What is functional thinking? Using cosine similarity matrix in a semantic ontological analysis

Knowing functions and functional thinking have recently moved from just knowledge for older students to incorporating younger students, and functional thinking has been identified as one of the core competencies for algebra. Although it is significant for mathematical understanding, there is no unified view of functional thinking and how different aspects of the concept are used as a theoretical base. In this paper, we analyse different definitions used in empirical studies. First, we did a systematic research review resulting in 19 empirical studies focusing on functional thinking with an appropriate theoretical underpinning. The definitions were analysed using an AI tool. After that, we analysed the results using intrinsic mathematical properties of how functions can be defined in mathematics to identify core aspects of the definitions. According to the analysis, two definitions capture most of the key aspects of functional thinking, and most empirical studies use these key concepts. These two definitions treat functional thinking as products or products and processes. One definition used in one empirical study stands out by theoretically operationalizing functional thinking as a process. As such, different ontological assumptions are made in the studies; however, in some cases, having the same epistemological outcome. From a methodological point of view, the cosine similarity matrix was a useful tool for an ontological analysis, but a qualitative analysis is still needed to make meaning of it

Miniaturized calorimeters for high pressure, strong magnetic field, and low temperature conditions

Calorimetry is a powerful approach for investigating condensed matter systems, with nanocalorimetry being particularly useful for studying small samples, with high resolution and accuracy. This thesis presents the development of nanocalorimeters specifically designed for extreme conditions, such as high pressure, strong magnetic fields, and low temperatures. Introducing high pressure or magnetic fields as tuning parameters in specific heat measurements at low temperatures can enhance the understanding of the underlying physical properties of novel materials. Two distinct nanocalorimeters are built and discussed in this thesis; one for sample rotations in high magnetic fields and another for high-pressure applications. The high-field nanocalorimeters are fabricated on SiNx membranes for specific heat measurements down to 30 mK. Miniaturization is performed to extend their use for angular-dependent measurements in high magnetic fields, so far used up to 41 T. In contrast, the high-pressure nanocalorimeters are fabricated on a robust substrate, which is small enough to fit inside small sample volumes of high-pressure cells. The key component of a calorimeter is a thermometer. Both these calorimeters use a newly developed thin film ceramic metal oxide thermometer, which shows high sensitivity and minimal magnetoresistance across a wide temperature range. A high-pressure setup is designed for transport and AC calorimetry measurements under elevated pressures. This setup employs a split gasket approach that incorporates multiple electrical connections entering the sample volume through a substrate. This setup reaches moderate pressures comparable to those in standard setups using similar anvils, with the advantage of reusable and easily reproducible components. Finally, specific heat measurements of Eu-doped GdCd7.88 quasicrystals and GdCd6 approximant systems are performed in fields up to 12 T, using a membrane-based nanocalorimeter. The results show the presence of spin-glass behavior in the quasicrystals and an antiferromagnetic transition in the approximant crystals at low temperatures

Understanding the long-term trends and seasonality of Arctic atmospheric aerosol : Through the lens of black carbon and new particle formation

The Arctic region is witnessing changes on an unprecedented level. Surface air temperatures have increased at a rate four times the global average. Two of the main climate forcers that are responsible for perturbing the radiative balance in the Arctic are greenhouse gases and atmospheric aerosols. Aerosols are tiny solid or liquid particles suspended in the atmosphere that range in size from a few nanometres to tens of microns.  These particles affect the climate by interacting with radiation and influencing cloud formation, brightness, and longevity.  The work presented in this thesis aims to improve our understanding of the drivers and mechanisms involved in controlling both the seasonal variations and the long-term changes in Arctic aerosols, and analyse the general aerosol lifecycle.  In a changing Arctic, both the emissions of anthropogenic and natural aerosol particles have and are expected to continue to change. For one, the long-range transport of anthropogenic aerosols is likely to continue to decline with reductions in emissions. Measurements of Arctic aerosols were carried out at a research observatory on Svalbard. In this thesis, a variety of instrumentation and measurements were used to assess seasonal and long-term changes in various aerosol-related variables.  The work in this thesis shows that the concentration of light-absorbing aerosol particles has decreased significantly over the past two decades, with the largest decrease in contributions from northern Siberia.  This thesis argues that a quarter of the overall reduction is due to changes to the removal processes via wet scavenging. In this thesis, the changes in environmental parameters along the transport pathway to the site are explored. From this perspective, precipitation is shown to act as both a source and a sink, impacting the number of particles depending on their size, whilst solar radiation is shown to promote an increase in the number of aerosol particles over the entire size spectrum.  Furthermore, using the first long-term time series measuring light-absorbing particles inside and outside of clouds, the process of nucleation scavenging is explored. Increased uptake of light-absorbing particles into cloud droplets is presented from April until October. Incorporation of these particles into cloud droplets is shown to be dependent on temperature and cloud water content. Lastly, the frequency in the production of small particles, barely a nanometre in diameter, in the vicinity of Svalbard is shown to be heavily influenced by solar radiation and the total surface area of pre-existing aerosol particles.  The Greenland Sea is shown to be a relatively larger source of these small particles compared to neighbouring seas.  Its shown that the total surface area of pre-existing aerosols within airmasses is reduced through cloud and precipitation events, setting the stage for new particle formation and the replenishment of aerosol particles in the presence of solar radiation.  Understanding how these findings can be broadened and applied across a larger geographical region remains to be answered. Additionally, the overall effect these mechanisms and changes can have on the radiative balance in the Arctic requires further exploration

