Homotopy Type Theory (HoTT) is a quite recent branch of research in mathematical logic, which provides interesting connections among various areas of mathematics. It was first introduced by Vladimir Voevodsky as a means to develop synthetic homotopy theory, and further advancements suggested that it can be used as a formal foundation to mathematics. Among its notable features, inductive and higher inductive types are of great interest, e.g. allowing for the study of geometric entities (such as spheres) in the setting of HoTT. However, so far in most of the literature higher inductive types are treated in an ad-hoc way; there is no easy general schema stating what an higher inductive type is, thus hindering the study of the related proof theory. Moreover, although Martin-Löf Type Theory has been deeply and widely studied, many proof theoretic results about its specific variant used in HoTT are folklore, and the proofs are missing. In this final talk, we provide an overview on some results we obtained, aiming to address these problems. In the first part of the talk, we will discuss a normalization theorem for the type theory underlying HoTT. In the second part of the talk we will propose a general syntax schema to encapsulate a relevant class of higher inductive types, potentially allowing for future study of the proof theory of HoTT enriched with such types.

I denna uppsats så undersöks digitala beställningsplattformar som har blivit en integrerad del irestaurangbranschen genom att dessa parter tillsammans integrerar sina resurser för att någemensamma mål. Denna integration har påverkat tjänstemarknadsföringen och äventjänstekvaliteten. Syftet med arbetet är att få en tydligare bild om hur kundupplevelsen har påverkatsav att digitala mellanhänder har fått större kontroll över tjänstemarknadsföringen. Undersökningenutgjordes av sekundärdata i form av tidigare undersökningar samt semi-strukturerade intervjuer medkunder som tidigare beställt genom digitala beställningsplattformar för mat. Intervjuerna gavinformation om subjektiva känslor, förväntningar och upplevelser som vi sedan jämfört med tidigareundersöknignar och vårt teoretiska ramverk. Undersökningen kom fram till att digitalabeställningsplattformar påverkar kundupplevelsen positivt genom sin tjänstemarknadsföring men attdet fortfarande finns stora brister i de digitala beställningsplattformarnas tjänstekvalitet vilket skaparstor variation i kundernas individuella upplevelser.

Senegal ranks second for mango production among West African countries and has the potential to competitively produce mangoes for the European market. Colletotrichum gloeosporioides Penz. and Sacc. has historically been considered the causal pathogen of anthracnose of mango and other fruits, but is now known to represent a species complex. Field trials to examine the efficacy of fungicides and biofungicides were conducted in southern and northern production regions of Senegal. In three southern trials, Sonata (Bacillus pumilus strain QST 2808), Serenade Optimum (Bacillus subtilis strain QST 713), and sodium molybdate provided 63%, 67% and 76% control of disease severity, respectively, whereas thiophanate methyl and azoxystrobin provided 77% and 78% control, respectively. Disease severities of all treatments were significantly lower than that of the control. Thiophanate methyl and azoxystrobin produced more disease-free mangoes (64 and 62%, respectively) than Serenade (49%), sodium molybdate (44%), and Sonata (38%). Differences within each trial were not statistically significant, but when all trials were combined, all treatments resulted in significantly more disease-free mangoes than the control. Among treatments, thiophanate methyl and azoxystrobin resulted in significantly more disease-free mangoes than Sonata. No results were obtained in the northern orchards due to an absence of disease development. Sequencing of the ITS gene region of 30 Colletotrichum isolates from mangoes from different regions in Senegal indicated that all belonged to the C. gloeosporioides species complex. Sequencing of the ApMat intergenic region identified all of them as most closely resembling C. siamense. / Master of Science in Life Sciences

Specific non-relativistic quantum mechanical one-dimensional systems, interacting via point interactions, are discussed within the resolvent algebra setting.

