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Tutkielman tavoitteena oli selvittää, minkälaisia virheitä lukiolaiset tekevät kertolaskusäännön tehtävissä sekä tutkia, tunnistavatko he toisistaan riippuvat ja riippumattomat tapahtumat. Aihetta on tärkeä tutkia, sillä kertolaskusääntö on yksi todennäköisyyden laskusäännöistä ja luo siten perustan todennäköisyyksien laskuille. Tutkielma alkaa teoriaosuudella, jossa ensiksi käydään läpi todennäköisyyslaskennan teoriaa ja tämän jälkeen virheiden sekä virhekäsitysten teoriaa. Teoriaosuuden jälkeen esitellään lyhyesti pitkän matematiikan ylioppilaskoe. Tutkimuksessa käydään läpi viisi pitkän matematiikan ylioppilaskokeen tehtävää ja ne analysoidaan. Työn lopuksi esitellään tehtäväpaketti tukemaan kertolaskusäännön opiskelua. Tutkimustuloksista havaittiin, että yleisimmät kertolaskusäännön virheet johtuivat vaikeuksista erottaa toisistaan riippuvat ja riippumattomat tapahtumat toisistaan. Virheistä noin 14% johtui tästä. Toinen yleinen virhe, mikä tuloksista nousi esille, oli sekaannukset kerto- ja yhteenlaskusäännön välillä. Virheistä noin 9% johtui tästä. Opettajan on tärkeä tiedostaa nämä yleiset virhetyypit, jotta voi osaltaan ennaltaehkäistä niiden syntymistä.

This thesis delves into the complex world of multi-model database migration, investigating its theoretical foundations, strategic implementation, and implications for modern data management. The research utilizes a mixed-methods approach, combining quantitative benchmarking tests with qualitative insights from industry practitioners to give a comprehensive knowledge of the migration process. The importance of smart migration techniques, as well as the crucial function of schema mapping in assuring data consistency are highlighted as key results. Success examples from a variety of industries highlight the practical relevance and advantages of multi-model database migration, while implications for theoretical advances and practical issues in organizational contexts are discussed. The strategic implementation framework leads businesses via rigorous project planning, schema mapping, and iterative optimization, stressing the joint efforts of multiple stakeholders. Future concerns include the influence of developing technologies, the dynamic interaction between migration and data security, and industry-specific subtleties impacting migration tactics as the technological environment advances. The synthesis of ideas leads to a common knowledge base, defining the data management strategy discourse. This investigation serves as a road map for informed decision-making, iterative optimization, and continual adaptation in database management, developing a better knowledge of multi-model database migration in the context of modern data ecosystems.

There has been a major decreasing trend in the amount of sea ice in the Arctic since the 1990s. The Arctic amplification (AA) warms the Arctic climate as a result of the global warming, strengthened by the ice albedo feedback loop. The ice albedo feedback loop is caused by melting of snow and ice surfaces. Melting of snow and ice causes changes to the surface albedo, which is a measure of the amount of incident solar radiation that is reflected. Melting snow and ice surface types and revealed open water or terrain have significantly lower albedo than the original snow and ice surfaces. Therefore more radiation is absorbed, which has a warming effect. CLARA-A3 dataset is analyzed in this thesis. Surface albedo (SAL) and top of atmosphere (ToA) albedo values are compared. Data from June and July of the years 2012 and 2014 are analyzed. The objective is to check the consistency of these data records. The surface albedo values are also modelled with the Simplified Model for Atmospheric Correction (SMAC) to further validate the data. The relationship between SAL and ToA is also studied. This is achieved by analysing snow and ice optical properties, interaction of solar radiation with Earth’s atmosphere and the effect of illumination and viewing geometry. The results of data analysis indicate consistency between the observed values for SAL and ToA albedo differences within the observed period. The results are also in line with predictions made based on previous studies on the seasonal trends in the Arctic albedo. Furthermore results modelled with SMAC show dependency with the observed results and thereby validate the data. However data from June 2012 and July 2014 are unfortunately contaminated, which means that there are less usable data and therefore of reduced accuracy. Data analysis conducted for a larger SAL and ToA dataset would be needed to provide a basis for studying the decadal and seasonal trend of the Arctic SAL and ToA albedo difference. The whole melting season beginning in March and ending in September is important to study to better understand seasonal variability and trends as well as decadal trends in the Arctic.

