Aspects of atomic decompositions and Bergman projections

The concept of an atomic decomposition was introduced by Coifman and Rochberg (1980) for weighted Bergman spaces on the unit disk. By the Riemann mapping theorem, functions in every simply connected domain in the complex plane have an atomic decomposition. However, a decomposition resulting from a conformal mapping of the unit disk tends to be very implicit and often lacks a clear connection to the geometry of the domain that it has been mapped into. The lattice of points, where the atoms of the decomposition are evaluated, usually follows the geometry of the original domain, but after mapping the domain into another this connection is easily lost and the layout of points becomes seemingly random. In the first article we construct an atomic decomposition directly on a weighted Bergman space on a class of regulated, simply connected domains. The construction uses the geometric properties of the regulated domain, but does not explicitly involve any conformal Riemann map from the unit disk. It is known that the Bergman projection is not bounded on the space L-infinity of bounded measurable functions. Taskinen (2004) introduced the locally convex spaces LV-infinity consisting of measurable and HV-infinity of analytic functions on the unit disk with the latter being a closed subspace of the former. They have the property that the Bergman projection is continuous from LV-infinity onto HV-infinity and, in some sense, the space HV-infinity is the smallest possible substitute to the space H-infinity of analytic functions. In the second article we extend the above result to a smoothly bounded strictly pseudoconvex domain. Here the related reproducing kernels are usually not known explicitly, and thus the proof of continuity of the Bergman projection is based on generalised Forelli-Rudin estimates instead of integral representations. The minimality of the space LV-infinity is shown by using peaking functions first constructed by Bell (1981). Taskinen (2003) showed that on the unit disk the space HV-infinity admits an atomic decomposition. This result is generalised in the third article by constructing an atomic decomposition for the space HV-infinity on a smoothly bounded strictly pseudoconvex domain. In this case every function can be presented as a linear combination of atoms such that the coefficient sequence belongs to a suitable Köthe co-echelon space.Puhtaan matematiikan alaan kuuluva artikkeliväitöskirja käsittelee sekä Coifmanin ja Rochbergin (1980) kehittämää atomidekompositiota että Bergmanin projektion jatkuvuutta tietyissä funktioavaruuksissa. Atomidekompositiossa tietyn alueen kuvaukset voidaan esittää summana yksinkertaisia rakennuspalikoita, atomeja. Klassisessa tapauksessa tämä alue on kompleksitason yksikkökiekko. Minkä tahansa osajoukon atomidekompositio voidaan melko helposti palauttaa klassisen yksikkökiekon tapaukseen Riemannin kuvauslauseen nojalla, mutta näin saatava atomidekompositio ei ole kovin konkreettinen ja sen yhteys alueen geometriaan jää epäselväksi. Ensimmäisessä artikkelissa rakennetaan atomidekompositio suoraan reguloidulle, yhdesti yhtenäiselle alueelle painotetussa Bergman-avaruudessa. Konstruktiossa käytetään alueen geometrisia piirteitä, mutta siinä ei eksplisiittisesti käytetä hyväksi Riemannin kuvausta yksikkökiekolta. On tunnettua, että Bergmanin projektio ei ole jatkuva rajoitettujen mitallisten funktioiden avaruudesta L-ääretön rajoitettujen analyyttisten funktioiden avaruuteen H-ääretön. Taskinen (2004) julkaisi tuloksen lokaalikonvekseista avaruuksista LV-ääretön ja HV-ääretön, jotka ovat tietyssä mielessä pienimmät sellaiset laajennukset avaruuksiin L-ääretön ja H-ääretön, että Bergmanin projektio avaruuksien välillä on jatkuva. Toisessa artikkelissa yllämainitut tulokset yleistetään useamman kompleksimuuttujan tapaukseen pseudokonveksille alueelle. Tällöin aluetta vastaavaa Bergmanin ydintä ei yleensä tunneta eksplisiittisesti, joten jatkuvuuden todistamiseksi käytetään yleistettyä Forelli-Rudin-approksimaatiota. Taskinen (2003) osoitti, että yksikkökiekolle avaruudessa HV-ääretön voidaan rakentaa atomidekompositio. Kolmannessa artikkelissa sama konstruktio tehdään pseudokonveksille alueelle avaruudessa HV-ääretön. Tässä tapauksessa funktioiden dekomposition kerroinjono kuuluu sopivaan Köthen jonoavaruuteen

Aggressiivisen verosuunnittelun teoria ja käytäntö : Tarkastelussa hybridijärjestelyt aggressiivisen verosuunnittelun välineenä

