as a true system and therefore gives no credit to the genes as independent elements. Genetists explain position effects in the following way : The products elaborated by the genes react with each other or with substances previously formed in the cell by the action of other gene products. Supposing that of two neighbouring genes A and B, the former reacts with a certain substance of the cellular medium (X) giving a product C which will suffer the action, of the latter (B). it follows that if the gene changes its position to a place far apart from A, the product it elaborates will spend more time for entering into contact with the substance C resulting from the action of A upon X, whose concentration is greater in the proximities of A. In this condition another gene produtc may anticipate the product of B in reacting with C, the normal course of reactions being altered from this time up. Let we see how many incongruencies and contradictions exist in such an explanation. Firstly, it has been established by genetists that the reaction due.to gene activities are specific and develop in a definite order, so that, each reaction prepares the medium for the following. Therefore, if the medium C resulting from the action of A upon x is the specific medium for the activity of B, it follows that no other gene, in consequence of its specificity, can work in this medium. It is only after the interference of B, changing the medium, that a new gene may enter into action. Since the genotype has not been modified by the change of the place of the gene, it is evident that the unique result we have to attend is a little delay without seious consequence in the beginning of the reaction of the product of B With its specific substratum C. This delay would be largely compensated by a greater amount of the substance C which the product of B should found already prepared. Moreover, the explanation did not take into account the fact that the genes work in the resting nucleus and that in this stage the chromosomes, very long and thin, form a network plunged into the nuclear sap. in which they are surely not still, changing from cell to cell and In the same cell from time to time, the distance separating any two genes of the same chromosome or of different ones. The idea that the genes may react directly with each other and not by means of their products, would lead to the concept of Goidschmidt and Piza, in accordance to which the chromosomes function as wholes. Really, if a gene B, accustomed to work between A and C (as for instance in the chromosome ABCDEF), passes to function differently only because an inversion has transferred it to the neighbourhood of F (as in AEDOBF), the gene F must equally be changed since we cannot almH that, of two reacting genes, only one is modified The genes E and A will be altered in the same way due to the change of place-of the former. Assuming that any modification in a gene causes a compensatory modification in its neighbour in order to re-establich the equilibrium of the reactions, we conclude that all the genes are modified in consequence of an inversion. The same would happen by mutations. The transformation of B into B' would changeA and C into A' and C respectively. The latter, reacting withD would transform it into D' and soon the whole chromosome would be modified. A localized change would therefore transform a primitive whole T into a new one T', as Piza pretends. The attraction point-to-point by the chromosomes is denied by the nresent writer. Arguments and facts favouring the view that chromosomes attract one another as wholes are presented. A fact which in the opinion of the author compromises sereously the idea of specific attraction gene-to-gene is found inthe behavior of the mutated gene. As we know, in homozygosis, the spme gene is represented twice in corresponding loci of the chromosomes. A mutation in one of them, sometimes so strong that it is capable of changing one sex into the opposite one or even killing the individual, has, notwithstading that, no effect on the previously existing mutual attraction of the corresponding loci. It seems reasonable to conclude that, if the genes A and A attract one another specifically, the attraction will disappear in consequence of the mutation. But, as in heterozygosis the genes continue to attract in the same way as before, it follows that the attraction is not specific and therefore does not be a gene attribute. Since homologous genes attract one another whatever their constitution, how do we understand the lack cf attraction between non homologous genes or between the genes of the same chromosome ? Cnromosome pairing is considered as being submitted to the same principles which govern gametes copulation or conjugation of Ciliata. Modern researches on the mating types of Ciliata offer a solid ground for such an intepretation. Chromosomes conjugate like Ciliata of the same variety, but of different mating types. In a cell there are n different sorts of chromosomes comparable to the varieties of Ciliata of the same species which do not mate. Of each sort there are in the cell only two chromosomes belonging to different mating types (homologous chromosomes). The chromosomes which will conjugate (belonging to the same "variety" but to different "mating types") produce a gamone-like substance that promotes their union, being without action upon the other chromosomes. In this simple way a single substance brings forth the same result that in the case of point-to-point attraction would be reached through the cooperation of as many different substances as the genes present in the chromosome. The chromosomes like the Ciliata, divide many times before they conjugate. (Gonial chromosomes) Like the Ciliata, when they reach maturity, they copulate. (Cyte chromosomes). Again, like the Ciliata which aggregate into clumps before mating, the chrorrasrmes join together in one side of the nucleus before pairing. (.Synizesis). Like the Ciliata which come out from the clumps paired two by two, the chromosomes leave the synizesis knot also in pairs. (Pachytene) The chromosomes, like the Ciliata, begin pairing at any part of their body. After some time the latter adjust their mouths, the former their kinetochores. During conjugation the Ciliata as well as the