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Machine learning is by no means a novel field, but a recent boom in interest has led to a rapid increase in funding for related research. Because of this, many pure-mathematicians may find themselves trying to transition to this currently lucrative area of research. Thus, there is some demand for literature which helps ease this transition for mathematicians with a geometry or topology background. In this thesis we provide an introduction to contemporary machine learning research for a geometrically or topologically inclined individual. We do so by tracing the study of manifolds from their inception to modern machine learning. The thesis begins with a brief history of manifolds to motivate the examination of a proof of the Whitney embedding theorem. The theorem is then proved in detail, following texts from Adachi and Mukherjee on differential geometry. Later, a brief introduction to manifold learning introduces the reader to the manifold hypothesis and connects the classical study with its machine learning counterpart. Then, we provide a canonical introduction to neural networks after which we share rigorous mathematical definitions. Finally, we introduce the necessary preliminaries and subsequently prove the universal approximation theorem with injective neural networks. While we consider the Whitney embedding theorem as having applications in machine learning research, the universal approximation theorem with injective neural networks has clearer uses beyond mathematics. The studies of inverse problems and compressed sensing are two areas for which injectivity is a necessary condition for the well-posedness of common questions. Both fields have many deep applications to scientific and medical imaging. Injectivity is also a prerequisite for a function to preserve the topological properties of its domain.

Wood is the fuel for the forest industry. Fellable wood is collected from the forests and requires transportation to the mills. The distance to the mills is quite often very long. The most used long- distance transportation means of wood in Finland is by road transportation with wood-trucks. The poor condition of the lower road network increases the transportation costs not only for the forest industry but for the whole natural resources industry. Timely information about the conditions of the lower road network is considered beneficial for the wood transportation and for the road maintenance planning to reduce the transportation related costs. Acquisition of timely information about the conditions of the lower road network is a laborious challenge to the industry specialists due to the vast size of the road network in Finland. Until the recent development in ubiquitous mobile computing collecting the road measurement data and the detection of certain road anomalies from the measurements has traditionally required expensive and specialized equipment. Crowdsensing with the capabilities of a modern smartphone is seen as inexpensive means with high potential to acquire timely information about the conditions of the lower road network. In this thesis a literature review is conducted to find out the deteriorative factors behind the conditions of the lower road network in Finland. Initial assumptions are drawn about the detectability of such factors from the inertial sensor data of a smartphone. The literature on different computational methods for detecting the road anomalies based on the obtained accelerometer and gyroscope measurement data is reviewed. As a result a summary about the usability of the reviewed computational methods for detecting the reviewed deteriorative factors is presented. And finally suggestions for further analysis for obtaining more training data for machine learning methods and for predicting the road conditions are presented.

Legacy systems are software systems that hold great value to organizations, but which are difficult to maintain. Legacy systems can be wrapped with a REST wrapper in order to reuse their data and business logic. The motivation for the wrapping is to decouple new development from the legacy system so that the new development is not directly dependent on the legacy system's internals. The hypothesis I've seen in the software industry is that REST wrapping makes new development faster because the complexity of the legacy system does not slow new development down. Eventually the goal is that the legacy system can be incrementally replaced without changes to the clients that use its services via the REST API. This thesis examines REST wrapping by reviewing existing literature. REST wrapping as a concept is placed in the theoretical context of modernization techniques applied to systems in their post-delivery life cycle. In addition to conceptual clarification, two case studies found from the literature and the author's experiences in the software industry are examined to determine whether they support the theoretical models of REST wrapping as a modernization technique. The literature provided support for the notion that REST wrapping provides a low-cost way to reuse legacy systems functionality and data. It was also found to reduce the complexity of developing new functionality on top of a legacy system. The biggest shortcoming of REST wrapping is that it leaves the legacy system mostly unchanged. Like wrapping in general also REST wrapping is a short-term solution to legacy system's problems. It can be seen as a way to buy time to develop a long-term solution for the legacy system. ACM Computing Classification System (CCS): Software and its engineering → Software evolution Applied computing → Service-oriented architectures Information systems → RESTful web services