Quantum computing has an enormous potential in machine learning, where problems can quickly scale to be intractable for classical computation. Quantum machine learning is research area that combines the interplay of ideas from quantum computing and machine learning. Powerful and useful machine learning is dependent on having large-scale datasets used to train the models to be able to solve real-life problems. Currently, quantum machine learning lacks a plethora of large-scale quantum datasets required to further develop the models and test the quantum machine learning algorithms. Lack of large datasets is currently limiting the quantum advantage in the field of quantum machine learning. In this thesis, the concept of quantum data and different types of applied quantum datasets used to develop quantum machine learning models is studied. The research methodology is based on a systematic and comparative literature review of the state of the art articles in quantum computing and quantum machine learning in the recent years. We classify datasets into inherent and non-inherent quantum data based on the nature of the data. The preliminary literature review addresses patterns in the applied quantum machine learning. Testing and benchmarking QML models primarily uses non-inherent quantum data, or classical data encoded into the quantum system, while separate research is focused on generating inherent quantum datasets.

This thesis discusses short-term parking pricing in the context of Finnish shopping centre parking halls. The focus is on one shopping centre located in Helsinki where parking fees are high and there is a constant need for raising the prices. Therefore, it is important to have a strategy that maximises parking hall income without compromising the customers' interest. If the prices are too high, customers will choose to park elsewhere or reduce their parking in private parking halls. There is a lot of competition with off-street parking competing against on-street parking and access parking, not to mention other parking halls. The main goal of this thesis is to raise problems with parking pricing and discuss how to find the most beneficial pricing method. To achieve this, this thesis project conducted an analysis on one Finnish shopping centre parking hall data. This data was analysed to discover the average behaviour of the parkers and how the raised parking fees affect both the parker numbers and the income of the parking hall. In addition, several pricing strategies from literature and real-life examples were discussed and evaluated, and later combined with the analysis results. The results showed that there are some similarities with results from literature but there were some surprising outcomes too. It seems that higher average hourly prices are correlated with longer stays, but still the parkers who tend to park longer have more inelastic parking habits than those who park for shorter durations. The calculated price elasticity of demand values show that compared to other parking halls, parking is on average more elastic in the analysed parking hall. This further emphasises the importance of milder price raises at least for the shorter parking durations. Moreover, there are noticeable but explainable characteristics in parker behaviour. Most of the parkers prefer to park for under one hour to take advantage of the first parking hour being free. This leads to profit losses in both the shopping centre and parking hall income. Therefore, a dynamic pricing strategy is suggested as one pricing option, since it adjusts the prices automatically based on occupancy rates. Although there are some challenges with this particular method, in the long run it could turn out to be the most beneficial for both the parking hall owners and the parkers. To conclude, choosing a suitable pricing strategy and model for a parking hall is crucial and the decisions should be based on findings from data.

Climate change and urbanization are among the largest environmental challenges facing the world today. The role of vegetation in urban environments is substantial from the perspectives of climate, ecology, and human-wellbeing. Plant phenology plays a key role in the functionality and feedbacks related to these ecosystem services and the characteristics of urban phenology can considerably differ from rural areas due to Urban Heat Island (UHI), vegetation composition, hydrological changes, light pollution, and air pollutants. Several previous studies using coarse resolution remote sensing data have reported longer Growing Season Length (GSL) in urban areas compared to their rural counterpart and the UHI effect is generally considered as the main driver for these differences. However, urban phenology studies have not been implemented on a regional European scale and high-resolution remote sensing data is needed to understand the characteristics of heterogenous and sparse urban vegetation. Therefore, the objectives of this study were (1) to analyse GSL along the urban-rural gradients in 38 European capital cities using Copernicus HR-VPP phenology dataset on a 10-meter spatial resolution, (2) to analyse GSL along the urban-rural gradient between the 38 European capital cities, and (3) to find out how Land Surface Temperature (LST), land cover and dominant leaf type influence on the GSL variation. The GSL pattern along the urban-rural gradients were classified into six categories based on linear and quadratic fits. The results showed that the GSL along the gradient in European capital cities is highly variate. It shortens along the gradient in 8 cities and the urban GSL is longer in 26 cities when compared to the overall surrounding zone, contradictory to the general outcome of previous studies. The influence of LST, land cover and dominant leaf type was examined with a Geographically Weighted Regression (GWR) model which considers the spatial nonstationary of variables. The final GWR model variables included LST, the proportion of urban land cover above 30 % of sealed surface and the proportion of broadleaved trees which all had spatially varying and nonlinear influences on GSL. These results and the variate gradient patterns suggest that despite the significance of LST, GSL variation along the urban-rural gradient is more driven by changes in land cover and vegetation characteristics. Spatial modelling techniques are needed to understand these locally varying relationships. There are several potential methodological and site-related explanations for the divergent findings of this and previous studies. The key methodological difference is the better spatial resolution which improves the accuracy of GSL detection, agricultural land cover masking and urban area definition. Site-related explanations include the different background climate and vegetation types, urban vegetation composition and species, and urbanization intensity. In addition, several heatwaves took place during the study period potentially contributing to the early senescence of urban vegetation. This study highlights the need for a high-resolution remote sensing data when analysing urban vegetation phenology and provides new information about the complex dynamics of urban phenology in general level and in European capital cities. These results can be beneficial for developing sustainable cities where urban vegetation plays a key role in adapting and mitigating climatic, ecological, and societal challenges.