chromosomes exchange parts. Finally, the ones as the others separate to initiate a new cycle of divisions. It seems to the author that the analogies are to many to be overlooked. When two chemical compounds react with one another, both are transformed and new products appear at the and of the reaction. In the reaction in which the protoplasm takes place, a sharp difference is to be noted. The protoplasm, contrarily to what happens with the chemical substances, does not enter directly into reaction, but by means of products of its physiological activities. More than that while the compounds with Wich it reacts are changed, it preserves indefinitely its constitution. Here is one of the most important differences in the behavior of living and lifeless matter. Genes, accordingly, do not alter their constitution when they enter into reaction. Genetists contradict themselves when they affirm, on the one hand, that genes are entities which maintain indefinitely their chemical composition, and on the other hand, that mutation is a change in the chemica composition of the genes. They are thus conferring to the genes properties of the living and the lifeless substances. The protoplasm, as we know, without changing its composition, can synthesize different kinds of compounds as enzyms, hormones, and the like. A mutation, in the opinion of the writer would then be a new property acquired by the protoplasm without altering its chemical composition. With regard to the activities of the enzyms In the cells, the author writes : Due to the specificity of the enzyms we have that what determines the order in which they will enter into play is the chemical composition of the substances appearing in the protoplasm. Suppose that a nucleoproteln comes in relation to a protoplasm in which the following enzyms are present: a protease which breaks the nucleoproteln into protein and nucleic acid; a polynucleotidase which fragments the nucleic acid into nucleotids; a nucleotidase which decomposes the nucleotids into nucleoids and phosphoric acid; and, finally, a nucleosidase which attacs the nucleosids with production of sugar and purin or pyramidin bases. Now, it is evident that none of the enzyms which act on the nucleic acid and its products can enter into activity before the decomposition of the nucleoproteln by the protease present in the medium takes place. Leikewise, the nucleosidase cannot works without the nucleotidase previously decomposing the nucleotids, neither the latter can act before the entering into activity of the polynucleotidase for liberating the nucleotids. The number of enzyms which may work at a time depends upon the substances present m the protoplasm. The start and the end of enzym activities, the direction of the reactions toward the decomposition or the synthesis of chemical compounds, the duration of the reactions, all are in the dependence respectively o fthe nature of the substances, of the end products being left in, or retired from the medium, and of the amount of material present. The velocity of the reaction is conditioned by different factors as temperature, pH of the medium, and others. Genetists fall again into contradiction when they say that genes act like enzyms, controlling the reactions in the cells. They do not remember that to cintroll a reaction means to mark its beginning, to determine its direction, to regulate its velocity, and to stop it Enzyms, as we have seen, enjoy none of these properties improperly attributed to them. If, therefore, genes work like enzyms, they do not controll reactions, being, on the contrary, controlled by substances and conditions present in the protoplasm. A gene, like en enzym, cannot go into play, in the absence of the substance to which it is specific. Tne genes are considered as having two roles in the organism one preparing the characters attributed to them and other, preparing the medium for the activities of other genes. At the first glance it seems that only the former is specific. But, if we consider that each gene acts only when the appropriated medium is prepared for it, it follows that the medium is as specific to the gene as the gene to the medium. The author concludes from the analysis of the manner in which genes perform their function, that all the genes work at the same time anywhere in the organism, and that every character results from the activities of all the genes. A gene does therefore not await for a given medium because it is always in the appropriated medium. If the substratum in which it opperates changes, its activity changes correspondingly. Genes are permanently at work. It is true that they attend for an adequate medium to develop a certain actvity. But this does not mean that it is resting while the required cellular environment is being prepared. It never rests. While attending for certain conditions, it opperates in the previous enes It passes from medium to medium, from activity to activity, without stopping anywhere. Genetists are acquainted with situations in which the attended results do not appear. To solve these situations they use to make appeal to the interference of other genes (modifiers, suppressors, activators, intensifiers, dilutors, a. s. o.), nothing else doing in this manner than displacing the problem. To make genetcal systems function genetists confer to their hypothetical entities truly miraculous faculties. To affirm as they do w'th so great a simplicity, that a gene produces an anthocyanin, an enzym, a hormone, or the like, is attribute to the gene activities that onlv very complex structures like cells or glands would be capable of producing Genetists try to avoid this difficulty advancing that the gene works in collaboration with all the other genes as well as with the cytoplasm. Of course, such an affirmation merely means that what works at each time is not the gene, but the whole cell. Consequently, if it is the whole cell which is at work in every situation, it follows that the complete set of genes are permanently in activity, their activity changing in accordance with the part of the organism in which they are working. Transplantation experiments carried out between creeper and normal fowl embryos are discussed in order to show that there is ro local gene action, at least in some cases in which genetists