Métodos para el análisis de programas probabilistas y no-deterministas utilizando probadores de teoremas. Methods for the analysis of probabilistic and nondeterministic programs using theorem provers.

La verificación y el análisis de programas con características probabilistas es una tarea necesaria del quehacer científico y tecnológico actual. El éxito y su posterior masificación de las implementaciones de protocolos de comunicación a nivel hardware y soluciones probabilistas a problemas distribuidos hacen más que interesante el uso de agentes estocásticos como elementos de programación. En muchos de estos casos el uso de agentes aleatorios produce soluciones mejores y más eficientes; en otros proveen soluciones donde es imposible encontrarlas por métodos tradicionales. Estos algoritmos se encuentran generalmente embebidos en múltiples mecanismos de hardware, por lo que un error en los mismos puede llegar a producir una multiplicación no deseada de sus efectos nocivos.Actualmente el mayor esfuerzo en el análisis de programas probabilísticos se lleva a cabo en el estudio y desarrollo de herramientas denominadas chequeadores de modelos probabilísticos. Las mismas, dado un modelo finito del sistema estocástico, obtienen de forma automática varias medidas de performance del mismo. Aunque esto puede ser bastante útil a la hora de verificar programas, para sistemas de uso general se hace necesario poder chequear especificaciones más completas que hacen a la corrección del algoritmo. Incluso sería interesante poder obtener automáticamente las propiedades del sistema, en forma de invariantes y contraejemplos.En este proyecto se pretende abordar el problema de análisis estático de programas probabilísticos mediante el uso de herramientas deductivas como probadores de teoremas y SMT solvers. Las mismas han mostrado su madurez y eficacia en atacar problemas de la programación tradicional. Con el fin de no perder automaticidad en los métodos, trabajaremos dentro del marco de "Interpretación Abstracta" el cual nos brinda un delineamiento para nuestro desarrollo teórico. Al mismo tiempo pondremos en práctica estos fundamentos mediante implementaciones concretas que utilicen aquellas herramientas.

Representations of lattice point sets : theory, algorithms, applications

Magdeburg, Univ., Fak. für Mathematik, Habil.-Schr., 2006

Analysis of heterogeneously catalyzed ester hydrolysis reactions in a fixed-bed chromatographic reactor

Reactive Chromatography, Fixed-Bed Reactor, Heterogeneous, Hydrolysis, Ester, Catalyst, Adsorption, Ion-Exchange Resin

Functional elucidation of pag through the generation of truncation and point mutants

T-cell signalling, PAG, adaptor proteins, lipid rafts, palmitoylation, chemokine induced migration

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 ...