Röntgentomografiassa on tarkoitus hankkia tietoa jonkin tutkittavan kappaleen sisärakenteesta rikkomatta itse kappaletta. Tomografialaitteet ottavat kappaleesta paljon röntgenkuvia eri suunnilta. Kuvien perusteella on mahdollista laskea esimerkiksi poikkileikkauskuva kappaleesta. Jos röntgendataa on tarpeeksi, pystytään kuvien avulla luomaan kappaleesta kolmiulotteinen malli. Tätä mallia voidaan tarkastella mistä kuvakulmasta tahansa. Poikkileikkauskuvia ja kolmiulotteisia malleja kutsutaan \emph{rekonstruktioiksi}, sillä sisärakenne "rakennetaan uudelleen" röntgenkuvista. 4D-tomografiassa mukaan tulee myös aikaulottuvuus. Röntgendataa kerätään usealta ajanhetkeltä ja rekonstruktioksi muodostuu animaatio, joka kuvaa kappaleen rakenteen muutosta ajan suhteen. Myös tätä animaatiota pystytään tarkastelemaan mistä kuvakulmasta tahansa minä ajanhetkenä tahansa. Tämän opinnäytetyön tarkoitus on soveltaa kahta eri algoritmia rekonstruktioiden laskemiseen jokaiselle ajanhetkelle erikseen. Liikkuvasta LEGO-robotista on tarkoitus saada aikaiseksi 4D-rekonstruktio. Yhtenä ongelmana on, muodostavatko yksittäiset rekonstruktiot järkevän kokonaisuuden, kun ne asetetaan peräkkäin? Entä millä tavalla eri algoritmeilla lasketut rekonstruktiot eroavat toisistaan?

Kalliojärvi, Ania and Erkkilä gold deposits are located in the Pirkanmaa migmatite belt in southern Finland. Nearest city is Tampere, approximately 15 km northeast of the deposits. The native gold occurs with sulphide dissemination in quartz veins and shear zones in hydrothermally altered mica schist, gneiss and granite-pegmatite intrusions and black schist. Black schist is common in Erkkilä deposit. Tourmaline pegmatite is common in Ania deposit. Gold grades are in the range of 0,1-26,7 g/t. The peak of metamorphism has reached upper amphibolite fasies in Erkkilä deposit (K-feldspar + sillimanite isograd). In Kalliojärvi the metamorphic index mineral is staurolite, which indicates middle amphibolite facies conditions. In Ania the metamorphism has progressed to the lower amphibolite facies stability field of garnet. These metamorphic associations indicate pressure of 8 kb to 6 kb and temperature of 790 to 525 °C. The hydrothermal alteration is strong in the mineralized zones, demonstrated by silicification and potassium metasomatism, which altered feldspars to sericite and biotite to chlorite. Plagioclase has also altered to albite and potassium feldspar, epidote and calcite and ilmenite has altered to rutile. In the mineralisation process fluids have enriched in the same ore forming elements in all three deposits. These elements include Fe, Cu, Ni, Co, Au, Ag, Hg, Pb, Bi, Sb, Te, S, Se, As. The major ore minerals are arsenopyrite, löllingite, pyrrhotite, pyrite and chalcopyrite. Other ore minerals are native bismuth, gold, bismuth tellurides, maldonite and oxide minerals. The major ore forming process has been open space filling. The ore minerals have crystallized as disseminations in intergranular spaces between silicates and carbonates, in quartz- and epidote-clinozoisite veins and walls of the fluid channels. The arsenopyrite geothermometry shows crystallization temperature from 438 to 609 °C with pyrrhotite and löllingite. The sulfur activity (logS2) has been from -3,70 to -8,30. Fluids transported gold predominantly as a reduced sulphur complex and a thioarsenide complex. The first generation native gold is intergrown and as inclusions in arsenopyrite and in grain borders of composite löllingite and arsenopyrite grains. The second generation native gold occurs as open space fillings in the gangue fractures, intergranular spaces between silicates and as inclusion in potassium feldspar and sulphides, Bi-, Sb- Te-minerals and metallic bismuth. The main crystallization of native gold and tellurides took place in the epizonal temperature range from 150 to 300 °C. According to the mineral liberation analyses in Ania the grain size of gold, 86,10 wt. %, is from 32 to 106 µm, in Erkkilä 98,22 wt. % is from 32 to 355 µm and in Kalliojärvi 76,02 wt. % is from 32 to 106 µm. In heavy mineral concentrates gold occurs as free grains and also intergrown with arsenopyrite and bismuth. A small portion of gold is as inclusions in other minerals in arsenopyrite and silicates. The mineralisation and crystallization of the ore minerals is epigenetic i.e. it was active after the last metamorphic event in shear zones of the host rock. All three gold deposits have crystallized after a complex, accretionary to collisional orogenic evolution of Svekofennian. The ore mineral crystallization occured in the hypozonal-epizonal temperature range from 600 to 150 °C.