use to recognize such an action. The author thinks that the pleiotropism concept should be applied only to the effects and not to the causes. A pleiotropic gene would be one that in a single actuation upon a more primitive structure were capable of producing by means of secondary influences a multiple effect This definition, however, does not preclude localized gene action, only displacing it. But, if genetics goes back to the egg and puts in it the starting point for all events which in course of development finish by producing the visible characters of the organism, this will signify a great progress. From the analysis of the results of the study of the phenocopies the author concludes that agents other than genes being also capaole of determining the same characters as the genes, these entities lose much of their credit as the unique makers of the organism. Insisting about some points already discussed, the author lays once more stress upon the manner in which the genes exercise their activities, emphasizing that the complete set of genes works jointly in collaboration with the other elements of the cell, and that this work changes with development in the different parts of the organism. To defend this point of view the author starts fron the premiss that a nerve cell is different from a muscle cell. Taking this for granted the author continues saying that those cells have been differentiated as systems, that is all their parts have been changed during development. The nucleus of the nerve cell is therefore different from the nucleus of the muscle cell not only in shape, but also in function. Though fundamentally formed by th same parts, these cells differ integrally from one another by the specialization. Without losing anyone of its essenial properties the protoplasm differentiates itself into distinct kinds of cells, as the living beings differentiate into species. The modified cells within the organism are comparable to the modified organisms within the species. A nervo and a muscle cell of the same organism are therefore like two species originated from a common ancestor : integrally distinct. Like the cytoplasm, the nucleus of a nerve cell differs from the one of a muscle cell in all pecularities and accordingly, nerve cell chromosomes are different from muscle cell chromosomes. We cannot understand differentiation of a part only of a cell. The differentiation must be of the whole cell as a system. When a cell in the course of development becomes a nerve cell or a muscle cell , it undoubtedly acquires nerve cell or muscle cell cytoplasm and nucleus respectively. It is not admissible that the cytoplasm has been changed r.lone, the nucleus remaining the same in both kinds of cells. It is therefore legitimate to conclude that nerve ceil ha.s nerve cell chromosomes and muscle cell, muscle cell chromosomes. Consequently, the genes, representing as they do, specific functions of the chromossomes, are different in different sorts of cells. After having discussed the development of the Amphibian egg on the light of modern researches, the author says : We have seen till now that the development of the egg is almost finished and the larva about to become a free-swimming tadepole and, notwithstanding this, the genes have not yet entered with their specific work. If the haed and tail position is determined without the concourse of the genes; if dorso-ventrality and bilaterality of the embryo are not due to specific gene actions; if the unequal division of the blastula cells, the different speed with which the cells multiply in each hemisphere, and the differential repartition of the substances present in the cytoplasm, all this do not depend on genes; if gastrulation, neurulation. division of the embryo body into morphogenetic fields, definitive determination of primordia, and histological differentiation of the organism go on without the specific cooperation of the genes, it is the case of asking to what then the genes serve ? Based on the mechanism of plant galls formation by gall insects and on the manner in which organizers and their products exercise their activities in the developing organism, the author interprets gene action in the following way : The genes alter structures which have been formed without their specific intervention. Working in one substratum whose existence does not depend o nthem, the genes would be capable of modelling in it the particularities which make it characteristic for a given individual. Thus, the tegument of an animal, as a fundamental structure of the organism, is not due to gene action, but the presence or absence of hair, scales, tubercles, spines, the colour or any other particularities of the skin, may be decided by the genes. The organizer decides whether a primordium will be eye or gill. The details of these organs, however, are left to the genetic potentiality of the tissue which received the induction. For instance, Urodele mouth organizer induces Anura presumptive epidermis to develop into mouth. But, this mouth will be farhioned in the Anura manner. Finalizing the author presents his own concept of the genes. The genes are not independent material particles charged with specific activities, but specific functions of the whole chromosome. To say that a given chromosome has n genes means that this chromonome, in different circumstances, may exercise n distinct activities. Thus, under the influence of a leg evocator the chromosome, as whole, develops its "leg" activity, while wbitm the field of influence of an eye evocator it will develop its "eye" activity. Translocations, deficiencies and inversions will transform more or less deeply a whole into another one, This new whole may continue to produce the same activities it had formerly in addition to those wich may have been induced by the grafted fragment, may lose some functions or acquire entirely new properties, that is, properties that none of them had previously The theoretical possibility of the chromosomes acquiring new genetical properties in consequence of an exchange of parts postulated by the present writer has been experimentally confirmed by Dobzhansky, who verified that, when any two Drosophila pseudoobscura II - chromosomes exchange parts, the chossover chromosomes show new "synthetic" genetical effects.

