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Siilinjärvi mine in Finland is the only mine within the European Union producing phosphate rock, a critical raw material for the European Union. With the current mining plans, the production is estimated to continue until 2035. The extent of the ore deposit and new locations for open pits are currently being investigated to ensure continuation of the mining operations also after 2035. The Siilinjärvi carbonatite-glimmerite deposit has been intruded by multiple waste-rock diabase dykes crosscutting the deposit and by a tonalite-diorite intrusion, creating a complex geological setting. To study the depth and lateral extent of the deposit, the diabase dykes, tonalite- diorite, major zones of weakness and the geophysical anomalies related to these features, active-source 2D reflection seismic, Ground Penetrating Radar (GPR) and magnetic surveys were conducted at the Siilinjärvi mine site in fall 2018 as part of the H2020 Smart Exploration project. Understanding the locations of the waste rocks and fracture and shear zones is crucial for mine planning and optimising the production prognoses. The interest of this study is in particular on imaging the sub-horizontal diabase dykes, whose locations and continuation are harder to predict. The focus area of this study is in the southern end of the Särkijärvi pit and the area just south of the pit, where the well-known geology of the pit can be used to constrain the interpretation. Processing of the reflection seismic data focused especially on the static corrections and the methods used to improve the signal-to-noise ratio. This was done so that the processed data could serve as a reference for new processing methods, focused on these aspects, developed within the Smart Exploration project and planned to be tested with the Siilinjärvi data. The static corrections were constrained by the limited number of first-break picks clear enough for picking from the data. In addition to the bandpass filtering, suppressing the S-wave arrivals was found to be crucial for increasing the signal-to-noise ratio, particularly in the near subsurface which is the main interest area of this study. The GPR and magnetic data were processed with standard processing workflows. The lateral and depth extent of the Siilinjärvi carbonatite-glimmerite deposit, the large-scale sub-horizontal waste- rock dykes and the major zones of weakness are imaged with the active-source reflection seismic data. The ore deposit is associated with a complex reflectivity pattern due to the intruded diabase dykes and tonalite-diorite, and the fracture and shear zones. The interpreted diabase dykes correlate with a large-scale sub-horizontal waste-rock dyke model created from the production drilling data as part of the Smart Exploration project, supporting the continuation of the sub-horizontal diabase dykes south of the pit. With GPR data, the smaller- scale sub-horizontal dykes within the shallow subsurface (<30 m) are imaged. The GPR data correlates with a detailed waste-rock dyke model created as part of the Smart Exploration project from the southern end of the Särkijärvi pit based on geological mapping, GigaPan images and a 3D photogrammetry model. The reflection seismic, GPR and magnetic data have very different scales and these different data are suitable for different purposes in mineral exploration and mine planning at Siilinjärvi. The carbonatite-glimmerite ore is associated with elevated magnetic total field values and at a larger scale the deposit could possibly be followed with magnetic surveys. With reflection seismic method, the large geological structures can be imaged at depth, and the data could be used for detailed planning of a new open pit. The higher resolution GPR measurements could then be implemented in the operating phase of the mine in a more routine manner to aid creation of reliable production prognoses.

Peatlands are complex ecosystems that not only respond to external changes but also influence their environment. Permafrost peatlands have an important role in the global carbon (C) cycle as they store about 200 Pg of C. As permafrost thaws this C can be released either as methane (CH4) or carbon dioxide (CO2). In addition to these peatlands also emit nitrous oxide (N2O). Climate warming may change this sink-source balance of peatlands. Hydrological conditions are an important factor in peatland C dynamics. As permafrost thaws it can shift these ecosystems towards wetter or dryer conditions. Peat decomposition under dry conditions can have a strong positive feedback to climate change due CO2 emissions. Though wetter conditions can increase CH4 emissions. Through topography and hydrology, permafrost also affects vegetation dynamics. In this thesis I am examining peat profiles collected from two subarctic permafrost peatlands located in Kevo, Finland and Karlebotn, Norway. The profiles included an un-frozen active layer profile and a permafrost sample collected from inside a palsa mound. These samples were analysed for vegetation composition and peat properties (C and N content, C/N ratio and bulk density), they were also 14C dated and incubated. The purpose was to simulate a warmer climate to which these ecosystems will be exposed to in the future and observe how they will respond. The observations focused on the three most common GHGs of peatlands, CH4, CO2 and N2O. The permafrost samples showed potential for CH4 and CO2 emissions, whereas the active layer only emitted CO2. The CH4 emissions were interpreted to represent old CH4, whereas the CO2 was interpreted to be produced by the peat.