Emerging analytical tools and strategies for PFAS discovery

Per- and polyfluoroalkyl substances (PFAS) are a diverse class of synthetic chemicals that have garnered significant attention due to their persistence, widespread occurrence, and adverse health effects. Thousands of PFAS are registered globally, occupying a wide chemical space and requiring diverse methods for their identification and quantification. Despite vast improvements in analytical coverage over the last two decades, there are increasing concerns that unknown or emerging compounds continue to be overlooked. To address these concerns, a number of new analytical strategies have emerged: one is the so-called fluorine mass balance (FMB) approach, which involves subtracting the fluorine attributed to target PFAS (∑PFAS) from the total- or extractable organic- fluorine (TF and EOF, respectively) to deduce the quantity of unknown PFAS in a sample. This approach can be used to prioritize samples with high levels of unidentified fluorine for further interrogation. A second approach involves high resolution mass spectrometry (HRMS)-based suspect and non-target screening, which aims to identify novel PFAS in environmental samples. This thesis develops and/or applies these emerging analytical methods in order to improve our understanding of PFAS sources and occurrence in the environment, with FMB experiments applied throughout Papers I to III, and suspect- and nontarget screening used in Papers II-IV. In Paper I, an FMB of different components of artificial turf (backing, filling, and blades) revealed high levels of total fluorine in all samples (ranges of 16−313, 12−310, and 24−661 μg of F/g in backing, filling, and blades, respectively), while EOF and target PFAS occurred in <42% of all samples (<200 and <1 ng of F/g, respectively). Further experiments confirmed the absence of both fluoride and perfluoroalkyl acid precursors in these samples. Collectively, these results point toward the occurrence of a polymeric organofluorine, consistent with patent literature, and shines a light on the use of fluoropolymers in plastic and rubber production which might complicate disposal of these products. In Paper II, both FMB and HRMS-based suspect screening were applied to liver samples from a variety of marine mammals. As part of this work, an ionization efficiency-based model for quantification of substances lacking analytical standards was trained and validated. Thereafter, the model was used to quantify PFAS detected by suspect screening, and ultimately reduced the quantity of unidentified organofluorine from 13-70% (median: 32%) down to 0-27% (median: 17%). Paper III delved further into FMB and non-target analysis of marine mammals, this time focusing on blubber, where unexpectedly high levels of unknown EOF were previously uncovered in the blubber of a Greenlandic killer whale. Using a combination of ion exchange solid phase extraction, gas chromatography-ion mobility-high resolution mass spectrometry (GC-IM-HRMS), and collision cross section (CCS)-based prioritization (i.e. CCS [Å2] < 0.2 Å2 × m/z + 100 Å2) the number of plausible organofluorine peaks was reduced from several thousand down to several hundred. Structures were proposed for the most abundant on this list based on fragmentation. Five novel fluorotelomer sulfones were identified at confidence level 1 (CL 1: identified with standard) and quantified, accounting for up to 75% of the EOF in blubber. Finally, in Paper IV methanol extracts of municipal wastewater treatment plant sludge, as well as sludge and dust standard reference materials (SRMs), were characterized by liquid chromatography-IM-HRMS, and the same CCS filter used in Paper III was applied, together with two additional PFAS prioritisation strategies (mass defect and mass/number of carbon atoms). A total of Fluorine mass balance, suspect, and non-target screening are critical tools for expanding our understanding of PFAS contamination in diverse environmental and biological matrices. Integrating these advancements is essential for more comprehensive exposure assessments and informed policy decisions.