The standardisation of airports has turned airports into similar non-places without history and connection to their surroundings. Recently the business environment of airports has become tougher, as airports are forced to compete for passengers in order to stay in business. The non-place character is a competition disadvantage for an airport, and therefore new means need to be developed in order to sustain competitiveness. A wide range of services as well as local culture are used to create a sense of place at an airport. The passengers are being offered new experiences and airports are even advertised with the experience orientation. The objective of this thesis is to find out whether the hard work on improving the image of the airports with spectacular projects has had an effect on how the passengers see the airport or does their view still represent the stereotypical image. The primary research question is how people perceive the airport today and are the perceptions in line with the definition of a non-place. I went through 195 airport reviews from ten European airports. Applying the discourse analysis I studied the different views of the airports that have arisen. The repeating patterns were divided into six themes according to their topics, in other words six different discourses were used to discuss airports. The customer reviews comprised the images of an airport as a physical building, a sensory environment, a hangout, a subject of a change, a social setting and as a visiting card of the area in question. A discourse analysis is based on a thought that the language is not a neutral describer of the reality, but rather the language builds the reality and is itself a product of culture. In other words, the themes that have arisen do not represent the absolute truth about the essence of an airport, but they rather provide different viewpoints on the concept of an airport. As I reviewed the discourses I found out that both the past and the present of the airports have their impacts on the images the passengers have about the airport in question. Though travelling is an essential part of the western lifestyle and the airports have become mundane, airports still represent modernity and terminals are important buildings. On the other hand, to this day the images of the past appear to have an impact on the experience of the flying passengers. According to the airport reviews, airports have both the characteristics of a place and a non-place. Still the passengers do not automatically see the standardisation of the airports as a negative feature, as the effectiveness and the similarity of the airports eases the travelling, and the widespread of the Internet helps keeping the important things always at hand. A part of the survey participants found that airports could standardise even further and concentrate on the needs of the passengers instead of local culture.

Tutkin tässä työssä lentopaikkaennusteiden osuvuutta ja ennustettavuutta vuosien 2010 ja 2014 aikana, käyttäen hyväksi Ilmatieteen laitoksen verifiointimenetelmää. Lentopaikkaennusteilla on tärkeä rooli nykypäivän lentotoiminnassa. Ennusteiden verifioinnilla nähdään millä tasolla ennustettavuus on, ja se on myös hyvä työkalu ennusteiden kehittämisessä. Oma motivaationi tutkielmaan liittyy työhöni lentosäämeteorologina, ja myös omien ennustustaitojeni kehitykseen. Lentopaikkaennusteen kannalta hankalimmat ennustettavat sääsuureet ovat näkyvyys ja pilven korkeus, jotka ovat myös tutkimukseni keskipisteenä. Lentopaikkaennusteella ennustetaan näkyvyyttä, pilviryhmää (sisältää pilven korkeuden ja määrän), tuulta ja vallitsevaa säätä lentokentällä. Tutkimuksessa käytetty verifiointimenetelmä pisteyttää lentopaikkaennusteen sen perusteella, kuinka lähelle se osuu lentokentällä tehtyjä METAR-havaintoja. Verifiointituloksista nähtiin, että vallitsevaa säätä ja tuulioloja osataan ennustaa erinomaisesti jokaisena vuodenaikana. Pilviryhmän ja näkyvyyden osalta havaittiin hyvin samankaltainen vuodenaikaisvaihtelu. Kesäkuukausina kumpikin suure saavuttaa erinomaiset tulokset. Syksyllä kuitenkin verifiointitulokset alkavat laskea, ja talvikuukausina ennustettavuus on heikoimmillaan. Keväällä tulokset alkavat jälleen parantua, vastaten käänteisesti syksyn tilannetta. Samankaltaisesta käytöksestään huolimatta, pilviryhmän tulokset havaittiin hieman näkyvyyden tuloksia heikoimmiksi. Tähän syyksi paljastui näkyvyyden runsaampi määrä erinomaisia tuloksia, ja pilviryhmän runsaampi määrä keskinkertaisia tuloksia. Näkyvyyden ennustettavuus vaikuttaisi olevan suuremman osan ajasta hyvä, mutta karkeita ennustevirheitä tulee hieman enemmän kuin pilviryhmällä. Pilviryhmällä taas ennuste on useammin pitkiä aikoja hieman pielessä. Tutkimuksen perusteella ennustettavuutta voidaan parantaa mm. ennusteessa käytettävien muutosryhmien paremmalla hyödyntämisellä ja paikallisten olojen paremmalla tuntemuksella. Myöskään automaattisten havaintojen virheiden vaikutusta ennusteiden saamiin tuloksiin ei voida jättää huomiotta.

