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The geochemical regolith data gathered from Dzhumba, a gold prospect in eastern Kazakhstan, was analyzed using factor analysis and then integrated into ArcGIS as spatial data. Principal axis factoring method was used for factor extraction combined with varimax orthogonal rotation and Kaiser normalization. Five clear factors were extracted from the data set of 47 elements in 3942 regolith samples. Kriging interpolation was used to generate spatial data surfaces from factor scores. The generated factors are composed of the geochemical associations in the raw data, and represent the underlying geological processes and formations of the area. The fourth factor generated represents gold mineralization with As, Sb, Au, Zr, Sc, Mn, Mo, Cu, K and Ni being the elements that are positively loaded onto factor 4. Therefore, single element maps of these elements have been produced alongside the factor maps in order to examine factor 4 more intensely. Also maps about structural geology and alteration in the Dzhumba project area have been produced in order to give better understanding of the factor maps. The data suggests that the deposit type is an orogenic gold deposit. Other factors created interesting results as well, and they gave information about the different geological units of the area. Factor 1 represents granitic rocks by their feldspar and trace element content, factor 2 represents black shales with possible mafic rock constituents, factor 3 represents a sulfide rich mafic mineral group or graphitic rocks that are most likely black shales and factor 5 possibly represents calcite alteration. Factor 4 is the main interest of this study. The most intense loadings for factor 4 are in Brigadnoe, Svistun and Dzhumba with a small peak in Belyi. Single element map for gold mostly corresponds to factor 4 for Svistun and Dzhumba, but Brigadnoe is represented with a small peak. However, gold has a major presence in Fedor-Ivanovskoe, which is absent from factor 4. Further exploration in Fedor-Ivanovskoe could be performed in order to clarify if this is due to an unrelated gold-only deposit or some other event. Possible future exploration in the area could benefit from factor 4 results, using As and Sb, or a combination of As, Sb, Zr, Sc, Mn, Mo, Cu, K and Ni as pathfinders for possible gold occurrences.

The use of machine learning and algorithms in decision making processes in our every day lifehas been growing rapidly. The uses range from bank loans and taxation to criminal sentencesand child care decisions. Because of the possible high importance of such decisions, we need tomake sure that the algorithms used are as unbiased as possible.The purpose of this thesis is to provide an overview of the possible biases in algorithm assisteddecision making, how these biases affect the decision making process, and go through someproposes on how to tackle these biases. Some of the proposed solutions are more technical,including algorithms and different ways to filter bias from the machine learning phase. Othersolutions are more societal and legal and address the things we need to take into account whendeciding what can be done to reduce bias by legislation or by enlightening people on the issuesof data mining and big data.

Minimum-cost minimum path cover is a graph-theoretic problem with an application in gene sequencing problems in bioinformatics. This thesis studies decomposing graphs as a preprocessing step for solving the minimum-cost minimum path cover problem. By decomposing graphs, we mean splitting graphs into smaller pieces. When the graph is split along the maximum anti-chains of the graph, the solution for the minimum-cost minimum path cover problem can be computed independently in the small pieces. In the end all the partial solutions are joined together to form the solution for the original graph. As a part of our decomposition pipeline, we will introduce a novel way to solve the unweighted minimum path cover problem and with that algorithm, we will also obtain a new time/space tradeoff for reachability queries in directed acyclic graphs. This thesis also includes an experimental section, where an example implementation of the decomposition is tested on randomly generated graphs. On the test graphs we do not really get a speedup with the decomposition compared to solving the same instances without the decomposition. However, from the experiments we get some insight on the parameters that affect the decomposition's performance and how the implementation could be improved.

Ultra-low frequency (ULF) waves in the Pc4-Pc5, 2 – 25 mHz range have been observed to accelerate trapped 1 – 10 MeV electrons in the Earth’s radiation belts. This acceleration can lead to particle losses and injections that occur on timescales comparable to the particle drift periods. Current models rely on diffusion equations written in terms of Fokker-Planck equations and are not suitable for describing fast temporal variations in the distribution function. This thesis is a study of fast transport of equatorially trapped electrons in the radiation belts. We look at solutions for the time evolution of the linear part of the perturbed distribution function using both analytical and numerical methods. Based on this work we build a simple model of fast transport in the radiation belts using a spectral PDE framework called Dedalus. The resulting program is a computationally inexpensive, simple approach to modelling drift-periodic signatures on fast timescales. In this study we investigate the behavior of the distribution function in three systems: a simple system without a wave term, and systems with a single non-resonant and resonant ULF wave. The wave solutions are evaluated with magnetic field perturbations of different magnitudes. The Earth’s magnetic field is modelled with the Mead field. The numerical solution of the perturbed differential equation is studied for relativistic equatorially trapped electrons. Phase-mixing is found to happen regardless of field fluctuations or resonance. The non-resonant wave solution shows time-delayed, spatially localized structures in the equatorial plane forming in the presence of large magnetic field fluctuations. These transients are also seen in the analytical solution and provide a new theoretical explanation for the ubiquitous observation of drift echoes in the inner and outer radiation belts of the Earth (Li et al., 2024).