This thesis investigates how the Lorenz model state sensitivity appears on the prior state error of the Extended Kalman Filter (EKF) process. The Lorenz model is a well-known ordinary differential equation system. Its simple nonlinear equations show that a chaotic system, like the atmosphere, does not have a single deterministic solution. Edward N. Lorenz also showed that the predictability of the state depends on the flow itself, and numerical weather prediction models, therefore, cannot always be trusted equally. For this reason, when computing a forecast, it is necessary to consider both the model and observations with their weight uncertainties to get the most probabilistic analysis state. The EKF is an algorithm that provides a powerful data assimilation method for nonlinear systems. Its operating principle is based on the evolution of prior state (model evolution) and observation updates. Each observation update calculates the most likely state based on the prior state and observation errors. The process continues from the new analysis state by evolving the model until the next observation update. In this study, I made the EKF utilizing the Lorenz model and sent ensembles from the analysis states on the Lorenz attractor. I calculated the variance of evolved ensembles and compared them to the magnitude of prior state error at the observation update time levels. The results showed that these two parameters are positively correlated. For the 18-timestep observation interval, Pearson’s correlation coefficient was 0.850, which indicates a very high correlation. Therefore, it can be concluded that when the prior state error is small, the ensemble on the Lorenz attractor indicates good predictability (i.e., dispersion of ensemble members is small) and vice versa.

As privacy gains consensus in the field of machine learning, numerous algorithms, such as differentially private stochastic gradient descent (DPSGD), have emerged to ensure privacy guarantees. Concurrently, fairness is garnering increasing attention, prompting research aimed at achieving fairness within the constraints of differential privacy. This thesis delves into algorithms designed to enhance fairness in the realm of differentially private deep learning and explores their mechanisms. It examines the role of normalization, a technique applied to these algorithms in practice, to elucidate its impact on fairness. Additionally, this thesis formalizes a hyperparameter tuning protocol to accurately assess the performance of these algorithms. Experiments across various datasets and neural network architectures were conducted to test our hypotheses under this tuning protocol. The decoupling of hyperparameters, allowing each to independently control specific properties of the algorithm, has proven to enhance performance. However, certain mechanisms, such as discarding samples with large norms and allowing unbounded hyperparameter adaptation, may significantly compromise fairness. Our experiments also confirm the critical role of hyperparameter values in influencing fairness, emphasizing the necessity of precise tuning to ensure equitable outcomes. Additionally, we observed differential convergence rates across algorithms, which affect the number of trials needed to identify optimal hyperparameter settings. This thesis aims to offer detailed perspectives on understanding fairness in differentially private deep learning and provides insights into designing algorithms that can more effectively enhance fairness.