Diatoms, green algae, and cyanobacteria react fast to changing environmental conditions. Algae are important primary producers in stream ecosystems, thus changes in periphyton can influence the whole stream ecosystem. There have not been many studies where algae biomass variation has been explained with a large water chemistry data. Furthermore, there is lack of studies where metal concentrations in the water are near to natural concentration levels. In this master’s thesis I examine how environmental variables affect the changes in algae biomass. Furthermore, the aim of this study is to examine do diatoms, green algae and cyanobacteria have different responses to environmental variables. Competition between three algae biomass groups is also researched. In this study research points were classified to three land use types. The aim of the classification was to enable variation as much as possible in shading and water chemistry variables in the study area. Eventually 51 research points were selected. Algae biomass was measured with BenthoTorch. Total phosphorus, total nitrogen, anions, cations, solid matter, dissolved matter and dissolved metals were measured in laboratory. Total biomass’ and algae groups’ response shapes where analyzed with GAM. Furthermore, competition between different algae groups were studied with Spearman’s correlation. The average total algae biomass was 2.94 μg cm-2 in the study area and diatoms were the most dominant group. Surprisingly the amounts of light and total phosphorus were sufficient in the study area and had no significant effect on the total algae biomass variation. However, total nitrogen, calcium, zinc, iron, and nickel were significant environmental variables in total biomass model. Total nitrogen, calcium, zinc and nickel where significant environmental variables for explaining diatom biomass variation. Total phosphorus and nitrogen were significant in cyanobacteria’s model and only zinc was significant in green algae’s model. Green algae had a weak but a significant negative correlation with diatoms and cyanobacteria. Total algae biomass growth was notable restricted in study area. The average amount of biomass matched a biomass volume in an oligotrophic stream. There were enough of light and total phosphorous in the study area, thus they had no significant effect on algae biomass. At high total nitrogen concentration levels biomass growth was inhibited. In addition, iron and nickel had a significant negative effect on total biomass. Zinc was an important mineral for algae biomass growth, specially to diatoms and green algae. Strong competition on resources did not occur between the algae groups. Negative correlations between algae groups where most likely explained with different responses to iron, nickel, and calcium. There is need for more studies to explain algae biomass in different natural stream ecosystems. For understanding better how different concentrations change algae biomass, more variation on environmental variables is needed. Furthermore, water hydrology and grazing should be measured. In addition, research on how water chemistry changes affect species composition in periphyton is recommended.