Bakgrund Enligt kursplanen i ämnet hem-och konsumentkunskap bör undervisningen genomsyras av begreppen hälsa, ekonomi och miljö och även handla om olika mattraditioner. Ämnet kan bidra med utbildning om alternativa proteinkällor till kött som baljväxter och framtida livsmedel som till exempel insekter. I den här studien undersöktes vad lärare ansåg vara viktigt i undervisningen inom mat- och måltidskultur och hur de gjorde sina val av livsmedel till undervisningen. Syfte Syftet med studien var att undersöka vad lärare anser vara viktigt i undervisningen inom mat- och måltidskultur och hur lärare gjorde sina val av livsmedel och alternativa proteinkällor. Metod I studien användes en kvalitativ metod med en semistrukturerad intervju. Tre lärare i åldrarna 46-66 år intervjuades via Teams. Intervjuerna transkriberades och analyserades med hjälp av kvalitativ innehållsanalys. Resultat Resultaten visade att lärarna ansåg att mat- och måltidskultur i undervisningen var viktig för att eleverna skulle få en förståelse för betydelsen av en trivsam samvaro kring måltiden och använda sig av ett bra bordsskick. Det var även viktigt att diskutera andra länders mat- och måltidskultur samt vid högtider tillaga något som förknippades med svenska traditioner. Trots en begränsad budget vid inköp försökte lärarna köpa livsmedel av god kvalitet. Kött valdes ofta bort som proteinkälla till förmån för vegetariska alternativ som baljväxter. Slutsats Lärarna ansåg att måltidskultur var en viktig del av undervisningen och att man även belyste andra länders matkulturer och traditioner. Lärarna var styrda av en begränsad budget när de gjorde sina inköp till undervisningen men försökte att köpa varor med kvalitet och ekologisk märkning. Vid alternativa proteinkällor till kött valde lärarna baljväxter och de kunde tänka sig att i framtiden använda insekter i undervisningen. / Background According to the curriculum in the subject of Home and Consumer Studies, the teaching should be permeated by the concepts of health, economy and environment and also deal with different food traditions. The subject can contribute with education about alternative protein sources to meat such as legumes and future foods such as insects. In this study, what teachers consider to be important in teaching food and meal culture and how they make their choices of food for teaching were investigated. Purpose The purpose of the study was to investigate what teachers consider important in teaching food and meal culture and how teachers made their choices of foods and alternative protein sources. Method The study used a qualitative method with a semi-structured interview. Three teachers aged 46-66 were interviewed via Teams. The interviews were transcribed and analyzed using qualitative content analysis. Results The results showed that the teachers considered that food and meal culture in teaching was important for the students to gain an understanding of the importance of a pleasant time together around the meal and to use good table manners. It was also important to discuss the food and meal culture of other countries and to prepare something associated with Swedish traditions on holidays. Despite a limited purchasing budget, the teachers tried to buy good quality food. Meat was often chosen as a protein source in favor of vegetarian alternatives such as legumes. Conclusion The teachers were guided by a limited budget when making their purchases for teaching, but tried to buy goods with quality and organic labeling. For alternative protein sources to meat, the teachers chose legumes and they could imagine using insects in teaching in the future.

This thesis treats mathematical models for host-parasitoid interactions. It is composed of three parts. In the first part, a class of such models is analyzed theoretically. It focuses on the phenomena of multiple coexistence equilibria of competing parasitoid species. The second part is about a model for determining how a parasitoid release should be timed to optimally control the invasive fruit fly Drosophila suzukii. The third part analyzes an experiment for releasing parasitoids in a greenhouse which is infested by D.suzukii. The models presented are used to discuss how to improve such biological control strategies.

Feynman path integrals introduced heuristically in the 1940s are a powerful tool used in many areas of physics, but also an intriguing mathematical challenge. In this work we used techniques of infinite dimensional integration (i.e. the infinite dimensional oscillatory integrals) in two different, but strictly connected, directions. On the one hand we construct a functional integral representation for solutions of a general high-order heat-type equations exploiting a recent generalization of infinite dimensional Fresnel integrals; in this framework we prove a a Girsanov-type formula, which is related, in the case of Schrödinger equation, to the Feynman path integral representation for the solution in presence of a magnetic field; eventually a new phase space path integral solution for higher-order heat-type equations is also presented. On the other hand for the three dimensional Schrödinger equation with magnetic field we provide a rigorous mathematical Feynman path integral formula still in the context of infinite dimensional oscillatory integrals; moreover, the requirement of independence of the integral on the approximation procedure forces the introduction of a counterterm, which has to be added to the classical action functional (this is done by the example of a linear vector potential). Thanks to that, it is possible to give a natural explanation for the appearance of the Stratonovich integral in the path integral formula for both the Schrödinger and the heat equation with magnetic field.

The study of patterns in combinatorial structures has grown up in the past few decades to one of the most active trends of research in combinatorics. Historically, the study of permutations which are constrained by not containing subsequences ordered in various prescribed ways has been motivated by the problem of sorting permutations with certain devices. However, the richness of this notion became especially evident from its plentiful appearances in several very different disciplines, such as pure mathematics, mathematical physics, computer science,biology, and many others. In the last decades, similar notions of patterns have been considered on discrete structures other than permutations, such as integer sequences, lattice paths, graphs, matchings and set partitions. In the first part of this talk I will introduce the general framework of pattern posets and some classical problems about patterns. In the second part of this talk I will present some enumerative results obtained in my PhD thesis about patterns in permutations, lattice paths and matchings. In particular I will describe a generating tree with a single label for permutations avoiding the vincular pattern 1 - 32 - 4, a finite automata approach to enumerate lattice excursions avoiding a single pattern and some results about matchings avoiding juxtapositions and liftings of patterns.

