On multifractal analysis and local dimensions of measures

Abstract. This thesis consists of two independent parts. Part I serves as an introduction to multifractal analysis and establishes key concepts in the field, whereas Part II considers a generalisation of multifractal analysis in doubling metric spaces. In multifractal analysis, one is interested in finely analysing the dimensional properties of measures by considering the behaviour of different level sets of the local dimension map. For some measures, these level sets are non-empty and exhibit fractal scaling according to a continuous spectrum of dimensions. These measures are called multifractal measures, and they are the main object of study in this thesis. The continuous spectrum of dimensions is called the multifractal spectrum of the measure, and it contains detailed information about the dimensional properties of the measure. For example, in the case of self-similar measures, the Hausdorff dimension of the underlying iterated function system (the support of the measure) and the Hausdorff dimension of the measure itself are easily obtained from the multifractal spectrum. A celebrated principle in multifractal analysis is the multifractal formalism. With origins in physics literature, more specifically the study of turbulence in fluids, this heuristic principle states that the multifractal spectrum of a measure can be obtained from the Lq-spectrum of the measure via a simple Legendre transform. Usually the aim in the theory of multifractals is to obtain a rigorous notion of the multifractal formalism, and this has already been done for a wide variety of measures. In Part I of the thesis, we refrain to perhaps the most simple non-trivial case, namely the class of strongly separated self-similar measures. Our goal by the end of Part I is to establish the multifractal formalism rigorously for these measures and along the way, we introduce some basic fractal geometry, and develop the theory of multifractals. The main references of Part I are the two excellent textbooks by Falconer, “Fractal Geometry” (1990) and “Techniques in Fractal Geometry” (1997). The second part of the thesis arises from the authors work as a university trainee in the Fractal Geometry Research Group at the Department of Mathematics in the summer of 2020. The discussion revolves mainly around local variants of Lq- and entropy dimensions of measures in doubling metric spaces, and aim of this part is to correct a slight inaccuracy found in an article by Käenmäki, Rajala and Suomala. To do this, we define restricted Lq-dimensions and show that they can be calculated by considering partitions of the underlying space. This simplifies the estimation of the local variants as well and as our main result, we obtain a correct proof for relationships between the local entropy dimensions and Lq-dimensions for (almost) arbitrary measures in doubling metric spaces

Low-Complexity Sub-band Digital Predistortion for Spurious Emission Suppression in Noncontiguous Spectrum Access

Noncontiguous transmission schemes combined with high power-efficiency requirements pose big challenges for radio transmitter and power amplifier (PA) design and implementation. Due to the nonlinear nature of the PA, severe unwanted emissions can occur, which can potentially interfere with neighboring channel signals or even desensitize the own receiver in frequency division duplexing (FDD) transceivers. In this article, to suppress such unwanted emissions, a low-complexity sub-band DPD solution, specifically tailored for spectrally noncontiguous transmission schemes in low-cost devices, is proposed. The proposed technique aims at mitigating only the selected spurious intermodulation distortion components at the PA output, hence allowing for substantially reduced processing complexity compared to classical linearization solutions. Furthermore, novel decorrelation based parameter learning solutions are also proposed and formulated, which offer reduced computing complexity in parameter estimation as well as the ability to track time-varying features adaptively. Comprehensive simulation and RF measurement results are provided, using a commercial LTE-Advanced mobile PA, to evaluate and validate the effectiveness of the proposed solution in real world scenarios. The obtained results demonstrate that highly efficient spurious component suppression can be obtained using the proposed solutions

Clinical efficacy of seasonal influenza vaccination : characteristics of two outbreaks of influenza A(H1N1) in immunocompromised patients

