A nerve lemma for gluing together incoherent discrete Morse functions

Two of the most useful tools in topological combinatorics are the nerve lemma and discrete Morse theory. In this note we introduce a theorem that interpolates between them and allows decompositions of complexes into non-contractible pieces as long as discrete Morse theory ensures that they behave well enough. The proof is based on diagrams of spaces, but that theory is not needed for the formulation or applications of the theorem.Comment: 4 page

Satisfaction classes in nonstandard models of first-order arithmetic

A satisfaction class is a set of nonstandard sentences respecting Tarski's truth definition. We are mainly interested in full satisfaction classes, i.e., satisfaction classes which decides all nonstandard sentences. Kotlarski, Krajewski and Lachlan proved in 1981 that a countable model of PA admits a satisfaction class if and only if it is recursively saturated. A proof of this fact is presented in detail in such a way that it is adaptable to a language with function symbols. The idea that a satisfaction class can only see finitely deep in a formula is extended to terms. The definition gives rise to new notions of valuations of nonstandard terms; these are investigated. The notion of a free satisfaction class is introduced, it is a satisfaction class free of existential assumptions on nonstandard terms. It is well known that pathologies arise in some satisfaction classes. Ideas of how to remove those are presented in the last chapter. This is done mainly by adding inference rules to M-logic. The consistency of many of these extensions is left as an open question.Comment: Thesis for the degree of licentiate of philosophy, 74 pages, 4 figure

Characterizing Quantifier Extensions of Dependence Logic

We characterize the expressive power of extensions of Dependence Logic and Independence Logic by monotone generalized quantifiers in terms of quantifier extensions of existential second-order logic.Comment: 9 page

Optimal Non-Linear Income Taxation in Search Equilibrium

The paper extends the basic Stiglitz (1982) model of optimal income taxation into general search equilibrium. When we extend the basic taxation model to include a more realistic treatment of the labor market, a number of new interesting mechanisms arise. When wages are fixed we find that a "work hour effect" gives the government incentives to lower the marginal tax rate for both high and low skilled workers. The optimal marginal tax on high skilled is thus negative, and the sign for the low skilled marginal tax is ambiguous. With wages determined by bargaining between firm and worker the results are changed. Both marginal tax rates are of ambiguous sign. The tax systems' effects on the wage formation and the unemployment rates may result in new intricate redistribution channels. Simulations show that the marginal tax rate for high skilled is increasing in the level of redistribution when wages are fixed, but decreasing in the level of redistribution when wages are determined by bargaining.Optimal non-linear income taxation; search; unemployment

Unemployment Benefits and Optimal Non-Linear Income Taxation

This paper explores the rationale for unemployment benefits as a complement to optimal non-linear income taxation. High-skilled workers and low-skilled workers face different exogenous risks of being unemployed. As long as the low-skilled workers face a higher unemployment risk, we find that there is a case for over-insuring the low-skilled, hence the unemployment benefits of the low-skilled should be higher than the pure insurance purpose would prescribe. This effect is likely to prevail in a model with a more realistic treatment of the labor market.Optimal non-linear income taxation; unemployment benefits

Journal Staff

Tolkningen av EKG är en viktig metod vid diagnostisering av onormala hjärttillstånd och kan användas i förebyggande syfte att upptäcka tidigare okända hjärtproblem. Att enkelt kunna mäta sitt EKG och få det analyserat och presenterat på ett pedagogiskt sätt utan att behöva rådfråga en läkare är något det finns ett konsumentbehov av. Denna rapport beskriver hur en EKG-signal behandlas med olika algoritmer och metoder i syfte att detektera hjärtslag och dess olika parametrar. Denna information används till att klassificera varje hjärtslag för sig och därmed avgöra om användaren har en normal eller onormal hjärtfunktion. För att nå dit har en mjukvaruprototyp utvecklats där algoritmerna implementerats. En enkätundersökning gjordes i syfte att undersöka hur utdata från mjukvaruprototypen skulle presenteras för en vanlig användare utan medicinsk utbildning. Sju filer med EKG-signaler från MIT-BIH Arrhythmia Database användes för testning av mjukvaruprototypen. Resultatet visade att prototypen kunde detektera en rad olika hjärtfel som låg till grund vid fastställning om hjärtat slog normalt eller onormalt. Resultatet presenterades på en mobilapp baserad på enkätundersökningen.The interpretation of the ECG is an important method in the diagnosis of abnormal heart conditions and can be used proactively to discover previ-ously unknown heart problems. Being able to easily measure the ECG and get it analyzed and presented in a clear manner without having to consult a doctor is improtant to satisfy consumer needs. This report describes how an ECG signal is treated with different algo-rithms and methods to detect the heartbeat and its various parameters. This information is used to classify each heartbeat separately and thus determine whether the user has a normal or abnormal cardiac function. To achieve this a software prototype was developed in which the algorithms were implemented. A questionnaire survey was done in order to examine how the output of the software prototype should be presented for a user with no medical training. Seven ECG files from MIT-BIH Arrhythmia database were used for validation of the algorithms. The developed algorithms could detect of if any abnormality of heart function occurred and informed the users to consult a physician. The presentation of the heart function was based on the result from the questioner