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.

Bases para o estudo da genética de populações dos Hymenoptera em geral e dos Apinae sociais em particular

This paper deals with problems on population genetics in Hymenoptera and particularly in social Apidae. 1) The studies on populations of Hymenoptera were made according to the two basic types of reproduction: endogamy and panmixia. The populations of social Apinae have a mixed method of reproduction with higher percentage of panmixia and a lower of endogamy. This is shown by the following a) males can enter any hive in swarming time; b) males of Meliponini are expelled from hives which does not need them, and thus, are forced to look for some other place; c) Meliponini males were seen powdering themselves with pollen, thus becoming more acceptable in any other hive. The panmixia is not complete owing to the fact that the density of the breeding population as very low, even in the more frequent species as low as about 2 females and 160 males per reproductive area. We adopted as selection values (or survival indices) the expressions according to Brieger (1948,1950) which may be summarised as follows; a population: p2AA + ²pq Aa + q2aa became after selection: x p2AA + 2pq Aa + z q²aa. For alge-braics facilities Brieger divided the three selective values by y giving thus: x/y p2 AA + y/y 2 pq Aa + z/y q²aa. He called x/y of RA and z/y of Ra, that are survival or selective index, calculated in relation to the heterozygote. In our case all index were calculated in relation to the heterozygote, including the ones for haploid males; thus we have: RA surveval index of genotype AA Ra surveval index of genotype aa R'A surveval index of genotype A R'a surveval index of genotype a 1 surveval index of genotype Aa The index R'A ande R'a were equalized to RA and Ra, respectively, for facilities in the conclusions. 2) Panmitic populations of Hymenoptera, barring mutations, migrations and selection, should follow the Hardy-Weinberg law, thus all gens will be present in the population in the inicial frequency (see Graphifc 1). 3) Heterotic genes: If mutation for heterotic gene ( 1 > RA > Ra) occurs, an equilibrium will be reached in a population when: P = R A + Ra - 2R²a _____________ (9) 2(R A + Ra - R²A - R²a q = R A + Ra - 2R²A _____________ (10) 2(R A + Ra - R²A - R²a A heterotic gene in an hymenopteran population may be maintained without the aid of new mutation only if the survival index of the most viable mutant (RA) does not exced the limiting value given by the formula: R A = 1 + √1+Ra _________ 4 If RA has a value higher thah the one permitted by the formula, then only the more viable gene will remain present in the population (see Graphic 10). The only direct proof for heterotic genes in Hymenoptera was given by Mackensen and Roberts, who obtained offspring from Apis mellefera L. queens fertilized by their own sons. Such inbreeding resulted in a rapid loss of vigor the colony; inbred lines intercrossed gave a high hybrid vigor. Other fats correlated with the "heterosis" problem are; a) In a colony M. quadrifasciata Lep., which suffered severely from heat, the percentage of deths omong males was greater .than among females; b) Casteel and Phillips had shown that in their samples (Apis melifera L). the males had 7 times more abnormalities tian the workers (see Quadros IV to VIII); c) just after emerging the males have great variation, but the older ones show a variation equal to that of workers; d) The tongue lenght of males of Apis mellifera L., of Bombus rubicundus Smith (Quadro X), of Melipona marginata Lep. (Quadro XI), and of Melipona quadrifasciata Lep. Quadro IX, show greater variationthan that of workers of the respective species. If such variation were only caused by subviables genes a rapid increasse of homozigoty for the most viable alleles should be expected; then, these .wild populations, supposed to be in equilibrium, could .not show such variability among males. Thus we conclude that heterotic genes have a grat importance in these cases. 4) By means of mathematical models, we came to the conclusion tht isolating genes (Ra ^ Ra > 1), even in the case of mutations with more adaptability, have only the opor-tunity of survival when the population number is very low (thus the frequency of the gene in the breeding population will be large just after its appearence). A pair of such alleles can only remain present in a population when in border regions of two races or subspecies. For more details see Graphics 5 to 8. 