Asukkaiden tyytyväisyyttä omaan asuinalueeseensa pidetään yhtenä yleisimmistä asuinalueiden laatua tarkastelevista mittareista. Asumistyytyväisyys on myös liitetty oleelliseksi osaksi ihmisen yleistä elämänlaatua ja asuinympäristöä voidaan pitää ihmisen arkielämän tärkeimpänä elinympäristön osa-alueena. Tässä tutkielmassa tutkimuskohteena olivat lähiöissä asuvien henkilöiden asumistyytyväisyys. Lähiöt ovat oleellinen osa suomalaista kaupunkikuvaa ja Suomessa lähiöiden, ja niissä asuvien ihmisten määrä on merkittävä. Kun puhutaan tyytyväisyydestä, niin puhutaan ihmisten subjektiivisesta kokemuksesta. Tutkittaessa aihetta, joka on ihmisten subjektiivisista kokemuksista riippuvainen, luo se tutkimukselle omat haasteensa. On tiedossa, että ihmisillä on suuria eroja siinä, kuinka he pystyvät ilmaisemaan epämukavuutta sekä tyytyväisyyttä. Kun siis tehdään tutkimusta, jossa tyytyväisyyden mittarina käytetään henkilön subjektiivista arviota, tulokset perustuvat siihen olettamukseen, että ihmisten omat arviot elämästään ja tyytyväisyyden tasostaan ovat luotettavia mittareita. Tämän tutkielman tavoitteena on selvittää, millä tekijöillä on yhteys suomalaisissa lähiöissä asuvien henkilöiden asumistyytyväisyyteen. Tutkimuksen aineistona toimii Helsingin yliopiston ja Suomen Akatemian rahoittaman PREFARE-hankkeen (2012–2015) aikana hankittu aineisto. Aineistoon on kyselydatan lisäksi yhdistetty vastaajien sijainnin perusteella kontekstuaalista rekisteritietoa, jotka saatiin ruututietokannasta. Aineisto on siis kaksitasoinen, yksilötaso, jossa vastaajia oli 7728 ja lähiötaso, jossa alueita oli 71. Aineiston analyysimenetelmänä toimi monitasoinen lineaarinen regressiomalli, jonka avulla pystyttiin analysoimaan monitasoista aineistoa. Analyysissä aineistosta luotiin asumistyytyväisyyttä kuvaava tyytyväisyysmuuttuja ja tutkielmassa tarkasteltiin aluetasonmuuttujien, yksilötason taustamuuttujien ja asuinympäristön kokemiseen liittyvien muuttujien yhteyksiä tähän tyytyväisyysmuuttujaan. Tutkielman oleellisin tulos oli maineen merkitys asumistyytyväisyyteen. Aluetason muuttujien yhteydet tyytyväisyysmuuttujaan kulkivat hyvin vahvasti mainemuuttujan kautta ja maineella oli myös tarkasteltavista muuttujista vahvin yhteys tyytyväisyyteen. Maineen lisäksi kaksi muuta kokemusmuuttujaa, turvallisuus ja naapurisuhteet olivat hyvin vahvassa yhteydessä asumistyytyväisyyden kanssa. Yksilötason taustamuuttujista vahvimmat yhteydet tyytyväisyysmuuttujaan olivat tulotasolla, iällä ja asunnon hallintamuodolla.

Quantum computers utilize qubits to store and process quantum information. In superconducting quantum computers, qubits are implemented as quantum superconducting resonant circuits. The circuits are operated only at the two energy states, which form the computational basis for the qubit. To suppress leakage to uncomputational states, superconducting qubits are designed to be anharmonic oscillators, which is achieved using one or more Josephson junctions, a nonlinear superconducting element. One of the main challenges in developing quantum computers is minimizing the decoherence caused by environmental noise. Decoherence is characterized by two coherence times, T1 for depolarization processes and T2 for dephasing. This thesis reviews and investigates the decoherence properties of superconducting qubits. The main goal of the thesis is to analyze the tradeoff between anharmonicity and dephasing in a qubit unimon. Recently developed unimon incorporates a single Josephson junction shunted by a linear inductor and a capacitor. Unimon is tunable by external magnetic flux, and at the half flux quantum bias, the Josephson energy is partially canceled by the inductive energy, allowing unimon to have relatively high anharmonicity while remaining fully protected against low-frequency charge noise. In addition, at the sweet spot with respect to the magnetic flux, unimon becomes immune to first-order perturbations in the flux. The sweet spot, however, is relatively narrow, making unimon susceptible to dephasing through the quadratic coupling to the flux noise. In the first chapter of this thesis, we present a comprehensive look into the basic theory of superconducting qubits, starting with two-state quantum systems, followed by superconductivity and superconducting circuit elements, and finally combining these two by introducing circuit quantum electrodynamics (cQED), a framework for building superconducting qubits. We follow with a theoretical discussion of decoherence in two-state quantum systems, described by the Bloch-Redfield formalism. We continue the discussion by estimating decoherence using perturbation theory, with special care put into the dephasing due to the low-frequency 1/f noise. Finally, we review the theoretical model of unimon, which is used in the numerical analysis. As a main result of this thesis, we suggest a design parameter regime for unimon, which gives the best ratio between anharmonicity and T2.