Aggressiivinen verosuunnittelu, verosuunnittelu ja veronkierto ovat herättäneet paljon keskustelua 2000-luvun alusta lähtien. Veropoliittiset aiheet, uudet direktiivit ja haitallisten verokäytänteiden eliminoiminen ovat olleet EU:n lainsäädännön ja talouspoliittisten päätösten keskiössä viime vuosina. Yhtenä huolenaiheena on ollut monikansallisten yritysten aggressiivinen verosuunnittelu, jonka yhteydessä yritykset käyttävät tarkoitusperiltään erilaisia verosuunnittelun metodeja minimoidakseen verotustaan. Tässä tutkielmassa keskitytään monikansallisten yritysten hyödyntämien aggressiiviseksi luokiteltujen verosuunnittelumetodien tutkimiseen. Tarkasteltavia metodeja ovat siirtohinnoittelu, verosopimuskeinottelu sekä velkajärjestelyiden hyödyntäminen ja alikapitalisointi. Lisäksi erityistarkastelussa ovat hybridijärjestelyt aggressiivisen verosuunnittelun välineenä. Tutkielmassa käsitellään myös kansainvälisen verotuksen periaatteita, haasteita ja haitallisen verokilpailun poistamiseen tähtääviä toimenpiteitä. Tutkimustapa on oikeusdogmaattinen, eli tutkielmassa olennaisessa roolissa on lainsäädännön nykytilan arviointi ja tämän hetkinen oikeudentila aggressiivisen verosuunnittelun aihepiiriin liittyen. Tutkimuksessa selvitetään, mitä on aggressiivinen verosuunnittelu teoriassa ja käytännössä ja pyritään hahmottamaan rajaa aggressiivisen verosuunnittelun ja veronkierron välillä. Teorian tarkastelussa tutkitaan aggressiivisen verosuunnittelun käsitettä ja sen suhdetta lähikäsitteisiin, verosuunnitteluun ja veronkiertoon. Rajaa pyritään hahmottamaan veronkiertoa käsittelevien oikeustapausten kautta ja tutkimustuloksista voidaan huomata, että raja aggressiivisen verosuunnittelun ja veronkierron välillä on erittäin häilyvä ja riippuu olennaisesti verosuunnittelujärjestelyiden liiketoiminnallisista perusteista ja niiden perusteluista sekä verovelvollisen argumentoinnista. Tutkimuksen viimeinen osa keskittyy hybridijärjestelyihin aggressiivisen verosuunnittelun välineenä. Hybridijärjestelyt ovat olleet viime aikoina yksi eniten huomiota saaneista aggressiivisen verosuunnittelun ja haitallisen verojen minimoinnin muodoista. Vuoden 2020 alusta voimaan tullut laki eräiden rajat ylittävien hybridijärjestelyjen verotuksesta on rajoittanut hybridien kautta saavutettavia veroetuja. Tutkielmassa avataan hybridien muotoja aggressiivisen verosuunnittelun välineenä ja hybridejä tarkastellaan hybridilain uusien säännösten kautta. Tutkimustuloksista selviää, että aggressiivisen verosuunnittelun vastaiset toimet, kuten BEPS-hanke ja uusi lainsäädäntötyö ovat rajoittaneet huomattavasti aggressiivisen verosuunnittelun ja etenkin hybridijärjestelyjen hyödyntämistä verotuksen minimoinnissa

Thalamic Atrophy Predicts 5-Year Disability Progression in Multiple Sclerosis

Purpose:Thalamus is among the first brain regions to become atrophic in multiple sclerosis (MS). We studied whether thalamic atrophy predicts disability progression at 5 years in a cohort of Finnish MS patients. Methods:Global and regional brain volumes were measured from 24 newly diagnosed relapsing MS (RMS) patients 6 months after initiation of therapy and from 36 secondary progressive MS (SPMS) patients. The patients were divided into groups based on baseline whole brain parenchymal (BP) and thalamic atrophy. Standard scores (zscores) were computed by comparing individual brain volumes with healthy controls. Azscore cutoff of -1.96 was applied to separate atrophic from normal brain volumes. The Expanded Disability Status Scale (EDSS), brain magnetic resonance imaging (MRI) findings, and relapses were assessed at baseline and at 2 years and EDSS progression at 5 years. Results:Baseline thalamus volume predicted disability in 5 years in a logistic regression model (p= 0.031). At 5 years, EDSS was same or better in 12 of 18 patients with no brain atrophy at baseline but only in 5 of 18 patients with isolated thalamic atrophy [odds ratio (OR) (95% CI) = 5.2 (1.25, 21.57)]. The patients with isolated thalamic atrophy had more escalations of disease-modifying therapies during follow-up. Conclusion:Patients with thalamic atrophy at baseline were at a higher risk for 5-year EDSS increase than patients with no identified brain atrophy. Brain volume measurement at a single time point could help predict disability progression in MS and complement clinical and routine MRI evaluation in therapeutic decision-making.</div