5) Sex-limited genes affecting only females, are of great importance toHymenoptera, being subject to the same limits and formulas as diploid panmitic populations (see formulas 12 and 13). The following examples of these genes were given: a) caste-determining genes in the genus Melipona; b) genes permiting an easy response of females to differences in feeding in almost all social Hymenoptera; c) two genes, found in wild populations, one in Trigona (Plebéia) mosquito F. SMITH (quadro XII) and other in Melipona marginata marginata LEP. (Quadro XIII, colonies 76 and 56) showing sex-limited effects. Sex-limited genes affecting only males do not contribute to the plasticity or genie reserve in hymenopteran populations (see formula 14). 6) The factor time (life span) in Hymenoptera has a particular importance for heterotic genes. Supposing one year to be the time unit and a pair of heterotic genes with respective survival indice equal to RA = 0, 90 and Ra = 0,70 to be present; then if the life time of a population is either one or two years, only the more viable gene will remain present (see formula 11). If the species has a life time of three years, then both alleles will be maintained. Thus we conclude that in specis with long lif-time, the heterotic genes have more importance, and should be found more easily. 7) The colonies of social Hymenoptera behave as units in competition, thus in the studies of populations one must determine the survival index, of these units which may be subdivided in indice for egg-laying, for adaptive value of the queen, for working capacity of workers, etc. 8) A study of endogamic hymenopteran populations, reproduced by sister x brother mating (fig. 2), lead us to the following conclusions: a) without selection, a population, heterozygous for one pair of alleles, will consist after some generations (theoretically after an infinite number of generation) of females AA fecundated with males A and females aa fecundated with males a (see Quadro I). b) Even in endogamic population there is the theoretical possibility of the presence of heterotic genes, at equilibrium without the aid of new mutations (see Graphics 11 and 12), but the following! conditions must be satisfied: I - surveval index of both homozygotes (RA e Ra) should be below 0,75 (see Graphic 13); II - The most viable allele must riot exced the less viable one by more than is permited by the following formula (Pimentel Gomes 1950) (see Gra-fic 14) : 4 R5A + 8 Ra R4A - 4 Ra R³A (Ra - 1) R²A - - R²a (4 R²a + 4 Ra - 1) R A + 2 R³a < o Considering these two conditions, the existance of heterotic genes in endogamic populations of Hymenoptera \>ecames very improbable though not - impossible. 9) Genie mutation offects more hymenopteran than diploid populations. Thus we have for lethal genes in diploid populations: u = q2, and in Hymenoptera: u = s, being u the mutation ratio and s the frequency of the mutant in the male population. 10) Three factors, important to competition among species of Meliponini were analysed: flying capacity of workers, food gathering capacity of workers, egg-laying of the queen. In this connection we refer to the variability of the tongue lenght observed in colonies from several localites, to the method of transporting the pollen in the stomach, from some pots (Melliponi-ni storage alveolus) to others (e. g. in cases of pillage), and to the observation that the species with the most populous hives are almost always the most frequent ones also. 11) Several defensive ways used for Meliponini to avoid predation are cited, but special references are made upon the camouflage of both hive (fig. 5) and hive entrance (fig. 4) and on the mimetism (see list in page ). Also under the same heading we described the method of Lestrimelitta for pillage. 12) As mechanisms important for promoting genetic plasticity of hymenopteran species we cited: a) cytological variations and b) genie reserve. As to the former, duplications and numerical variations of chromosomes were studied. Diprion simile ATC was cited as example for polyploidy. Apis mellife-ra L. (n •= 16) also sugests polyploid origen since: a) The genus Melipona, which belongs to a" related tribe, presents in all species so far studied n = 9 chromosomes and b) there occurs formation of dyads in the firt spermatocyte division. It is su-gested that the origin of the sex-chromosome of Apis mellifera It. may be related to the possible origin of diplo-tetraploidy in this species. With regards to the genie reserve, several possible types of mutants were discussed. They were classified according to their survival indices; the heterotic and neutral mutants must be considered as more important for the genie reserve. 