Background: Influenza A(H1N1) causes serious complications in immunocompromised patients. The efficacy of seasonal vaccination in these patients has been questioned. Aim: To describe two outbreaks of influenza A(H1N1) in immunocompromised patients. Methods: Two outbreaks of influenza A(H1N1) occurred in our institution: on the kidney transplant ward in 2014 including patients early after kidney or simultaneous pancreas-kidney transplantation, and on the oncology ward in 2016 including patients receiving chemotherapy for malignant tumours. Factors leading to these outbreaks and the clinical efficacy of seasonal influenza vaccination were analysed. Findings: Altogether 86 patients were exposed to influenza A(H1N1) during the outbreaks, among whom the seasonal influenza vaccination status was unknown in 10. Only three out of 38 vaccinated patients were infected with influenza A(H1N1), compared with 20 out of 38 unvaccinated patients (P = 0.02). The death of one out of 38 vaccinated patients was associated with influenza, compared with seven out of 38 unvaccinated patients (P = 0.06). Shared factors behind the two outbreaks included outdated facilities not designed for the treatment of immunosuppressed patients. Vaccination coverage among patients was low, between 40% and 70% despite vaccination being offered to all patients free of charge. Vaccination coverage of healthcare workers on the transplant ward was low (46%), but, despite high coverage on the oncology ward (92%), the outbreak occurred. Conclusion: Seasonal influenza vaccination was clinically effective with both a reduced risk of influenza infection and a trend towards reduced mortality in these immunocompromised patients. Several possible causes were identified behind these two outbreaks, requiring continuous awareness in healthcare professionals to prevent further outbreaks. (C) 2017 The Healthcare Infection Society. Published by Elsevier Ltd. All rights reserved.Peer reviewe

Cloud Condensation Nuclei properties of model and atmospheric HULIS

Humic like substances (HULIS) have been identified as a major fraction of the organic component of atmospheric aerosols. These large multifunctional compounds of both primary and secondary sources are surface active and water soluble. Hence, it is expected that they could affect activation of organic aerosols into cloud droplets. We have compared the activation of aerosols containing atmospheric HULIS extracted from fresh, aged and pollution particles to activation of size fractionated fulvic acid from an aquatic source (Suwannee River Fulvic Acid), and correlated it to the estimated molecular weight and measured surface tension. A correlation was found between CCN-activation diameter of SRFA fractions and number average molecular weight of the fraction. The lower molecular weight fractions activated at lower critical diameters, which is explained by the greater number of solute species in the droplet with decreasing molecular weight. The three aerosol-extracted HULIS samples activated at lower diameters than any of the size-fractionated or bulk SRFA. The Köhler model was found to account for activation diameters, provided that accurate physico-chemical parameters are known

Normaaliluvut

Tiivistelmä. Tutkielmassa tutustutaan ranskalaisen matemaatikon Émile Borelin vuonna 1909 esittelemiin normaalilukuihin. Normaaliluvut ovat yksinkertaistettuna sellaisia reaalilukuja, joiden desimaaliesityksessä jokainen yhtä pitkä lukusarja esiintyy yhtä suurella tiheydellä. Tutkielmassa annetaan muutamia esimerkkejä normaaliluvuista sekä esitellään Borelin normaalilukulauseelle, jonka mukaan melkein kaikki luvut ovat normaaleja, todennäköisyysteoreettinen todistus

Expression of Dihydropyridine and Ryanodine Receptors in Type IIA Fibers of Rat Skeletal Muscle

In this study, the fiber type specificity of dihydropyridine receptors (DHPRs) and ryanodine receptors (RyRs) in different rat limb muscles was investigated. Western blot and histochemical analyses provided for the first time evidence that the expression of both receptors correlates to a specific myosin heavy chain (MHC) composition. We observed a significant (p=0.01) correlation between DHP as well as Ry receptor density and the expression of MHC IIa (correlation factor r=0.674 and r=0.645, respectively) in one slow-twitch, postural muscle (m. soleus), one mixed, fast-twitch muscle (m. gastrocnemius) and two fast-twitch muscles (m. rectus femoris, m. extensor digitorum longus). The highest DHP and Ry receptor density was found in the white part of m. rectus femoris (0.058±0.0060 and 0.057±0.0158 ODu, respectively). As expected, the highest relative percentage of MHC IIa was also found in the white part of m. rectus femoris (70.0±7.77%). Furthermore, histochemical experiments revealed that the IIA fibers stained most strongly for the fluorophore-conjugated receptor blockers. Our data clearly suggest that the expression of DHPRs and RyRs follows a fiber type-specific pattern, indicating an important role for these proteins in the maintenance of an effective Ca2+ cycle in the fast contracting fiber type IIA