Regularization strategy for inverse problem for 1+1 dimensional wave equation

An inverse boundary value problem for a 1+1 dimensional wave equation with wave speed $c(x)$ is considered. We give a regularisation strategy for inverting the map $\mathcal A:c\mapsto \Lambda,$ where $\Lambda$ is the hyperbolic Neumann-to-Dirichlet map corresponding to the wave speed $c$. More precisely, we consider the case when we are given a perturbation of the Neumann-to-Dirichlet map $\tilde \Lambda=\Lambda +\mathcal E$, where $\mathcal E$ corresponds to the measurement errors, and reconstruct an approximate wave speed $\tilde c$. We emphasize that $\tilde \Lambda$ may not not be in the range of the map $\mathcal A$. We show that the reconstructed wave speed $\tilde c$ satisfies $\| \tilde c-c\|_{L^\infty}<C \|E\|^{1/18}$. Our regularization strategy is based on a new formula to compute $c$ from $\Lambda$

Puunkaatojen maisematyöluvat Turun kaupungissa

Maisematyölupa on maankäyttö- ja rakennuslain alainen ennakkovalvontajärjestelmä, jolla käsitellään maisemaa muuttavia toimenpiteitä, kuten maanrakennustyö ja puiden kaataminen. Tämän opinnäytetyön tilaaja oli Turun kaupungin ympäristötoimialan rakennusvalvonta. Työn tarkoituksena oli selvittää, miten eri kaupungit toimivat puunkaatojen maisematyölupa-asioissa. Tavoitteena oli kehittää Turun rakennusvalvonnan käytännön maisematyölupaprosessia ja löytää viranomaisen työtä helpottavia keinoja. Teoriaosuudessa on käyty läpi maankäyttö- ja rakennuslaista tulevia maisematyöluvan ehtoja ja edellytyksiä sekä perehdytty, miten toimenpide arvioidaan maisemallisesti merkittäväksi tai vähäiseksi. Rakennusvalvontaviranomaisen tehtäviä on esitelty yleisellä tasolla. Teoriaosuuden lopuksi on esitelty Turun rakennusvalvonnan puunkaatojen lupamenettely. Työn tutkimusmenetelmänä käytettiin avoimista kysymyksistä koostuvaa kyselyä. Kyselyllä haluttiin selvittää, millaisista eri vaiheista kaupunkien maisematyölupaprosessit koostuvat. Vastausten perusteella kahdelle osallistujalle tehtiin tarkentavia lisäkysymyksiä. Jatkokysymyksillä haluttiin tarkentavaa tietoa vähäisten toimenpiteiden menettelytavoista. Kehitysehdotuksena voidaan esittää, että maisematyölupia myöntävän viranomaisen työtä helpottaisi, jos Turussa otettaisiin käyttöön kirjallinen ohje vähäiseksi arvioiduista puunkaatotoimenpiteistä. Ohjeen perusteella tontilta voi kaataa tietyn määrän puita ilman lupaa ja viranomaisen teke-mää arviointia toimenpiteen merkittävyydestä.The work permit of landscape is an advance management system under the land use and building act, which deals with landscape-changing actions such as excavation work and felling of trees. This thesis was commissioned by the Building Control of the Environmental Division of the City of Turku. The purpose was to find out how different cities proceed with the work permits of landscape concerning tree felling. The aim was to develop the process of landscape work permit in the sector of building control of Turku and to find ways to facilitate the work of public authority. The theoretical part of this thesis considers the terms and conditions of work permits of landscape which rise from the land use and building act, and the grounds to estimate an act to be scenically significant or insignificant. The tasks of building control authority are presented on a general level. Finally, the permit procedure of tree felling in Turku Building Con-trol is presented. The research method of open questions consisting of questionnaires was used. The survey wanted to examine what the different stages of urban landscape work permits were. Based on the answers, some specifying additional questions were made to two participants. The follow-up questions were made to specify information regarding the procedures of minor actions. As a developmental proposal this thesis suggests an introduction of a written instruction in tree felling actions which are estimated to be minor. Such kind of procedure would facilitate the work of authority accepting the work permits of landscape in the city of Turku. According to the instruction, a certain number of trees could be logged from the plot without permission and an assessment of the significance of the action made by public authority

The changes in the understorey vegetation composition and functional groups of forested mires in Finland during 1985-2006

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First-Line Chemotherapy with Anthracycline and Taxane Combination in Metastatic Breast Cancer. Detection of bone metastases with TRACP 5b

Background: In Finland, breast cancer (BC) is the most common cancer among women, and prostate cancer (PC) that among men. At the metastatic stage both cancers remain essentially incurable. The goals of therapy include palliation of symptoms, improvement or maintenance of quality of life (QoL), delay of disease progression, and prolongation of survival. Balancing between efficacy and toxicity is the major challenge. With increasing costs of new treatments, appropriate use of resources is paramount. When new treatment regimes are introduced into clinical practice a comprehensive assessment of clinical benefit, adverse effects and cost is necessary. Both BC and PC show a predilection to metastasize to bone. Bone metastases cause significant morbidity impairing the patients´ QoL. Diagnosis of bone metastases relies mainly on radiological methods, which however lack optimal sensitivity and specificity. New tools are needed for detection and follow-up of bone metastases. Aims: Anthracyclines and taxanes are effective chemotherapeutic agents in the treatment of metastatic breast cancer (MBC) with different mechanisms of action. Therefore, evaluation of the combination of anthracyclines with taxanes was a justifiable approach in the treatment of MBC patients. We assessed the efficacy, toxicity, cost of treatment and QoL of BC patients treated with first-line chemotherapy for metastatic disease with the combination epirubicin and docetaxel. We also evaluated the diagnostic potential of tartrate-resistant acid phosphatase 5b (TRACP 5b) and carboxyterminal telopeptides of type I collagen (ICTP) in the diagnosis of bone metastases in BC and TRACP 5b in PC patients. Results: The combination of epirubicin and docetaxel was effective in this phase II study, but required individual dose adjustment to avoid neutropenic infections, and the use of growth factors to maintain a feasible dose level. The response rate was 54 % (95 % CI 37-71) and the median overall survival (OS) was 26 months. Of the patients, 87 % were treated for infections. The treatment of adverse events required additional use of health resources mainly due to neutropenic infections, thereby raising direct treatment costs by 20 %. Despite adverse events, the global QoL was not significantly compromised during the treatment. Clinically evident acute cardiac toxicity was not observed. The combination of serum TRACP 5b and ICTP was at least equally sensitive and specific in detection of of bone metastases as commonly used total alkaline phosphatise (tALP) in BC patients. In contrast, TRACP 5b was less specific and sensitive than tALP as a marker of skeletal changes in PC patients. Conclusions: Treatment with epirubicin and docetaxel showed high efficacy in first-line chemotherapy of MBC. The relatively high incidence of neutropenic infections requiring hospitalization increased the treatment costs. Despite adverse events, the global QoL of the patients was not significantly compromised. The combination of TRACP 5b and ICTP showed similar activity as tALP in detecting bone metastases in MBC. In contrast, TRACP 5b was less specific and sensitive than tALP as a marker of skeletal changes in PC.Siirretty Doriast