Teachers understanding of inclusive education and challenges in implementation in the English education system in Cameroon

This study examines teachers understanding of inclusive education in the English education subsystem in Cameroon and the challenges they experience in its implementation. Based on interviews with some selected teachers, the findings reveal a strong focus on students with disabilities as well as the view of inclusive education as the removal of cultural barriers that pervade access and participation in education. The results also indicate policy inadequacies, school organisational insufficiencies, teacher incompetence and societal barriers to be some of the challenges these teachers encounter when implementing inclusive education

Synthetic approaches to cohomology, homology and homotopy

This thesis is based on five papers on the development of synthetic homotopy theory in homotopy type theory (HoTT), a relatively recent system of mathematics which extends Martin-Löf type theory with higher inductive types and univalence. The thesis is, in particular, concerned with the development of (co)homology theories and operations, but it also covers other (often related) cornerstone results from homotopy theory. Most results presented here have been computer formalised, i.e. digitally verified by a computer, in the verification software (or proof assistant) Cubical Agda. Paper I presents a construction and computer formalisation of cohomology rings in HoTT. To this end, the associativity of cup products is proved – a seemingly easy problem which has turned out to be rather difficult in HoTT due to complicated coherences which arise when attempting a naïve proof. The paper also contains various computations of cohomology groups and rings, the Gysin sequence and a discussion of computational aspects of the computer implementation in Cubical Agda. The paper, in many ways, serves as an introduction to the remainder of the thesis. Paper II presents a computer formalisation of Brunerie’s (2016) computation of the fourth homotopy group of the 3-sphere. In addition to this, we provide a vastly simplified version of Brunerie’s proof by introducing a new way of computing (both by hand and by normalisation in Cubical Agda) the so-called Brunerie number, i.e. the order of the homotopy group in question. Paper III is devoted to solving another surprisingly difficult problem in HoTT, namely that of showing that the smash product is (1-coherent) symmetric monoidal. This is done by developing a heuristic for constructing homotopies over large iterated smash products. This heuristic is also expressed as a formal theorem which, in essence, presents iterated smash products as retracts of homotopically simpler spaces. Paper IV presents work on cellular homology in HoTT. We develop basic theory of CW complexes and prove a constructive analogue of the cellular approximation theorem, as well as a special case of the CW-approximation theorem which states that two different notions of n-connectedness are equivalent. The cellular approximation theorem is then used to prove functoriality of cellular homology, and the special case of the CW-approximation theorem is used to prove the Hurewicz theorem. We also verify that our homology theory satisfies the Eilenberg–Steenrod axioms. Paper V uses the cohomology theory from Paper I in order to construct the Steenrod squares, a set of cohomology operations for mod 2 cohomology. We use (and generalise) a definition of these operations due to Brunerie (2017), but go much further and prove their characterising properties, e.g. the Cartan formula and the Adem relations. This is done by reducing most problems to a ‘master theorem’ which is a simple-to-state but difficult-to-prove Fubini-like statement concerning so-called unordered joins. We use the squares to complete an alternative computation of the fourth homotopy group of the 3-sphere suggested in Paper II

Advances in Sustainable Catalytic Transformations for Organic Synthesis

The use of metal catalysts is key for many chemical industrial processes. Many of these rely on noble metals which, despite their excellent performance, are scarce and present environmental and societal challenges. Thus, the development of alternative and sustainable synthetic protocols are of utmost importance. Transitioning to abundant metals, such as first-row transition metals (also known as base metals), is the most logical and preferred strategy. However, this transition is not straightforward due to the different reactivity that these metals present. Another strategy to minimize the impact of noble metals is to use them in a more efficient manner. The work of this thesis contributes to the development of synthetic methods for organic chemistry motivated by sustainability aspects. The strategies explored were transitioning to base metal catalysis, use of light and electricity as energy sources, and the immobilization of homogeneous catalysts. First, a method was developed using an iron complex for the synthesis of allenylboronates from propargyl acetates. Secondly, a heterogeneous photocatalyst PCN-222(Pd) was developed and used for the aerobic cross-condensation of amines. Thirdly, the immobilization of Ru(BINAP)(OAc)2 on cellulose was developed and used for the asymmetric hydrogenation of aliphatic α,β-unsaturated carboxylic acids. Finally, the use of nickel foam as electrocatalyst for the hydrogenation of alkenes was investigated and compared with the traditional Pd/C and H2 gas method via life cyle, toxicological and safety assessments.  Although catalysis is a tool that can assist in achieving this goal, it is important to highlight that many other aspects require attention, such as recyclability, the use of greener solvents, transition to renewable feedstocks like bio-ethanol, and shorter synthetic protocols, to name a few. Finally, it is important to understand that addressing all the sustainability aspects of an organic chemistry process is very challenging. However, the improvement of part of these aspects can contribute to the development of a sustainable chemistry in a step-wise manner.