Sea-surface wind observations of previous generation scatterometers have been successfully assimilated into Numerical Weather Prediction (NWP) models. Impact studies conducted with these assimilation implementations have shown a distinct improvement to model analysis and forecast accuracies. The Advanced Scatterometer (ASCAT), flown on Metop-A, offers an improved sea-surface wind accuracy and better data coverage when compared to the previous generation scatterometers. Five individual case studies are carried out. The effect of including ASCAT data into High Resolution Limited Area Model (HIRLAM) assimilation system (4D-Var) is tested to be neutral-positive for situations with general flow direction from the Atlantic Ocean. For northerly flow regimes the effect is negative. This is later discussed to be caused by problems involving modeling northern flows, and also due to the lack of a suitable verification method. Suggestions and an example of an improved verification method is presented later on. A closer examination of a polar low evolution is also shown. It is found that the ASCAT assimilation scheme improves forecast of the initial evolution of the polar low, but the model advects the strong low pressure centre too fast eastward. Finally, the flaws of the implementation are found small and implementing the ASCAT assimilation scheme into the operational HIRLAM suite is feasible, but longer time period validation is still required.

X-ray computed tomography is an imaging method where the inner structure of an object is reconstructed from X-ray images taken from multiple directions around the object. When measurements from only a few measurement directions are available, the problem becomes severely ill-posed and requires regularization. This involves choosing a regularizer with desirable properties, as well as a value for the regularization parameter. In this thesis, sparsity promoting regularization with respect to the Haar wavelet basis is considered. The resulting minimization problem is solved using the iterative soft thresholding algorithm (ISTA). For the selection of the regularization parameter, it is assumed that an a priori known level of sparsity is available. The regularization parameter is then varied on each iteration of the algorithm so that the resulting reconstruction has the desired level of sparsity. This is achieved using variants of proportional-integral-derivative (PID) controllers. PID controllers require tuning to guarantee that the desired sparsity level is achieved. We study how different tunings affect the reconstruction process, and experiment with two adaptive variants of PID controllers: an adaptive integral controller, and a neural network based PID controller. The two adaptive methods are compared to each other, and additionally the adaptive integral controlled ISTA is compared to two classical reconstruction methods: filtered back projection and Tikhonov regularization. Computations are performed using both real and simulated X-ray data, with varying amounts of available measurement directions. The integral control is shown to be crucial for the regularization parameter selection while the proportional and derivative terms can be of use if additional control is required. Of the two adaptive variants, the adaptive integral control performs better with respect to all measured figures of merit. The adaptive integral controlled ISTA also outperforms the classical reconstruction methods both in terms of relative error and visual inspection when only a few measurement directions are available. The results indicate that variants of the PID controllers are effective for sparsity based regularization parameter selection. Adaptive variants are very end user friendly, avoiding the manual tuning of parameters. This makes it easier to use sparsity promoting regularization in real life applications. The PID control allows the regularization parameter to be selected during the iteration, thus making the overall reconstruction process relatively fast.

Työssäni tutkin mahdollisuutta käyttää akustista ajankääntömenetelmää (time-reversal) teollisen ultraäänipuhdistimen puhdistustehon kohdentamiseen. Akustisella ajankääntömenetelmällä pystytään kohdistamaan painekenttä takaisin alkuperäiseen pisteeseen, tallentamalla ko. pisteestä lähetetyt painesignaalit akustisilla antureilla (etusuunta) ja lähettämällä ne takaisin ajassa käännettyinä (takasuunta). Tässä työssä tutkitun kohdentamismenetelmän perusteena toimii elementtimenetelmällä toteutettu simulaatiomalli, jossa sekä ultraäänipuhdistin, että puhdistettava järjestelmä oli mallinnettu tarkasti. Simulaatiomallin avulla voitiin puhdistettavasta alueesta valita mielivaltainen piste johon halutaan kohdentaa puhdistustehoa. Simuloidun etusuuntaisen ajon tuloksena tuotetut signaalit tuotiin ulos mallista ja takasuuntainen ajo suoritettiin kokeellisessa ympäristössä käyttäen simuloituja signaaleja. Työssä esitetään vertailu simuloidun ja kokeellisen ajankääntömenetelmään perustuvan kohdentamisen tuloksista ja osoitetaan, että simuloiduilla signaaleilla on mahdollista kohdentaa akustista tehoa ennalta valittuun mielivaltaiseen pisteeseen. Lisäksi työssä esitetään analyysi anturien määrän vaikutuksesta kohdentamiskykyyn, tarkastellaan ultraäänipuhdistimen avaruudellista kohdentamiskykyä sekä vahvistetaan simulaatioissa tehdyn lineaarisen oletuksen paikkansapitävyys.