Estudos citológicos em Hemíoteros da família Coreidae

A more or less detailed study of the spermatogenesis in six species of Hemiptera belonging to the Coreid Family is made in the present paper. The species studied and their respective chromosome numbers were: 1) Diactor bilineatus (Fabr.) : spermatogonia with 20 + X, primary spermatocytes with 10 + X, X dividing equationaliv in the first division and passing undivided to one pole in the second. 2) Lcptoglossus gonagra (Fabr.) : spermatogonia with 20 + X, primary spermatocytes with 10 + X, X dividing equationally in the first division and passing undivided to one pole in the second. 3) Phthia picta (Drury) : spermatogonia with 20 + X, primary spermatocytes with 10 + X, X dividing equationally in the first division and passing undivided to one pole in the second. 4) Anisocelis foliacea Fabr. : spermatogonia with 26 + X fthe highest mumber hitherto known in the Family), primary .spermatocytes with 13 + X, X dividing equationally in the first division an passing undivided to one pole in the second. 5) Pachylis pharaonis (Herbtst) : spermatogonia with 16 + X, primary spermatocytes with 8 + X. Behaviour of the heteroehromosome not referred. 6) Pachylis laticornis (Fabr.) : spermatogonia with 14 + X, primary spermatocytes with 7 + X, X passing undivided to one pole in the first division and therefore secondary spermatocytes with 7 + X and 7 chromosomes. General results and conclusions a) Pairing modus of the chromosomes (Telosynapsis or Farasynapsis ?) - In several species of the Coreld bugs the history of the chromosomes from the diffuse stage till diakinesis cannot be follewed in detail due specially to the fact that lhe bivalents, as soon as they begin to be individually distinct they appear as irregular and extremely lax chromatic areas, which through an obscure process give rise to the diakinesis and then to the metaphase chomosomes. Fortunately I was able to analyse the genesis of the cross-shaped chromosomes, becoming thus convinced that even in the less favorable cases like that of Phthia, in which the crosses develop from four small condensation areas of the diffuse chromosomes, nothing in the process permit to interpret the final results as being due to a previous telosynaptic pairing. In the case of long bivalents formed by two parallel strands intimately united at both endsegments and more or less widely open in the middle (Leptoglossus, Pachylis), I could see that the lateral arms of the crosses originate from condensation centers created by a torsion or bending in the unpaired parts of the chromosomes In the relatively short bivalents the lateral branches of the cross are formed in the middle but in the long ones, whose median opening is sometimes considerable, two asymetrical branches or even two independent crosses may develop in the same pair. These observations put away the idea of an end-to-end pairing of the chromosomes, since if it had occured the lateral arms of the crosses would always be symetrical and median and never more than two. The direct observation of a side- toside pairing of the chromosomal threads at synizesis, is in foil agreement with the complete lack of evidence in favour of telosynapsis. b) Anaphasic bridges and interzonal connections - The chromosomes as they separate from each other in anaphase they remain connected by means of two lateral strands corresponding to the unpaired segmenas observed in the bivalents at the stages preceding metaphase. In the early anaphase the chromosomes again reproduce the form they had in late diafcinesis. The connecting threads which may be thick and intensely coloured are generally curved and sometimes unequal in lenght, one being much longer than the other and forming a loop outwardly. This fact points to a continuous flow of chromosomal substance independently from both chromosomes of the pair rather than to a mechanical stretching of a sticky substance. At the end of anaphase almost all the material which formed the bridges is reduced to two small cones from whose vertices a very fine and pale fibril takes its origin. The interzonal fibres, therefore, may be considered as the remnant of the anaphasic bridges. Abnormal behaviour of the anaphase chromosomes showed to be useful in aiding the interpretation of normal aspects. It has been suggested by Schrader (1944) "that the interzonal is nothing more than a sticky coating of the chromosome which is stretched like mucilage between the daughter chromosomes as they move further and further apart". The paired chromosomes being enclosed in a commom sheath, as they separate they give origin to a tube which becomes more and more stretched. Later the walls of the tube collapse forming in this manner an interzonal element. My observations, however, do not confirm Schrader's tubular theory of interzonal connections. In the aspects seen at anaphase of the primary spermatocytes and described in this paper as chromosomal bridges nothing suggests a tubular structure. There is no doubt that the chromosomes are here connected by two independent strands in the first division of the spermatocytes and by a single one in the second. The manner in which the chromosomes separate supports the idea of transverse divion, leaving little place for another interpretation. c) Ptafanoeomc and chromatoid bodies - The colourabtlity of the plasmosome in Diactor and Anisocelis showed to be highly variable. In the latter