In this master’s thesis, linear zwitterionic poly(ethylene imine) methyl-carboxylates (l-PEI-MCs) were synthesized through a four-step synthesis. The synthesis started with the polymerization of 2-ethyl-2-oxazoline (EtOx) monomers into poly(2-ethyl-2-oxazoline) (PEtOx) homopolymers with polymerization degree of 50 and 100. Living cationic ring-opening polymerization (LCROP) enabled a good control over the molecular weights. Subsequently, the side chains of PEtOxs were cleaved off by acidic hydrolysis. This resulted in linear poly(ethylene imine)s (l-PEIs) bearing a secondary amine group in repeating units of the polymer chain. These amine units were then functionalized with methyl-carboxylate moieties by first introducing tert-butyl ester functionalities to l-PEI chains, and subsequently cleaving off the tert-butyl groups. The final polymer is a polyzwitterion, featuring both an anionic carboxylate and a cationic tertiary amine group within a single repeating unit. Polymers produced in each step were characterized via 1H-NMR and FT-IR spectroscopy and their thermal properties were analyzed by differential scanning calorimetry (DSC). The molecular weights and dispersities (Ð) of PEtOx polymers were additionally estimated by gel permeation chromatography (GPC). Via 1H-NMR, the degree of polymerization for PEtOxs and the hydrolysis degree for l-PEIs were determined. FT-IR gave a further insight into the structures of polymers, successfully confirming the ester functionality of modified l-PEI. The disappearance of the tert-butyl proton signal in 1H-NMR spectrum after deprotection verified the successful removal of tert-butyl groups, resulting in the final product with methyl-carboxylate functionalities. By DSC, different thermal transitions, i.e., glass transition (Tg), melting (Tm) and crystallization (Tc), were observed, and the effects of molar mass and polymer modifications on these transitions were being investigated. The state of the art explores the literature regarding synthesis and properties of poly(2-oxazoline)s (POx), poly(ethylene imine)s (PEIs), and polyzwitterions. The theory behind living cationic ring-opening polymerization of 2-oxazolines and acidic hydrolysis of POxs is described. Different post-polymerization modification strategies to functionalize PEIs are being discussed. In addition, possible applications for each of these polymer classes are shortly outlined.

Sobolev functions generalize the concept of differentiability for functions beyond classical settings. The spaces of Sobolev functions are fundamental in mathematics and physics, particularly in the study of partial differential equations and functional analysis. This thesis provides an overview of construction of an extension operator on the space of Sobolev functions on a locally uniform domain. The primary reference is Luke Rogers' work "A Degree-Independent Sobolev Extension Operator". Locally uniform domains satisfy certain geometric properties, for example there are not too thin cusps. However locally uniform domains can possess highly non-rectifiable boundaries. For instance, the interior of the Koch snowflake represents a locally uniform domain with a non-rectifiable boundary. First we will divide the interior points of the complement of our locally uniform domain into dyadic cubes and use a collection of the cubes having certain geometric properties. The collection is called Whitney decomposition of the locally uniform domain. To extend a Sobolev function to a small cube in the Whitney decomposition one approach is to use polynomial approximations to the function on an nearby piece of the domain. We will use a polynomial reproducing kernel in order to obtain a degree independent extension operator. This involves defining the polynomial reproducing kernel in sets of the domain that we call here twisting cones. These sets are not exactly cones, but have some similarity to cones. Although a significant part of Rogers' work deals extensively with proving the existence of the kernel with the desired properties, our focus will remain in the construction of the extension operator so we will discuss the polynomial reproducing kernel only briefly. The extension operator for small Whitney cubes will be defined as convolution of the function with the kernel. For large Whitney cubes it is enough to set the extension to be 0. Finally the extension operator will be the smooth sum of the operators defined for each cube. Ultimately, since the domain is locally uniform the boundary is of measure zero and no special definition for the extension is required there. However it is necessary to verify that the extension "matches" the function correctly at the boundary, essentially that their k-1-th derivatives are Lipschitz there. This concludes the construction of a degree independent extension operator for Sobolev functions on a locally uniform domain.