Tässä tutkielmassa käsitellään magneettikuvausavusteisessa rintabiopsiassa havaittuja kolmea kuva-artefaktia; biopsia-alueen heikkoa intensiteettiä, merkkitikun pään katoamista kuva-alueelta, sekä rasvasaturaation epäonnistumista merkkitikun ollessa kuva-alueella. Merkkitikun pään on havaittu katoavan kuvausalueelta ja huonontavan rasvasaturaatiota kuvantamisvaiheessa, jossa merkkitikku mallintaa biopsianeulan sisäänmenokohtaa. Biopsia-alueen signaalikatoa on havaittu sekä biopsian jälkeisissä rasvasaturoiduissa, että rasvasaturoimattomissa T1-painotteisissa kenttäkaikukuvissa. Merkkitikun huono näkyvyys kuva-alueella, rasvasaturaation epäonnistuminen, ja biopsia-alueen intensiteetti kato vaikeuttavat näytteenottoa ja johtavat pahimmassa tilanteessa väärään diagnoosiin. Biopsia-alueelle injektoidun paikallispuudutteen vaikutusta alueen intensiteettiin ei ole aiemmin tutkittu. Paikallispuudutteena käytetään useimmiten kahta erilaista lidokaiinivalmistetta: Lidokaiini 10 mg/ml ja Lidokaiini 10 mg/ml c. adrenalin. Lidokaiinipuudutteiden vaikutusta kuvakontrastiin tutkittiin mittaamalla puudutteiden relaksaatioajat. Merkkitikun katoamista tutkittiin asettamalla gadoliniumtäytteinen merkkitikku testikappaleen lähelle, ja kuvaten testikappaletta rasvasaturoidulla 3D-T1-painotteisella kenttäkaikusekvenssillä. Merkkitikku nähtiin kuvissa kuitenkin hyvin selkeästi, eikä merkkitikun huomattu aiheuttavan muutosta rasvasaturaatioon. Magneettikentän tasauksen ja siten myös rasvasaturaation tulisi onnistua, vaikka merkkitikku on kuva-alueella. Merkkitikkumittauksesta selvisi, että rasvasaturoidussa T1-painotteisessa kenttäkaikukuvassa kummankin puudutteen intensiteetti on suurempi tai yhtä suuri rasvakudoksen kanssa. Adrenaliinia sisältävän lidokaiinipuudutteen T2-ajaksi saatiin noin 2058 ± 20 ms, ja lidokaiinipuudutteen T2-ajaksi saatiin noin 1030 ± 5 ms 3,0 T magneettikentässä. Lidokaiinipuudutteen T1-ajaksi saatiin noin 2749 ± 13 ms 3,0 T magneettikentässä, ja noin 2588 ± 87 ms 1,5 T magneettikentässä. Adrenaliinilidokaiinipuudutteen T1-ajaksi saatiin 2923 ± 12 ms 3,0 T magneettikentässä, ja noin 2670 ± 90 ms 1,5 T magneettikentässä. Lidokaiinin ja adrenaliinilidokaiinin T1-ajat olivat yli 15-kertaisia parafiiniöljyn T1-aikaan verrattuna. Tällöin kumpikin puudute näkyy tummana rasvakudokseen verrattuna rasvasaturoimattomissa T1painotteisessa kuvassa. Lidokaiinipuudutteen T2*-ajaksi mitattiin noin 536 ± 15 ms ja adrenaliinia sisältävän lidokaiinipuudutteen T2*-ajaksi noin 766 ± 29 ms 1,5 T magneettikentässä. Puudutteiden T2*-ajat ovat selvästi rasvakudoksen ja rintarauhaskudoksen tyypillisiä T2-aikoja suurempia. Tällöin puudutteiden tulisi näkyä rasvakudosta ja rintarauhaskudosta kirkkaampana T2*painotteisissa kuvissa. Saadut tulokset selittävät biopsia-alueen signaalikadon rasvasaturoimattomissa T1-painotteisissa kuvissa, mutta rasvasaturoitujen kuvien signaalikato jää epäselväksi.

Atmospheric ice crystals scatter sunlight, thus affecting Earth's climate through the radiation properties of cirrus clouds. Many uncertainties remain in the characteristics of naturally occuring surface roughness and its effect on the scattering properties of ice crystals. Light scattering by ice crystals with rough surfaces was studied in this thesis by placing a small rough surface element on an infinitely large, planar vacuum-ice boundary. The surface element was generated using a statistical model based on fractional Brownian motion. The horizontal roughness scale was described by the Hurst exponent, and the vertical roughness scale with the root-mean-square roughness parameter. The surface elements were generated using a Matlab program Artificial Surface, publicly available on Mathworks. The scattering computations were performed with the surface mode of the publicly available Discrete Dipole Approximation software ADDA (version 1.34b). Several incident directions using a single visible wavelength of 0.5 micrometers from both above and below the planar surface were studied. A refractive index for ice was used throughout the computations. Results were averaged over ten rough surface realizations for specific roughness parameters. Scattering by the rough surface elements was compared to corresponding smooth surface elements. The rougher the surface element was, the more of the scattered intensity was transmitted through the planar surface. The rough surface elements had distinctively smoother angular distributions for the degree of linear polarization than their smooth counterparts. Also, it was found that while roughness itself affects polarization, the exact surface morphology did not seem to have a significant effect. The vertical roughness scale had a larger effect on the light scattering results than the horizontal scale. The model for surface roughness, along with the light scattering methodology used here, could be applied to light scattering computations for large ice crystals with surface roughness by combining the results to a geometric optics model. However, additional work is required to remove the effects caused by the infinite planar boundary. The methodology is not limited to ice crystals, and could be applied to, e.g., other atmospheric particles and atmosphereless astronomical bodies.