Generalized Polya urns via stochastic approximation

We collect, survey and develop methods of (one-dimensional) stochastic approximation in a framework that seems suitable to handle fairly broad generalizations of Polya urns. To show the applicability of the results we determine the limiting fraction of balls in an urn with balls of two colors. We consider two models generalizing the Polya urn, in the first one ball is drawn and replaced with balls of (possibly) both colors according to which color was drawn. In the second, two balls are drawn simultaneously and replaced along with balls of (possibly) both colors according to what combination of colors were drawn.Comment: Licentiate thesis, 40 pages, 1 figur

Limit theorems for stochastic approximation algorithms

Abstract We prove a central limit theorem applicable to one dimensional stochastic approximation algorithms that converge to a point where the error terms of the algorithm do not vanish. We show how this applies to a certain class of these algorithms that in particular covers a generalized Pólya urn model, which is also discussed. In addition, we show how to scale these algorithms in some cases where we cannot determine the limiting distribution but expect it to be non-normal

PÄÄLLYSTETYÖN TYÖTAPATARKASTELU

Tämän opinnäytetyön tarkoituksena on tarkastella puutteellisten suunnitelmien vaiku-tusta urakointiin tien saneerauskohteessa. Työ on tehty käyttämällä esimerkkikohteena osia Haminan sisääntuloväylien saneeraushankkeesta, jotka Destia Oy toteutti kesän 2015 aikana. Työn keskittyy lähinnä tien saneerauksessa päällysrakenteen olemassa olevan tasauksen epätasaisuuden aiheuttamiin ongelmakohtiin suhteessa tehtyihin suunnitelmiin sekä ongelmien poistamiseksi urakassa toteutettuihin ratkaisuihin. Opinnäytetyön teoriaosuudessa esitellään tien rakenteita kokonaisuutena ja tien ra-kennekerroksissa käytettäviä materiaaleja sekä tarkastellaan tiehen kohdistuvia lähin-nä liikenteestä aiheuttavia kuormituksia ja muita rasituksia. Teoriaosuus perustuu sekä lähdekirjallisuuteen että käytännön urakoinnista peräsin olevaan kokemusperäiseen tietoon. Työssä tuodaan esille tien puutteellisten suunnitelmien työteknisiä ja laadullisia vaikutuksia lopputulokseen ja sen pitkäaikaiskestävyyteen. Ongelmakohtien kartoituksen jälkeen työssä käydään läpi tien tasauksen uudelleen suunnittelun työvaiheet. Suunnittelussa lähtökohtana oli kustannusten, työmäärien ja massojen optimoiminen sekä samalla laadukkaan lopputuotteen saavuttaminen. Opinnäytetyön tuloksena saatiin kartoitettua ongelmakohtia, joista voi aiheutua suunnittelun ja toteutuksen ristiriitatilanteita. Kun suunnittelua tehdään vähäisillä lähtötiedoilla voi suunnitelmien noudattaminen, etenkin saneerauskohteissa, olla hankalaa. Työnaikainen muutossuunnittelu tai vaihtoehtoisten ratkaisujen esittäminen urakoitsijan toimesta edellyttää sujuvaa vuorovaikutusta tilaajan kanssa. Työssä on otettu esiin toteuttajan vastuu rakentamisen aikana, mikä tarkoittaa muun muassa suunnitelmissa havaittujen epäkohtien esiintuomista tilaajalle. Työn tarkoitus oli tuoda esille myös ratkaisukeskeiseen ja laadukkaaseen rakentamiseen tähtäävä näkökulma. On myös todettava että tässä työssä asiaa on käsitelty vain yhden urakan pohjalta ja soveltuva toteutustapa tulee valita kohteissa aina tapauskohtaisesti.The purpose of this thesis was to study the impact of inadequate planning on the con-tract work on road renovation project. Part of the Hamina Entry Highway modernization project, which Destia Oy carried out during the summer of 2015, was used as the target The thesis focuses mainly on the issues arising from the unevenness of the already existing alignment of the road and the relation of the made plans versus the solutions used. The theoretical part of the thesis presents the different structures of a road as a whole and the different materials used in structural layers as well as the stress caused mainly by traffic but also by other factors. The theoretical part presented in this study is based both literature and empirical knowledge from contracting. The study wishes to highlights the effects of poor planning on both the work process and the quality and durability of the final outcome. After mapping the problem areas the study examines the different phases of road alignment. The plan was based optimization of cost, labor and masses while achieving the best possible end result. As a result of the thesis it was possible to map out our problem areas that could possi-bly cause contradictions between the initial plan and the actual implementations. When the planning is carried out without sufficient knowledge it may be challenging to follow, particularly in renovation projects. Possible changes and updates in the plan by the contractor after the project has already started always require a well-functioning interaction between the contractor and the client. The thesis raises the issue of the implementing entity`s accountability during the renovation process, which include for example informing the commissioner about the faults in the plans. It should, however, be noted that this thesis is based on one contract and suitable method should always be case-specific