This thesis is an exploration of food delivery couriers’ everyday experiences, practices and sensemaking processes through a posthumanist and sociomaterial approach that highlights the idea that technology and society are mutually shaping one another, and that considers the agency of non-human entities such as algorithms, transcendental. Moreover, by adopting a sociomaterial perspective, we can have a better understanding of how social and technological systems, as well as human and non-human beings, are interrelated, how they shape, and are shaped by one another. This work’s aims are threefold: First, it explores couriers’ experiences at work and describes their daily practices in order to understand the enactment of agency from a sociomaterial and post-humanist philosophical tradition. Second, it explores the material implications of algorithmic management in couriers’ lives, and finally, it explores the way couriers perform their work in context, both through the tethered geographical elements of the city, and amidst the platform’s multiple entanglements and spatiotemporal arrangements. The research design of this thesis has a strong qualitative research methodology, including methods such as walk-along interviews, semi-structured interviews, ethnographic reporting techniques, and the author’s 3-month work experience as a food delivery courier. The findings of this work suggest that we should acknowledge the platform as a constant becoming entity where couriers’ sensemaking processes are produced at the intersection of their experience of the city and their relationship with the managing algorithms of the platform. A performative sociomaterial practice that constantly produces knowledge that is used by couriers to negotiate their participation in the platform. This thesis expands previous understandings of digital workers’ experiences of algorithmic management by incorporating a sociomaterial and performative approach in the analysis of couriers’ sensemaking processes. Furthermore, by considering the relationships and interactions between human and nonhuman agencies in the food delivery platform industry, this work contributes not only to the understanding of agency within digital platforms but also to a broader understanding of agency in our increasingly digitally mediated societies.

This thesis introduces the theory of conformal welding and shows that every quasisymmetric function is a welding homeomorphism. Conformal weldings appear naturally in Teichmüller theory when we consider the conditions under which two Riemann surfaces can be joined together. In the second chapter we investigate the properties of quasisymmetric and quasiconformal functions and derive various inequalities for them. Later in the chapter we define the so-called Beurlin-Ahlfors extension to quasisymmetric functions and show that this function is in fact quasiconformal. In the third chapter, we begin by introducing the fundamentals of Sobolev spaces and present some theorems that allow us to study the properties of compositions of quasiconformal functions. We prove Stoilow's factorization theorem and use it to show that the solution to Beltrami's equation can naturally be normalized so that the solution is unique. Using Stoilow's factorization and a few other lemmas and theorems we derived earlier, we finally show the main result of the thesis that is, we show that every quasisymmetric function is a welding homeomorphism. In the last chapter, we answer the question of whether perhaps all increasing homeomorphisms are welding homeomorphisms. The answer is no and this is shown by the counterexample invented by Bishop.

Eutrophication is a global challenge, where chemical processes in bottom sediments play a key role. Yet, eutrophication science lacks understanding of the role of terrestrial matter on the processes that mobilize or immobilize phosphorus, a central algal nutrient, in sediments. Eroded field soil is carried into sea by runoff and soil is settled on the bottom and then buried. During burial the sediment microbial processes change the redox-conditions which affect the chemistry of settled soil. Here, methods were developed to follow the evolution of the chemical state of soil during burial with iron K-edge X-ray absorption near edge spectroscopy, with a novel home-laboratory based spectrometer. The chemical state of soil, and especially the chemistry of iron is linked to the release and binding of phosphorus in bottom sediments. The chemical path of field soil was simulated with anaerobic incubation, where organic carbon and sulfates were added to represent various sea bottom conditions. In order to measure the spectra of soil-water mixtures, a sample preparation method was developed, where the sample is gellified in both aerobic and anaerobic conditions. The gel makes the suspension uniform and homogeneous. We also developed a sample environment for anaerobic measurements. The measured spectra were compared with spectra obtained from reference iron compounds and the iron species were quantified. The sulfate and addition of organic carbon enhanced the formation of iron sulfides, causing iron bound phosphorus to be released to water. As expected, the release of phosphorus was higher in anaerobic conditions than in aerobic conditions. The addition of organic carbon and sulfate enhanced the formation of iron sulfides, causing iron bound phosphorus to be released to the aquatic system. The results shed light on iron chemistry in anoxic sediments, which can be used in management of eutrophication.