13) The mean radius from a mother to a daghter colony was estimated as 100 meters. Since the Meliponini hives swarm only once a year we may take 100 meters a year as the average dispersion of female Meliponini in ocordance to data obtained from Trigona (tetragonisca) jaty F. SMITH and Melipona marginata LEP., while other species may give different values. For males the flying distance was roughly estimated to be 10 times that for females. A review of the bibliography on Meliponini swarm was made (pg. 43 to 47) and new facts added. The population desity (breeding population) corresponds in may species of Meliponini to one male and one female per 10.000 square meters. Apparently the males are more frequent than the females, because there are sometimes many thousands, of males in a swarm; but for the genie frequency the individuals which have descendants are the ones computed. In the case of Apini and Meliponini, only one queen per hive and the males represented by. the spermatozoos in its spermateca are computed. In Meliponini only one male mate with the queen, while queens of Apis mellijera L. are fecundated by an average of about 1, 5 males. (Roberts, 1944). From the date cited, one clearly sees that, on the whole, populations of wild social bees (Meliponini) are so small that the Sewall Wright effect may become of great importance. In fact applying the Wright's formula: f = ( 1/aN♂ + 1/aN♀) (1 - 1/aN♂ + 1/aN♀) which measures the fixation and loss of genes per generation, we see that the fixation or loss of genes is of about 7% in the more frequent species, and rarer species about 11%. The variation in size, tergite color, background color, etc, of Melipona marginata Lep. is atributed to this genetic drift. A detail, important to the survival of Meliponini species, is the Constance of their breeding population. This Constance is due to the social organization, i. e., to the care given to the reproductive individuals (the queen with its sperm pack), to the way of swarming, to the food storage intended to control variations of feeding supply, etc. 14) Some species of the Meliponini are adapted to various ecological conditions and inhabit large geographical areas (e. g. T. (Tetragonisca jaty F. SMITH), and Trigona (Nanno-trigona testaceicornis LEP.) while others are limited to narrow regions with special ecological conditions (e. g. M. fuscata me-lanoventer SCHWARZ). Other species still, within the same geographical region, profit different ecological conditions, as do M. marginata LEP. and M. quadrifasciata LEP. The geographical distribution of Melipona quadrifasciata LEP. is different according to the subspecies: a) subsp anthidio-des LEP. (represented in Fig. 7 by black squares) inhabits a region fron the North of the S. Paulo State to Northeastern Brazil, ,b) subspecies quadrifasciata LEP., (marked in Fig. 7 with black triangles) accurs from the South of S. Paulo State to the middle of the State of Rio Grande do Sul (South Brazil). In the margined region between these two areas of distribution, hi-brid colonies were found (Fig. 7, white circles); they are shown with more details in fig. 8, while the zone of hybridization is roughly indicated in fig. 9 (gray zone). The subspecies quadrifasciata LEP., has 4 complete yellow bands on the abdominal tergites while anthidioides LEP. has interrupted ones. This character is determined by one or two genes and gives different adaptative properties to the subspecies. Figs. 10 shows certains meteorological isoclines which have aproximately the same configuration as the limits of the hybrid zone, suggesting different climatic adaptabilities for both genotypes. The exis-tance of a border zone between the areas of both subspecies, where were found a high frequency of hybrids, is explained as follows: being each subspecies adapted to a special climatic zone, we may suppose a poor adaptation of either one in the border region, which is also a region of intermediate climatic conditions. Thus, the hybrids, having a combination of the parent qualities, will be best adapted to the transition zone. Thus, the hybrids will become heterotic and an equilibrium will be reached with all genotypes present in the population in the border region.