species, one may find in the same cyst nuclei provided with two intensely coloured bodies, the larger of which being the plasmosome, sided by those in which only the heterochromosome took the colour. In the former one the plasmosome strongly coloured seen in the primary metaphase may easily be taken for a supernumerary chromosome. At anaphase this body stays motionless in the equator of the cell while the chromosomes are moving toward the poles. There, when intensely coloured ,it may be confused with the heterochromosome of the secondary spermatocytes, which frequently occupies identical position in the corresponding phase, thus causing missinterpretation. In its place the plasmosome may divide into two equal parts or pass undivided to one cell in whose cytoplasm it breaks down giving rise to a few corpuscles of unequal sizes. In Pachylis pharaonis, as soon as the nuclear membrane breate down, the plasmosome migrates to a place in the periphery of the cell (primary spermatocyte), forming there a large chromatoid body. This body is never found in the cytoplasm prior to the dissolution of the nuclear membrane. It is certain that chromatoid bodies of different origin do exist. Here, however, we are dealing, undoubtedly, with true plasmosomes. d) Movement of the heterochromosome - The heterochromosome in the metaphase of the secondary spermatocytes may occupy the most different places. At the time the autosomes prient themselves in the equatorial plane it may be found some distance apart in this plane or in any other plane and even in the subpolar and polar regions. It remains in its place during anaphase. Therefore, it may appear at the same level with the components of one of the anaphase plates (synchronism), between both plates (succession) or between one plate and tbe pole (precession), what depends upon the moment the cell was fixed. This does not mean that the heterochromosome sometimes moves as quickly as the autosomes, sometimes more rapidly and sometimes less. It implies, on the contrary, that, being anywhere in the cell, the heterochromosome m he attained and passed by the autosomes. In spite of being almost motionless the heterochromosome finishes by being enclosed in one of the resulting nuclei. Consequently, it does move rapidly toward the group formed by the autosomes a little before anaphase is ended. This may be understood assuming that the heterochromosome, which do not divide, having almost inactive kinetochore cannot orient itself, giving from wherever it stays, only a weak response to the polar influences. When in the equator it probably do not perform any movement in virtue of receiving equal solicitation from both poles. When in any other plane, despite the greater influence of the nearer pole, the influence of the opposite pole would permit only so a slow movement that the autosomes would soon reach it and then leave it behind. It is only when the cell begins to divide that the heterochromosome, passing to one of the daughter cells scapes the influence of the other and thence goes quickly to join the autosomes, being enclosed with them in the nucleus formed there. The exceptions observed by BORING (1907) together with ; the facts described here must represent the normal behavior of the heterocromosome of the Hemiptera, the greater frequency of succession being the consequence of the more frequent localization of the heterochromosome in the equatorial plane or in its near and of the anaphase rapidity. Due to its position in metaphase the heterochromosome in early anaphase may be found in precession. In late anaphase, oh the contrary ,it appears almost always in succession. This is attributed to the fact of the heterochromosome being ordinairily localized outside the spindle area it leaves the way free to the anaphasic plate moving toward the pole. Moreover, the heterochromosome being a round element approximately of the size of the autosomes, which are equally round or a little longer in the direction of the movement, it can be passed by the autosomes even when it stands in the area of the spindle, specially if it is not too far from the equatorial plane. e) The kinetochore - This question has been fully discussed in another paper (PIZA 1943a). The facts treated here point to the conclusion that the chromosomes of the Coreidae, like those of Tityus bahiensis, are provided with a kinetochore at each end, as was already admitted by the present writer with regard to the heterochromosome of Protenor. Indeed, taking ipr granted the facts presented in this paper, other cannot be the interpretation. However, the reasons by which the chromosomes of the species studied here do not orient themselves at metaphase of the first division in the same way as the heterochromosome of Protenor, that is, with the major axis parallelly to the equatorial plane, are claiming for explanation. But, admiting that the proximity of the kinetochores at the ends of chromosomes which do not separate until the second division making them respond to the poles as if they were a single kinetochore ,the explanation follows. (See PIZA 1943a). The median opening of the diplonemas when they are going to the diffuse stage as well as the reappearance of the bivalents always united at the end-segments and open in the middle is in full agreement with the existence of two terminal kinetochores. The same can be said with regard to the bivalents which join their extremities to form a ring.