Recursive Methods in Urn Models and First-Passage Percolation

This PhD thesis consists of a summary and four papers which deal with stochastic approximation algorithms and first-passage percolation. Paper I deals with the a.s. limiting properties of bounded stochastic approximation algorithms in relation to the equilibrium points of the drift function. Applications are given to some generalized Pólya urn processes. Paper II continues the work of Paper I and investigates under what circumstances one gets asymptotic normality from a properly scaled algorithm. The algorithms are shown to converge in some other circumstances, although the limiting distribution is not identified. Paper III deals with the asymptotic speed of first-passage percolation on a graph called the ladder when the times associated to the edges are independent, exponentially distributed with the same intensity. Paper IV generalizes the work of Paper III in allowing more edges in the graph as well as not having all intensities equal

Reinforced Random Walk

This thesis aim is to present results on a stochastic model called reinforced random walk. This process was conceived in the late 1980’s by Coppersmith and Diaconis and can be regarded as a generalization of a random walk on a weighted graph. These reinforced walks have non-homogeneous transition probabilities, which arise from an interaction between the process and the weights. We survey articles on the subject, perform simulations and extend a theorem by Pemantle. Tack Ett stort tack till min handledare Sven Erick Alm för vägledning i matematiken, efterforskningen och inte minst för uppslaget till denna uppsats. Ditt stöd och kunnande gjorde arbetet till en rolig och utvecklande process. Tack ocks˚a till alla som medverkar i utvecklingen av bra och gratis mjukvara, speciellt personerna bakom L ATEX och R. Det förstnämnda programmet typsatte detta arbete och det sistnämnda användes för simuleringarn

Bleeding risk in patients with venous thromboembolic events treated with new oral anticoagulants

New oral anticoagulants (NOACs) is the preferred treatment in secondary prophylaxis of venous thromboembolic events (VTE). The aim of this study was to investigate possible risk factors associated with major bleeding in VTE-patients treated with NOACs. In this retrospective register-based study we screened the Swedish anticoagulation register Auricula (during 2012.01.01-2017.12.31) to find patients and used other national registers for outcomes. Primary endpoint was major bleeding defined as bleeding leading to hospital care. Multivariate Cox-regression analysis was used to reveal risk factors. 18 219 patients with NOAC due to VTE were included. 85.6% had their first VTE, mean age was 69.4 years and median follow-up time was 183 days. The most common NOAC was rivaroxaban (54.8%), followed by apixaban (42.0%), dabigatran (3.2%) and edoxaban (0.1%). The rate of major bleeding was 6.62 (95% CI 6.19-7.06) per 100 treatment years in all patients and 11.27 (CI 9.96-12.57) in patients above 80 years of age. Statistically independent risk factors associated with major bleeding were age (normalized HR 1.38, CI 1.27-1.50), earlier major bleeding (HR 1.58, Cl 1.09-2.30), COPD (HR 1.28, CI 1.04-1.60) and previous stroke (HR 1.28, Cl 1.03-1.58) or transient ischemic attack (TIA) (HR 1.33, Cl 1.01-1.76). Prior warfarin treatment was protective (HR 0.67, CI 0.58-0.78). This real world cohort shows a high bleeding rate especially among the elderly and in patients with previous major bleeding, COPD and previous stroke or TIA. This should be considered when deciding on treatment duration and NOAC dose in these patients.First published online: 2 November 2020</p