Northern and high-altitude environments are expected to change dramatically due to climate change which strongly affects vegetation. Regarding to this, there has been interest on investigating how climatic factors affect vegetation distribution. One of the widely used methods to study species environment relationship is spatial species distribution modelling, in which the aim is to estimate suitable niches for species. However, only a few comprehensive distribution predictions for whole species groups have been made at a fine resolution and covering large extents. In the case of arctic-alpine plants Fennoscandia offers a good research area in terms of northern location, variable topography and wide climatic gradients. In this thesis the aim was to discover how climate affects the distribution and species richness patterns of arctic-alpine vascular plants. Relationship between arctic-alpine vegetation and climate was investigated by producing distribution predictions for each species based on important climatic variables and topography. Species data included observations from national species portals of Sweden and Norway, as well as field observations from three test regions Kevo, Northwestern-Lapland and Rastigaissa. The explanatory variables used were efficient temperature sum, water balance, minimum temperature of the coldest month and relative height. The species distribution predictions were produced using a 1 km2 grid covering whole Fennoscandia. Four different modelling methods (GAM, GLM, GBM, RF) were used and the predictions done with two different data sets. First the models were calibrated using only the observations from species portals, and the predictions were evaluated at the Lapland´s test regions. On the second modelling round the whole data was used in model calibration. From the modelling results both individual species distributions and the distribution of the whole vegetation group were investigated, as well as the relative importance of the explanatory variables. Then individual species distribution predictions were combined to visualize and study arctic-alpine species richness and its hotspots. Distribution of arctic-alpine vegetation was affected most by efficient temperature sum and minimum temperature of the coldest month. However, the relative importance of the variables varied for different species. Also the differences in the calibration data affected the results. Mainly species´ predicted distributions are located on areas where growing season is short and winter temperatures are low, even though there was some variation in the responses caused by the latter variable. Temperature variables were also significant in explaining species richness and its hotspots. It was shown that species richness focuses to the coldest areas and benefits from a bigger topography gradient. The results of this thesis show that climate defines both the distribution and the richness of arctic-alpine vegetation in Fennoscandia. However, resolution of one square kilometer does not fully capture the heterogeneity of the arctic-alpine area since temperature and moisture conditions vary greatly locally, for example depending on snow cover. Research on different scales is still needed to understand complicated species environment relationships.

Tässä kirjallisuuskatsauksessa perehdyttiin ensisijaisesti puuvartisten- ja ruohokasvien soluseinien fenyylipropanoidien ja ferulahappojen biosynteesiin ja kytkeytymisreaktioihin. Fenyylipropanoidireitti alkaa fenyylialaniinista ja johtaa monien prekursoreiden kuten lignaanien, flavonoidien, salisyylihappojen ja ligniiniprekursoreiden syntymiseen. Tutkielmassa keskityttiin ligniiniprekursoreiden muodostumiseen ja erityisesti sen biosynteesireitin välituotteen, ferulahapon hapetettuihin kytkeytymisreaktioihin kasvien soluseinillä. Fenyylipropanoiditutkimuksen lähtökohtana on jo vuosia ollut selvittää biosynteesireittejä ja menetelmiä, joiden avulla ligniini saadaan kasvin soluseinältä liukenemaan ja hiilihydraatti otettua talteen. Eräs tapa tunnistaa näitä hajoamistapahtumia on tutkia fenyylipropanoidien kytkentöjen muodostumista. Tässä pro gradu -tutkielmassa fenyylipropanoidireitin välituotteiden entsyymien säätelyä tarkasteltiin luonnonvaraisissa ja geneettisesti muunnelluissa kasveissa. Bieosynteesireitti selkeytyi paljon. Lisäksi siirtogeenisillä kasveilla havaittiin kokonaan uusia kytkentöjä ja rakenteita. Eräillä geeniyhdistelmillä voitiin lisätä tuntuvasti hiilihydraattimäärää samalla kun ligniinin kokonaismäärä väheni. Näin arveltiin voitavan kasvattaa biomassan määrää puukasveilla. Ferulahapot dehydrogenoituvat entsymaattisesti hapettavissa olosuhteissa fenoksiradikaaleiksi, jotka reagoivat edelleen muodostaen toisen radikaalimonomeerin tai -polymeerin kanssa kytkentöjä. Soluseinä tuottaa radikaalireaktioissa tarvitsemansa hapettimet ja entsyymit, vetyperoksidin ja peroksidaasin itse. Ferulahapon monomeerit ja dimeerit muodostavat esterisidoksia soluseinän hemiselluloosan kanssa. Näin syntyneet ferulaattidimeerit ja -trimeerit muodostivat ristikytkentöjä hiilihydraattien ja ligniinin välille sekä yhden tai useamman polysakkaridiketjun välille. Ferulahappojen katsottiin olevan lignifioitumisen aloituskohtia soluseinillä ja yhdistävän kaksi suurta polymeerista verkkorakennetta toisiinsa. Myös soluseinän hiilihydraattien koostumuksen havaittiin vaikuttavan muodostuvien kytkentöjen rakenteeseen. Lopuksi tarkasteltiin vielä ferulahapon antioksidatiivisia ominaisuuksia. Todettiin ligniinin ja ferulahapon määrän korreloivan soluseinän peroksidaasi- ja vetyperoksidimäärän kanssa. Kaveissa monet taudinaiheuttajat, vioittuneet kasvin osat sekä UV-säteily lisäsivät peroksidaasien tuotantoa ja edelleen ferulahappojen määrää. Fenoksiradikaalina ferulahappo kykeni eliminoimaan vetyperoksidin haitallisten happiradikaalien vaikutuksia pelkistämällä ne hapettuen itse radikaalisessa kytkeytymisreaktiossa. Tämä johti mielenkiintoisiin tulevaisuuden näkymiin ferulahaposta funktionaalisena elintarvikkeena, lääkeaineena sekä kosmeettisena valmisteena.