Lattice point inequalities and face numbers of polytopes in view of central symmetry

Magdeburg, Univ., Fak. für Mathematik, Diss., 2012

O problema técnico-econômico da adubação

The authors discuss from the economic point of view the use of a few functions intended to represent the yield y corresponding to a level xof the nutrient. They point out that under conditions of scarce capital what is actually most important is not to obtain the highest profit per hectare but the highest return per cruzeiro spent, so that we should maximize the function z = _R - C_ = _R_ - 1 , C C where R is the gross income and C the cost of production (fixed plus variable, both per hectare). Being C = M + rx, with r the unit price of the nutrient and Af the fixed cost of the crop, wo are led to the equation (M + rx)R' - rR = 0. With R = k + sx + tx², this gives a solution Xo = - Mt - √ M²t² - r t(Ms - Kr)- _____________________ rt on the other hand, with R = PyA [1 - 10-c(x + b)], x0 will be the root of equation (M + rx)cL 10 + r 10c(x + b) = 0 (12). Another solution, pointed out by PESEK and HEADY, is to maximize the function z = sx + tx² _________ m + rx where the numerator is the additional income due to the nutrient, and m is the fixed cost of fertilization. This leads to a solution x+ = - mt - √m²t² - mrst (13) _________________ rt However, we must have x+< _r_-_s_ I if we want to satisfy t _dy_ > r. dx This condition is satisfied only if we have m < _(s__-__r)² (14), - 4 t a restriction apparently not perceived by PESEK and HEADY. A similar reasoning using Mitscherlich's law leads to equation (mcL 10 + r) + cr(L 10)x - r 10cx = 0 (15), with a similar restriction. As an example, data of VIEGAS referring to fertilization of corn (maize) gave the equation y - 1534 + 22.99 x - 0. 1069 x², with x in kg/ha of the cereal. With the prices of Cr$ 5.00 per kilo of maize, Cr$ 26.00 per kilo of P2O3,. and M = Cr$ 5,000.00, we obtain x0 = 61 kg/ha of P(2)0(5). A similar reasoning using Mitscherlich's law leads to x0 = 53 kg/ha. Now, if we take in account only the fixed cost of fertilization m = Cr$ 600.00 per hectare, we obtain from (13) x+ = 51 kg/ha of P2O5, while (14) gives x+ - 41 kg/ha. Note that if m = Cr$ 5,000.00, we obtain by formula (13) x+ = 88 kg/ha of P2O5, a solution which is not valid, since condition (14) is not satisfied.

Optimal design in the presence of random or fixed block effects

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

Befristete Arbeitsverträge : Ein praxisorientierter Leitfaden

This master thesis explains fixed-term contracts in practice. To illustrate this point, examples are provided for better understanding. It will be discussed at both the fixed-term with an objective reason and without objective reason. The second variant is also called moderate Expiration Calendar. Not only the benefits and advantages for the employer are enumerated, but also the special challenges and problems that may arise. Particularly with regard to the prohibition of previous employment.This thesis presents the interests fo employers and companies. The central research question is: What are the possibilities of limitation and there is the prohibition of previous employment unconstitutional? A special attention is given to the contractual formulation examples of limited contracts. It deals exclusively with applicable German and European law. A comparison with previous case-law does not take place in this master thesis.

Ornithological notes from Point Barrow, Alaska, by Louis B. Bishop.

v.29:no.12(1944)

Examples of retracts in a free group that are not the fixed subgroup of any group of automorphisms

Let F be a free group of rank at least three. We show that some retracts of F previously studied by Martino-Ventura are not equal to the fixed subgroup of any group of automorphisms of F. This shows that, in F, there exist subgroups that are equal to the fixed subgroup of some set of endomorphisms but are not equal to the fixed subgroup of any set of automorphisms. Moreover, we determine the Galois monoids of these retracts, where, by the Galois monoid of a subgroup H of F, we mean the monoid consisting of all endomorphisms of F that fix H.

Stable coalition structures with fixed decision scheme

This paper studies the stability of a finite local public goods economy in horizontal differentiation, where a jurisdiction's choice of the public good is given by an exogenous decision scheme. In this paper, we characterize the class of decision schemes that ensure the existence of an equilibrium with free mobility (that we call Tiebout equilibrium) for monotone distribution of players. This class contains all the decision schemes whose choice lies between the Rawlsian decision scheme and the median voter with mid-distance of the two median voters when there are ties. We show that for non-monotone distribution, there is no decision scheme that can ensure the stability of coalitions. In the last part of the paper, we prove the non-emptiness of the core of this coalition formation game