Categories in Control

Control theory uses "signal-flow diagrams" to describe processes where real-valued functions of time are added, multiplied by scalars, differentiated and integrated, duplicated and deleted. These diagrams can be seen as string diagrams for the symmetric monoidal category FinVect_k of finite-dimensional vector spaces over the field of rational functions k = R(s), where the variable s acts as differentiation and the monoidal structure is direct sum rather than the usual tensor product of vector spaces. For any field k we give a presentation of FinVect_k in terms of the generators used in signal flow diagrams. A broader class of signal-flow diagrams also includes "caps" and "cups" to model feedback. We show these diagrams can be seen as string diagrams for the symmetric monoidal category FinRel_k, where objects are still finite-dimensional vector spaces but the morphisms are linear relations. We also give a presentation for FinRel_k. The relations say, among other things, that the 1-dimensional vector space k has two special commutative dagger-Frobenius structures, such that the multiplication and unit of either one and the comultiplication and counit of the other fit together to form a bimonoid. This sort of structure, but with tensor product replacing direct sum, is familiar from the "ZX-calculus" obeyed by a finite-dimensional Hilbert space with two mutually unbiased bases.Comment: 42 pages LaTe

Learning an Artist's Style: Just What Does a Pigeon See in a Picasso?

Judgments of style in art, music, and literature are commonplace, although the mechanisms providing for this structural sensitivity are not well understood. Watanabe, Sakamoto, and Wakita (1995) showed that pigeons trained to discriminate colour slides of paintings of Picasso from those of Monet could generalise this discrimination not only to new paintings of Picasso and Monet, but also to paintings of other cubist and impressionist painters. These results suggest that the bases for such judgments of artistic style may be simpler than normally thought. This tacit sensitivity to artistic style is explored in terms of a simple PCA network model applied to pixel-maps of the paintings. The eigenvectors obtained from the singular value decomposition of sets of these pixel-maps provide for descriptions of the stimuli in terms of visual “macro-features”. These macro-features provide a simple basis not only for recognising previously-experienced paintings, but for the successful discrimination of novel paintings into various style categories. A summary of simulations of the performance of Watanabe et al.’s pigeons using precisely the same stimuli and tasks is provided. The results suggest that the eigen-decomposition is a necessary first-step, and that the bases for judgments of style may indeed be quite simple

The Golden Retriever Rule: Alaska’s Identity Privilege for Animal Adoption Agencies and for Adoptive Animal Owners

Sedan 1900-talets mitt har användandet av tegelkonstruktioner i bostadsbyggandet minskat kraftigt; materialet har under modernismen upplevts otidsenligt och byggnadssättet har ansetts ineffektivt. Trots att kanalmurstekniken, som är en byggteknik med bärande tegelkonstruktion och högt isoleringsvärde, togs fram på 1930-talet för att följa hårdare energihushållningskrav, har ändå lätta träregelkonstruktioner dominerat det svenska småhusbyggandet. Kraven på energihushållning har under åren ökat successivt och livscykelanalysen (LCA) har utvecklats. LCA är en metodik som analyserar produkters eller tjänsters klimatbelastning ur livscykelperspektiv. Svårigheter har dock funnits i att omsätta metodiken på större komponenter än enskilda material. Därför har europastandarder tagits fram som enkom tjänar till att systematisera livscykelanalyser av hela byggnader och de kommer att följas i denna studie. Syftet med examensarbetet är att jämföra hur ett typhus med tegel som stommaterial belastar miljön under produktion och drift i en livscykel satt till 100 år, jämfört med ett motsvarande trätyphus. Till tegelhusets nackdel talar den höga energiåtgången vid materialframställningen. Trä å sin sida löper stor risk för förkortad livscykel i och med riskerna för fuktskador. För att undersöka skillnaderna i trä- och tegelkonstruktioner har en typhusritning i kanalmurskonstruktion analyserats mot en motsvarande träkonstruktion, där byggnadstyperna har samma boarea och väggkonstruktionerna samma värmemotstånd. För att få fram husens skillnad energiåtgång under driftskedet har energibehovsberäkningar utförts för byggnaderna. Livscykelanalysen har utförts i programvaran Anavitor utifrån 3D-modeller med byggnadsinformation som matchas mot en materialdatabas med livscykeldata. Ur jämförelsen har resultat kunnat hämtas på vilken av konstruktionerna som belastar miljön minst över livscykeln, med avseende på klimatbelastning räknat i koldioxidekvivalenter. Resultat visar att ett tegelhus belastar miljön dubbelt så mycket som ett trähus i produktionsfasen medan tegelhuset är miljövänligare avseende underhåll och drift. Efter 100 år är skillnaden 7,3 ton koldioxidekvivalenter, till trähusets fördel. Enligt livscykelanalysen har byggnaderna, enligt de antaganden som gjorts, belastat miljön lika efter 168 år. Till tegelhusets fördel talar dess säkerhet gällande livslängd, beständighet, fuktsäkerhet och goda möjlighet till återbruk av stommaterialet.Since the mid-1900s has brick building marginalized; the material has in the modernist era been experienced as dated and the construction method considered inefficient. In the 1930s the canal wall technique were developed to meet the coming stringent energy requirements. Despite opportunities to meet modern building norms have yet lightweight timber structures dominated the Swedish construction sector concerning single-family houses since then. The requirements for energy conservation have increased over the years to an even greater degree, and Life Cycle Assessment (LCA) has been developed; a methodology that analyzes products from a life cycle perspective. There have been difficulties to put the methodology on larger components than individual materials. Therefore, European Standards have been developed that specifically serve to systematize Life Cycle Assessments of entire buildings, which will be followed in this study. The purpose of this study is to compare which impact a standard house with brick structure has a on the environment in a lifecycle set to 100 years, compared with a corresponding timber structure. To the disadvantage for a brick house speaks the high energy consumption in material production. Timber structures at their part are at high risk for shortened life cycle due to risk of moisture damage. To examine the differences in wood and brick structures has a standard house drawing in canal wall technique been analyzed against a corresponding wooden construction. The building types have the same floor area and the wall constructions have the same heat resistance. To receive the differences in energy use during the operational phase between the buildings has energy calculations been made. The life cycle analysis has been performed in the software Anavitor based on 3D models with building information that is matched against a database of materials life cycle data. The results from the comparison are measured in terms of carbon dioxide equivalents, and will show which construction type will make least impact on the environment. Results show that a brick house has doubled environmental impact compared to a wooden house in the production phase. The brick house is a better alternative concerning environmental impact during operational phase and maintenance. After 100 years, the difference is 7,3 tons of carbon dioxide equivalents to the advantage of the wooden house. According to the LCA and the assumptions made, the buildings have charged the environment equally after 168 years. To the advantage of the brick house speaks its longevity, durability, moisture resistance and good opportunity for reuse of the bricks

Stick or switch? Consumer switching in 14 retail markets across Europe. ESRI Research Bulletin 2019/12

Consumer advocates and regulators encourage the public to search for better deals in markets for services like telecoms, energy and insurance, arguing that there are opportunities to save money and get better service by switching. Consumer switching can also help spur competition. Yet rates of switching vary a lot across markets: many people seldom think about changing their package or service provider and fewer still actually switch. If research can identify some of the barriers that deter people from searching or switching in particular markets, maybe policies can be designed to help enable and encourage switching behaviour. This study examines some of the factors that affect switching rates for European consumers across a wide range of markets