Tutkielmassa perehdytään Fermat’n pieneen lauseeseen ja sen todistuksiin. Fermat’n pientä lausetta tarkastellaan myös alkulukutestauksen näkökulmasta. Loppupuolella määritellään Eulerin φ-funktio ja esitetään Eulerin lause. Eulerin lauseen käytännöllisyyttä tarkastellaan jakojäännösten selvittämisessä. Tutkielman johdanto on pieni katsaus Pierre de Fermat’n ja Leonhard Eulerin elämään. Johdannossa käsitellään myös Fermat’n pienen lauseen sekä Eulerin lauseen historiaa. Tutkielmassa on käytetty useita lukuteoreettisia käsitteitä, jotka määritellään heti johdannon jälkeen luvussa Tutkielmassa käytettyjä määritelmiä. Tutkielma esittää Fermat’n pienen lauseen kolmessa eri muodossa, jotka kaikki ovat keskenään ekvivalentteja. Lauseen käyttöä havainnollistetaan myös muutamalla esimerkillä. Luvussa Fermat’n pienen lauseen todistuksia kyseinen lause todistetaan ensin suoraviivaisesti ja sen jälkeen induktiolla. Lopuksi lausetta havainnollistetaan kuvitellun helminauhan avulla. Tutkielma osoittaa, että Fermat’n pieni lause toteutuu millä tahansa alkuluvulla p. Fermat’n pienen lauseen toteutuminen jollain luvulla ei kuitenkaan yksin riitä osoittamaan lukua alkuluvuksi. Otsikon Pseudoalkuluvut alla käsitellään lukuja, jotka eivät ole alkulukuja, mutta joilla Fermat’n pieni lause toteutuu. Jotta voitaisiin varmistua, että luku on alkuluku, E. Lucas kehitti 1800-luvun loppupuolella alkulukutestin, joka hyödyntää Fermat’n pientä lausetta. Testi on esitetty, todistettu ja sitä on havainnollistettu esimerkein kohdassa Lucas-Lehmer alkulukutesti. Testin todistukseen vaaditaan muutamia aputuloksia, jotka on esitetty ennen varsinaista testiä. Tutkielma määrittelee Eulerin φ-funktion ja havainnollistaa sen käyttöä esimerkillä. Tämän jälkeen tutkielmassa johdetaan kaava, jonka avulla φ-funktion arvon voi kätevästi laskea. Kaavan johtamista varten on todistettu muutama aputulos. Kaavan käytöstä on esimerkki. Tutkielmassa käsitellään Eulerin lause. Heti määritelmän jälkeen Eulerin lauseella ratkaistaan jakojäännöksiä. Sitten Eulerin lause todistetaan ensin induktion ja binomikaavan avulla ja sitten redusoidun jäännösluokkasysteemin avulla. Ennen kumpaakin todistusta esitellään ja todistetaan todistuksissa käytettäviä aputuloksia. Lopuksi tutkielma käsittelee suurten potenssien jakojäännösten ratkaisemista Eulerin lauseen ja binäärijärjestelmän avulla.