Broadband photoacoustic spectroscopy of 14CH4 with a high-power mid-infrared optical frequency comb

We report a photoacoustic spectroscopy setup with a high-power mid-infrared frequency comb as the light source. The setup is used in broadband spectroscopy of radiocarbon methane. Owing to the high sensitivity of a cantilever-enhanced photoacoustic cell and the high-power light source, we can reach a detection limit below 100 ppb in a broadband measurement with a sample volume of only a few milliliters. The first infrared spectrum of 14CH4 is reported and given a preliminary assignment. The results lay a foundation for the development of optical detection systems for radiocarbon methane.We report a photoacoustic spectroscopy setup with a high-power mid-infrared frequency comb as the light source. The setup is used in broadband spectroscopy of radiocarbon methane. Owing to the high sensitivity of a cantilever-enhanced photoacoustic cell and the high-power light source, we can reach a detection limit below 100 ppb in a broadband measurement with a sample volume of only a few milliliters. The first infrared spectrum of (CH4)-C-14 is reported and given a preliminary assignment. The results lay a foundation for the development of optical detection systems for radiocarbon methane. (c) 2019 Optical Society of AmericaPeer reviewe

Materials Science and Technology - Nuclear Materials, Advanced Course - Kon-67.5100 Postgraduate Seminar on Engineering Materials - Seminar papers 8 October, 2015

The Engineering materials research group of Department of Engineering Design and Production of Aalto University arranged a postgraduate course on nuclear materials. The course consisted of three day long lecture session given in April 20-22, 2015. Lectures were given by professionals from nuclear power related research institutes (Aalto and VTT), nuclear industry and authority. The course also included a seminar session held October 8, 2015. The seminar session was targeted to postgraduate students, who prepared articles from their field of expertise. This proceeding is the collection of these seminar articles

Thalamic Atrophy Without Whole Brain Atrophy Is Associated With Absence of 2-Year NEDA in Multiple Sclerosis

Purpose: To study which brain volume measures best differentiate early relapsing MS (RMS) and secondary progressive MS (SPMS) patients and correlate with disability and cognition. To test whether isolated thalamic atrophy at study baseline correlates with NEDA (no evidence of disease activity) at 2 years.Methods: Total and regional brain volumes were measured from 24 newly diagnosed RMS patients 6 months after initiation of therapy and 2 years thereafter, and in 36 SPMS patients. Volumes were measured by SIENAX and cNeuro. The patients were divided into subgroups based on whole brain parenchyma (BP) and thalamic atrophy at baseline. Standard scores (z-scores) were computed by comparing individual brain volumes against healthy controls. A z-score cut-off of −1.96 was applied to separate atrophic from normal brain volumes. The Expanded Disability Status Scale (EDSS) and Symbol Digit Modalities Test (SDMT) were assessed at baseline and at 2 years. Differences in achieving NEDA-3, NEDA-4, EDSS progression, and SDMT change were analyzed between patients with no thalamic or BP atrophy and in patients with isolated thalamic atrophy at baseline.Results: At baseline, 7 SPMS and 12 RMS patients had no brain atrophy, 8 SPMS and 10 RMS patients had isolated thalamic atrophy and 2 RMS and 20 SPMS patients had both BP and thalamic atrophy. NEDA-3 was reached in 11/19 patients with no brain atrophy but only in 2/16 patients with isolated thalamic atrophy (p = 0.012). NEDA-4 was reached in 7/19 patients with no brain atrophy and in 1/16 of the patients with isolated thalamic atrophy (p = 0.047). At 2 years, EDSS was same or better in 16/19 patients with no brain atrophy but only in 5/17 patients with isolated thalamic atrophy (p = 0.002). There was no significant difference in the EDSS, relapses or SDMT between patients with isolated thalamic atrophy and no atrophy at baseline.Conclusion: Patients with isolated thalamic atrophy were at a higher risk for not reaching 2-year NEDA-3 and for EDSS increase than patients with no identified brain atrophy. The groups were clinically indistinguishable. A single measurement of thalamic and whole brain atrophy could help identify patients needing most effective therapies from early on

Cognitive and Neuropsychiatric Symptom Differences in Early Stages of Alzheimer's Disease: Kuopio ALSOVA Study