Comparing semantic frameworks for dependently-sorted algebraic theories

Algebraic theories with dependency between sorts form the structural core of Martin-Löf type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical structures have been introduced to model them (contextual categories, categories with families, display map categories, etc.) Comparisons of these models are scattered throughout the literature, and a detailed, big-picture analysis of their relationships has been lacking. We aim to provide a clear and comprehensive overview of the relationships between as many such models as possible. Specifically, we take comprehension categories as a unifying language and show how almost all established notions of model embed as sub-2-categories (usually full) of the 2-category of comprehension categories.Received the Best Paper award at APLAS 2024</p

Educating Responsible Media Users : Opportunities and Challenges in Enhancing Source Criticism Skills among Students in Social Studies for Grades 4-6

Syftet med detta självständiga arbete är att undersöka hur SO-lärare i årskurs 4-6 upplever att de planerar och genomför undervisning om källkritik i samhällskunskap, samt vilka utmaningar och möjligheter de möter. Detta undersöks genom att besvara följande frågeställningar: “Hur beskriver SO-lärare i årskurs 4-6 sin planering av och undervisning om källkritik i samhällskunskap?” och “Vilka utmaningar och möjligheter med källkritiksundervisning i samhällskunskap i årskurs 4-6 framträder i SO-lärarnas berättelser?”. Studien bygger på kvalitativa intervjuer med sju SO-lärare (L1-L7) och syftar till att belysa hur undervisningen kan anpassas för att stärka elevers medie- och informationskunnighet i en digital tidsålder. Dessa intervjuerna analyserades ur ett pragmatiskt perspektiv med en fenomenografisk ansats. Resultaten visar att lärare ofta ställs inför utmaningar kopplade till elevers användning av sociala medier, där plattformar som TikTok och Instagram används som informationskällor trots låg trovärdighet. Flera lärare beskrev behovet av att integrera autentiska exempel från elevernas vardag i undervisningen, vilket tidigare forskning stödjer som en effektiv metod för att öka elevers engagemang och reflektion. En central problematik är elevers bristande förståelse för algoritmernas påverkan på informationsflöden, vilket lyfts fram av både lärarna och tidigare studier

”Manipulation och hot är en del av vardagen” : En intervjustudie om statliga tjänstemäns upplevelser av otillåten påverkan vid klientnära arbete

Uppsatsen utgår från en kvalitativ ansats och ett kriminologiskt perspektiv för att studera ett mindre utforskat fält och fenomenet otillåten påverkan. Fenomenet är ett paraplybegrepp som inrymmer olika medvetna beteenden som används för att förmå tjänstepersoner att fatta ett visst beslut. Det kan vara i form av kriminaliserade handlingar, men även andra olämpliga beteenden i kontexten av fältets yrkesmässiga relationer mellan anställda och klienter. Syftet är att få insikt i statliga tjänstemäns upplevelser och därigenom utöka kunskapen om otillåten påverkan. Frågeställningarna är vilka erfarenheter som förekommer samt tänkbara faktorer som kan påverka upplevelserna. Studien genomförs med hjälp av en tematisk intervjuguide och semistrukturerade intervjuer, vilka transkriberas, kodas och tematiskt analyseras. Analysen relateras till Goffmans begreppsram och tidigare forskning om emotionellt arbete, institutionell kultur och tjänstemäns upplevelser inom säkerhetsyrken. Studiens urval består av fem statliga tjänstemän arbetande inom samma organisation, av låsta institutioner, utspridda över Sverige. Inledningsvis var fältet skeptiskt till medverkan vilket ställde höga krav på ett strikt forskningsetiskt förhållningssätt med ett hemlighetshållande av tjänstemännens identitet, med hänsyn till deras säkerhet och fältet i stort. Utifrån mina förkunskaper och genom studiens utformning fick jag ett förtroende från deltagarna och gavs möjligheten att få insyn i fältets dolda rum. Bidraget till forskningsfältet är en inblick i fältets definition och komplexiteten av otillåten påverkan. Resultaten redogör för manipulation som vanligast förekommande medan kriminaliserade handlingar inledningsvis separerades från definitionen. Fenomenet betraktas vara normaliserat och något som tjänstemännen förväntas hantera i yrkesutövningen. Vidare insikt är hur arbetsplatsernas institutionella kultur och deltagarnas erfarenheter präglar bedömningen och hantering av beteenden, vilket medför skillnader i upplevelser. Ett av de primära fynden är fältets upprätthållande av en fasad som vidare påverkar tjänstemännens yrkesroll och livsstil.