Bakgrund/problem: Då svensk matproduktion länge varit dominerad av massproduktion och förädlade livsmedel, pekar nu trenden mot att allt fler intresserar sig för lokalproducerad mat. Detta innebär en möjlighet för lokalproducenter att sälja och marknadsföra sina varor i en större omfattning jämfört med tidigare. För att detta skall realiseras visar forskning att det krävs samarbete aktörerna emellan för att maximera värdet. Dock är forskningen begränsad i att förklara hur dessa samarbeten bör utformas. Syfte: Syftet med studien är att undersöka om en brandingmöjlighet skulle kunna ge upphov till ett horisontellt värdeskapande och vilka dimensioner som i så fall skulle vara kritiska i en affärsmodell för att möjliggöra denna typ av värdeskapande. Metod: Vätterns nutida förutsättningar för framtida matsamarbeten har formats som en fallstudie där kvalitativt arbetssätt använts för att samla empiriskt material. Resultatet bygger på en kombination av långa och korta intervjuer där respondenter från tre olika infallsvinklar hörts. Dessa tre infallsvinklar; samordning, aktör och marknadsföring har valts för att kunna få en holistisk syn på den angivna problematiken. Resultat/Bidrag: Resultatet av studien påvisar att en identifierad brandingmöjlighet via identitetsbyggande faktorer kan bygga ett starkt varumärke, vilket kan ligga till grund för ett horisontellt värdeskapande. För att det horisontella värdeskapandet i slutändan ska möjliggöras kräver affärsmodellen fyra kritiska dimensioner (balans av aktörer, finansiell och mobiliserande kraft, tillfredsställande ledning samt nätverkande). / Background/problem: For a long time the food industry has been dominated by mass production and refined food, though times are changing and more people are getting interested in locally produced food. This enables great possibilities for local food producers, which give them great opportunities to sell and market their goods, but it requires them to cooperate with each other. The present research is rather limited on how to create these types of cooperation in the food industry. Purpose: The purpose of this research paper is to examine if a branding opportunity can enable horizontal value co-creation and which dimensions that will be critical in a business model in order to enable that type of value co-creation. Method: A case study has been formed based upon the present conditions of Vättern to enable a food based cooperation, where qualitative methods have been used to collect data. The result is based upon a combination of in-depth and shorter interviews where the respondents represent three approaches; coordinator, stakeholder and marketing. These approaches were chosen in order to enable a holistic perspective on the problem area. Results/contribution: The study shows that a branding opportunity can result in a strong brand, which can build a foundation for horizontal value co-creation. In order to enable horizontal value cocreation, the business model requires four critical dimensions, (operators in balance, financial- and mobilizing muscle, a satisfying management and lastly, networking), which are identified in this study.

To date, most studies on the effectiveness of geotextiles on soil erosion rates were conducted in laboratory experiments for <1 h. Hence, at Hilton, East Shropshire, UK, this study investigated the effectiveness of palm-mat geotextiles (Borassus and Buriti mats) in reducing rainsplash erosion, runoff and soil loss and changing selected soil properties under field conditions over two years (January 2007-January 2009). Mat-cover effects on rainsplash erosion were studied in two sets on a loamy sand soil (0o slope). In both sets, six randomly-selected plots (each 1 m2) were completely matcovered and six were bare. Unlike Buriti mats, Borassus mat-cover on bare soil significantly (P<0.001) decreased rainsplash erosion (by ~89%). Duplicate runoff plots (10 x 1 m on a 15o slope) had five treatments (bare, permanent grass, Borassus completely-cover, Borassus buffer strip and Buriti buffer strip). Using Borassus buffer strips (area coverage ~10%) on bare soil decreased runoff by ~71% (P>0.05) and soil erosion by ~92% (P<0.001). Borassus buffer strip, Buriti buffer strip and Borassus completely-covered plots had similar effects in decreasing runoff and soil loss. However, the longevity of Borassus mats was ~twice that of Buriti mats. Despite physical protection, runoff control and sediment entrapment, biomat buffer zones may considerably alter and protect flow direction by presenting barriers and creating several cross-drains. Except Borassus completely-covered plots, all plots had significant (P<0.05) increases in topsoil (0-5 cm) bulk density and decreased aggregate stability. However, buffer strips were more effective in trapping fine particles than Borassus completely-covered plots. No treatments had significant (P>0.05) effects on changes in pH, soil organic matter, total soil carbon or N. Plots with Borassus mats significantly (P<0.05) increased total P and decreased total Ca. Treatments had no significant effects on changes in total S, Mg, Zn, Cu, Fe, Mn, Mo or Cl concentrations. Borassus buffer strips can effectively conserve soil and water and improve and maintain selected soil properties, with results similar to Borassus completely-covered plots. The mechanisms explaining the effectiveness of buffer zones require further studies under varied pedo-climatic conditions.