Smoothing singularities of Riemannian metrics while preserving lower curvature bounds

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

Dominance of positivity of the Green's function associated to a perturbed polyharmonic dirichlet boundary value problem by pointwise estimates

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

Optimal control of a Stefan problem with gradient-based methods in FEniCS

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Masterarbeit, 2016

The orthogonal subcategory problem in homotopy theory

It is known that, in a locally presentable category, localization exists with respect to every set of morphisms, while the statement that localization with respect to every (possibly proper) class of morphisms exists in locally presentable categories is equivalent to a large-cardinal axiom from set theory. One proves similarly, on one hand, that homotopy localization exists with respect to sets of maps in every cofibrantly generated, left proper, simplicial model category M whose underlying category is locally presentable. On the other hand, as we show in this article, the existence of localization with respect to possibly proper classes of maps in a model category M satisfying the above assumptions is implied by a large-cardinal axiom called Vopënka's principle, although we do not know if the reverse implication holds. We also show that, under the same assumptions on M, every endofunctor of M that is idempotent up to homotopy is equivalent to localization with respect to some class S of maps, and if Vopënka's principle holds then S can be chosen to be a set. There are examples showing that the latter need not be true if M is not cofibrantly generated. The above assumptions on M are satisfied by simplicial sets and symmetric spectra over simplicial sets, among many other model categories.

Periodic orbits of the planar collision restricted 3-body problem

Using the continuation method we prove that the circular and the elliptic symmetric periodic orbits of the planar rotating Kepler problem can be continued into periodic orbits of the planar collision restricted 3–body problem. Additionally, we also continue to this restricted problem the so called “comets orbits”.

Polynomial-time complexity for instances of the endomorphism problem in free groups

We say the endomorphism problem is solvable for an element W in a free group F if it can be decided effectively whether, given U in F, there is an endomorphism Φ of F sending W to U. This work analyzes an approach due to C. Edmunds and improved by C. Sims. Here we prove that the approach provides an efficient algorithm for solving the endomorphism problem when W is a two- generator word. We show that when W is a two-generator word this algorithm solves the problem in time polynomial in the length of U. This result gives a polynomial-time algorithm for solving, in free groups, two-variable equations in which all the variables occur on one side of the equality and all the constants on the other side.

Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.