Pedestrian streets have been a recognized method of revitalizing inner-city trade for decades. At first many shop owners are sceptical to what changes a pedestrianizations brings about, but experience shows pedestrian streets have been successful and raises the sales of businesses located on it. However, certain businesses are not favoured by a pedestrianization while others can gain a lot from it. This master's thesis examines the commercial structure of pedestrian streets in order to find out what businesses are located on pedestrian streets. The results are compared with the commercial structure of the shopping district in which the pedestrian street is located. In this way the differences in the commercial structure is found out. The thesis also looks into how frequent chain stores are on pedestrian streets and in shopping districts. The research material was gathered using a commercial inventory in three Finnish towns: Ekenäs, Kerava and Pori. The material was classified into categories and the results drawn onto a map as well as analyzed by basic statistical methods. The results are separated for pedestrian streets, shopping centres and other locations and put into the overall categories of retailers, restaurants and other services. The results show that there are clear differences in commercial structure when comparing pedestrian streets with the surrounding shopping district. Pedestrian streets have much more retailers, especially fashion shops, than has other locations. Shopping centres show a similar commercial structure to pedestrian streets, while the rest of the shopping district has fewer retailers and more service businesses. Restaurants are more evenly spread out over the shopping district as a whole. The results for chain stores are ambiguous. There are some hints that they are more common on pedestrian streets, especially in bigger towns. The results gained are however not sufficient to make far reaching conclusions. During the last 10–15 years pedestrian streets in Finland has become more dominated by restaurants on the expense of other services, while the number of retailers has remained the same. Finnish pedestrian streets still show a different commercial structure to pedestrian streets in Scandinavia that have more retailers and fewer services than their Finnish counterparts. The case specific results show a lot of local variance. Local factors are in many cases stronger than general theories of shop localization on pedestrian streets. In general the findings support the theoretical framework. The results give more exact information on the commercial structure of pedestrian streets and shopping districts and what impacts on this structure.

In this thesis we give self-sufficient introduction to the complex Langevin method, which is a promising simulation method for the quantum field theories with finite chemical potential. We begin by revising the the stochastic methods needed for mathematical understanding of Langevin equation. This revision is done trough the examples of a Brownian motion. After the stochastical preliminaries are deled with, we also give a short introduction to quantum field theories on the lattice and with both finite temperature and chemical potential. We show that introduction of chemical potential can cause a sign problem, which can yield traditional Monte Carlo simulations non usable for this problem. We notice a similarity of form between the stochastic path integrals and the Feynman path integrals. We use this similarity to define a stochastic quantization method, that lets us to use stochastic evolution equations to find the correlation function in quantum field theory. This method is then expanded for complex actions that arise from the use of the finite chemical potential in the quantum field theory. We discuss the possible problems with this expansion and deduct that there is no complete mathematical understanding of complex Langevin equation. After all these theoretical considerations we do our own simulations to inspect if this model works. We find out, that for the U(1) one link model and for the SU(3) spin model, the method works as long as we are not using imaginary noise. Unfortunately we also find out that three dimensional XY-model converges to wrong results. We find no reason for this behavior.

The history of set theory is a long and winding road. From its inception, set theory has grown to become its own flourishing branch of mathematics with a pivotal role in the attempt to establish a foundation for all of mathematics and as such its influence is felt in every corner of the mathematical world as it exists today. This foundational effort, in the form of establishing new set theoretic axioms, is still ongoing and a big driving force behind this movement is the many unanswered questions that remain out of reach of the set theory of today. One of the most well known of these open questions is that of the Continuum Hypothesis. In this thesis we will first dive into the history of set theory, starting by looking at the role that infinity has played in the history of mathematics. From the ancients Greeks to Cantor who finally brings infinity into mathematics in a major way through set theory. We look at the development of a foundation for mathematics through the axiomatization of set theory and then focus on the role the Continuum Hypothesis played in this effort, leading up to Gödel’s and Cohen’s proofs that showed its independence and beyond that to the research being done today. We then turn our attention to potential candidates for new axioms that would solve the Continuum Hypothesis. First we take a closer look at Gödel’s constructible universe, in which the Continuum Hypothesis is true. We look at how it is built and consider the potential results of accepting the corresponding Axiom of Constructibility as a new axiom of set theory. In the final section we examine Chris Freiling’s proposed Axioms of Symmetry, which imply the negation of the Continuum Hypothesis. After looking at Freiling’s constructions in detail we consider the arguments for and against accepting them as new axioms.