6 resultados para Calculus of variations.

em Helda - Digital Repository of University of Helsinki


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In this study I discuss G. W. Leibniz's (1646-1716) views on rational decision-making from the standpoint of both God and man. The Divine decision takes place within creation, as God freely chooses the best from an infinite number of possible worlds. While God's choice is based on absolutely certain knowledge, human decisions on practical matters are mostly based on uncertain knowledge. However, in many respects they could be regarded as analogous in more complicated situations. In addition to giving an overview of the divine decision-making and discussing critically the criteria God favours in his choice, I provide an account of Leibniz's views on human deliberation, which includes some new ideas. One of these concerns is the importance of estimating probabilities in making decisions one estimates both the goodness of the act itself and its consequences as far as the desired good is concerned. Another idea is related to the plurality of goods in complicated decisions and the competition this may provoke. Thirdly, heuristic models are used to sketch situations under deliberation in order to help in making the decision. Combining the views of Marcelo Dascal, Jaakko Hintikka and Simo Knuuttila, I argue that Leibniz applied two kinds of models of rational decision-making to practical controversies, often without explicating the details. The more simple, traditional pair of scales model is best suited to cases in which one has to decide for or against some option, or to distribute goods among parties and strive for a compromise. What may be of more help in more complicated deliberations is the novel vectorial model, which is an instance of the general mathematical doctrine of the calculus of variations. To illustrate this distinction, I discuss some cases in which he apparently applied these models in different kinds of situation. These examples support the view that the models had a systematic value in his theory of practical rationality.

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A repetitive sequence collection is one where portions of a base sequence of length n are repeated many times with small variations, forming a collection of total length N. Examples of such collections are version control data and genome sequences of individuals, where the differences can be expressed by lists of basic edit operations. Flexible and efficient data analysis on a such typically huge collection is plausible using suffix trees. However, suffix tree occupies O(N log N) bits, which very soon inhibits in-memory analyses. Recent advances in full-text self-indexing reduce the space of suffix tree to O(N log σ) bits, where σ is the alphabet size. In practice, the space reduction is more than 10-fold, for example on suffix tree of Human Genome. However, this reduction factor remains constant when more sequences are added to the collection. We develop a new family of self-indexes suited for the repetitive sequence collection setting. Their expected space requirement depends only on the length n of the base sequence and the number s of variations in its repeated copies. That is, the space reduction factor is no longer constant, but depends on N / n. We believe the structures developed in this work will provide a fundamental basis for storage and retrieval of individual genomes as they become available due to rapid progress in the sequencing technologies.

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The aim of this thesis was to study what kind of home-made menstrual pads were used in the early 20th century in Finland, how the home-made pads were made and which techniques and materials were used. The use and taking care of menstrual pads were also explored. The history of menstrual pads has been studied in Sweden, Germany and United States but none of those studies has concentrated on home-made pads. Instead, there are many studies about womanhood and menstruation. In many studies home-made menstrual pads are only briefly mentioned. Menstrual pads were not commonly used in Finland at the beginning of the 20th century, but already in the 1940s the use of menstrual pads had become common in every stratum of society. Home-made menstrual pads were used even until the 1960s. In Finland, factory-made disposable menstrual pads became common only in the 1930s and they were only slowly accepted. The study material consisted of nine interviews, three archival inquiries, health care guidebooks from 1893 to 1943 and authentic menstrual pads, menstrual belts and other objects related to them. The interviewed women were born between 1915 and 1939. The narrative approach was used in the study and it also guided the analysis. The interview and archival data were studied according to the basic rules of oral history studies. Literature consisted of publications from several disciplines. The extensive primary material played the most important role in this study. The reconstructions of the menstrual pads were made according to the interviewed women s advice. In Finland there were innumerable variations of home-made menstrual pads. The pads were most commonly crocheted and knitted either by hand or by knitting machine. Pads were also sewn of cloth, old bed linen or old underwear. The menstrual pads were self-made or made by a female relative. Word of mouth was important in spreading information on how to make pads, because there were hardly any instructions available. The biggest pads were 54 cm long and 13 cm wide. The most widely used pad model was a rectangle, which had triangle-shaped ends with a buttonhole or a loop. The pad was attached to the menstrual belt or to the buttons of the suspender belt. Knitted and crocheted pads had one, two or three layers. In sewn pads, there could be even more layers. Cellulose wadding or pieces of cloth could be placed inside the pad to increase the absorption ability. The experiences of the comfort of self-made pads varied. The crocheted and sewn pads were found chafing, knitted ones were found soft and comfortable. The menstrual pads were laborious to wash and boil in lye water. Therefore disposable pads made everyday life easier. The home-made menstrual pads were part of a unique tradition of handicrafts and folk culture. Hand-made pads were one of the most common handicraft products and were a part of every woman s life. Even so, the menstrual pads were unnoticeable. The large number of variations was probably caused by the silence around menstrual topics and by the lack of instructions for making pads. Variations are also explained by the uniqueness of every handicraft product. In Finland the home-made pads were used until relatively recent times. This was caused by the conditions of wartime and the following years and the rarity of commercial pads. Furthermore, until the late 20th century Finland was an agricultural society where all innovations spread slowly. Home-made menstrual pad was a secret handicraft of women and every woman needed to know how to make it by herself.

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The question at issue in this dissertation is the epistemic role played by ecological generalizations and models. I investigate and analyze such properties of generalizations as lawlikeness, invariance, and stability, and I ask which of these properties are relevant in the context of scientific explanations. I will claim that there are generalizable and reliable causal explanations in ecology by generalizations, which are invariant and stable. An invariant generalization continues to hold or be valid under a special change called an intervention that changes the value of its variables. Whether a generalization remains invariant during its interventions is the criterion that determines whether it is explanatory. A generalization can be invariant and explanatory regardless of its lawlike status. Stability deals with a generality that has to do with holding of a generalization in possible background conditions. The more stable a generalization, the less dependent it is on background conditions to remain true. Although it is invariance rather than stability of generalizations that furnishes us with explanatory generalizations, there is an important function that stability has in this context of explanations, namely, stability furnishes us with extrapolability and reliability of scientific explanations. I also discuss non-empirical investigations of models that I call robustness and sensitivity analyses. I call sensitivity analyses investigations in which one model is studied with regard to its stability conditions by making changes and variations to the values of the model s parameters. As a general definition of robustness analyses I propose investigations of variations in modeling assumptions of different models of the same phenomenon in which the focus is on whether they produce similar or convergent results or not. Robustness and sensitivity analyses are powerful tools for studying the conditions and assumptions where models break down and they are especially powerful in pointing out reasons as to why they do this. They show which conditions or assumptions the results of models depend on. Key words: ecology, generalizations, invariance, lawlikeness, philosophy of science, robustness, explanation, models, stability

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Yhteenveto: Maankosteusvaihtelut talvella hiekkamaassa