Background/Aim: Alzheimer’s disease (AD) causes impairment in memory and other cognitive functions as well as neuropsychiatric symptoms and limitations in the activities of daily living (ADL). The aim of this study was to examine whether demographic variables, dementia severity, ADL and neuropsychiatric symptoms are associated with cognition in very mild or mild AD. Methods: We analyzed the baseline data of 236 patients with very mild or mild AD participating in a prospective AD follow-up study (ALSOVA). The Consortium to Establish a Registry for Alzheimer’s Disease neuropsychological battery total score was used in the evaluation of the global cognitive performance. Results: Cognition was associated with dementia severity and ADL but not with neuropsychiatric symptoms. ADL functions were associated with both cognitive performance and neuropsychiatric symptoms. Conclusion: Even patients with very mild or mild AD may exhibit neuropsychiatric symptoms not related to cognitive impairment. The results of this study emphasize the importance of taking a multidimensional approach to the diagnostic and prognostic evaluation of AD patients already in the early stages of the disease

Dietary changes and cognition over 2 years within a multidomain intervention trial-The Finnish Geriatric Intervention Study to Prevent Cognitive Impairment and Disability (FINGER)

Introduction: Association between healthy diet and better cognition is well established, but evidence is limited to evaluate the effect of dietary changes adopted in older age. Methods: We investigated the role of dietary changes in the Finnish Geriatric Intervention Study to Prevent Cognitive Impairment and Disability (FINGER) with 1260 at-risk participants (60-77 years) who were randomized to intensive multidomain intervention (including dietary counseling) or regular health advice for 2 years. Parallel process latent growth curves of adherence to dietary recommendations and cognitive performance were analyzed. Results: Adherence to healthy diet at baseline predicted improvement in global cognition, regardless of intervention allocation (P = .003). Dietary improvement was associated with beneficial changes in executive function, especially in the intervention group (P = .008; P = .051 for groups combined). Discussion: Dietary changes initiated during the intervention were related to changes in executive function in 2 years. Long-term diet appeared more influential for global cognition. (C) 2018 The Authors. Published by Elsevier Inc.Peer reviewe

Field measurement intercomparison - Field measurements of dissolved oxygen concentration

In the framework of the European Metrology Research Programme (EMRP) project ENV05 OCEAN (Metrology for ocean salinity and acidity), the dissolved oxygen field (in situ) intercomparison (FieldOxy 2014) test was organized onboard R/V Aranda on April 23, 2014 in the Gulf of Finland. The aim of the intercomparison was to enable the participants to assess their performance in measuring dissolved oxygen concentration in seawater under field conditions. The intercomparison measurement was organized jointly by the Finnish Environment Institute (Proftest SYKE. Envical SYKE) and University of Tartu. Total of 21 participants from 10 institutes in Finland, Estonia, France, Germany and Sweden participated in the intercomparison. Totally, 13-18 oxygen sensors were tested depending of the test depth. Additionally, six Winkler titrimetric setups participated in the intercomparison. The metrologically traceable Winkler titration result (the assigned value) was measured by the Winkler setup of University of Tartu onboard R/V Aranda. In total, 88 % of the results were satisfactory when total deviation of 8 % from the assigned values were accepted. Only three results were questionable and five results were unsatisfactory. A possible reason for several of the unsatisfactory results might be problems with calibration of electrochemical oxygen sensors. The movement of the water during the PT may have been insufficient for the electrochemical sensors, which may have resulted biased measurement results. Overall the share of satisfactory results was very good

Associations between Prospective and Retrospective Subjective Memory Complaints and Neuropsychological Performance in Older Adults : The Finger Study

Objectives: Subjective memory complaints (SMCs) are among the key concerns in the elderly, but their role in detecting objective cognitive problems is unclear. The aim of this study was to clarify the association between SMCs (both prospective and retrospective memory complaints) and neuropsychological test performance in older adults at risk of cognitive decline. Methods: This investigation is part of the FINGER project, a multicenter randomized controlled trial aiming at preventing cognitive decline in high-risk individuals. The cognitive assessment of participants was conducted at baseline using a modified neuropsychological test battery (NTB). SMCs were evaluated with the Prospective and Retrospective Memory Questionnaire (PRMQ) in a sub-sample of 560 participants (mean age, 69.9 years). Results: Having more prospective SMCs was associated with slower processing speed, but not with other NTB domains. Retrospective SMCs were linked to poorer function on NTB total score, processing speed, and memory. Executive function domain was not associated with any PRMQ ratings. Depressive symptoms and poor quality of life diluted the observed associations for NTB total score and memory. However, the association between PRMQ and processing speed remained even after full adjustments. Conclusions: Our results indicate that self-reported memory problems, measured with PRMQ, are associated with objectively measured cognitive performance. Such complaints in healthy elderly people also seem to reflect reduced mental tempo, rather than memory deficits. Slowing of processing speed may thus be negatively related to memory self-efficacy. It is also important to consider affective factors among those who report memory problems.Peer reviewe