Licentiatavhandling Uppsala, Univ : 2004. / Härtill 2 uppsatser.

<p>This thesis will give an introduction to the concepts of cellular automata and higher order cellular automata, and go through several examples of both. Cellular automata are discrete systems of cells in an n-dimensional grid. The cells interact with each other through the use of a rule depending only on local characteristics, which lead to some global behaviour. Higher order cellular automata are hierarchical structures of cellular automata with added possibilities for dynamic local interaction. We first give an introduction for non-mathematicians. A mathematical definition of cellular automata follows, and we illustrate the many possibilities with a few examples. Higher order cellular automata are introduced and defined, and we look at the consequences higher order cellular automata has on optimization of computer implementations. Finally we apply higher order structures to some of the examples, and study the effects.</p>

This thesis will give an introduction to the concepts of cellular automata and higher order cellular automata, and go through several examples of both. Cellular automata are discrete systems of cells in an n-dimensional grid. The cells interact with each other through the use of a rule depending only on local characteristics, which lead to some global behaviour. Higher order cellular automata are hierarchical structures of cellular automata with added possibilities for dynamic local interaction. We first give an introduction for non-mathematicians. A mathematical definition of cellular automata follows, and we illustrate the many possibilities with a few examples. Higher order cellular automata are introduced and defined, and we look at the consequences higher order cellular automata has on optimization of computer implementations. Finally we apply higher order structures to some of the examples, and study the effects.

.

Inom den moderna matematiken har delområdet topologi fått ett allt större intresse och ett ökat användningsområde. Den här uppsatsen, som har karaktär av litteraturstudie, behandlar dels översiktligt grundläggande punktmängdstopologi (allmän topologi), men arbetets centrala del är dock inriktad på algebraisk topologi. Det har visat sig att när de grundläggande, traditionella, verktygen inom topologin inte räckt till så har det varit fruktbart att omformulera problemen och det man vill undersöka så att algebra har kunnat tillämpas. Här redovisas några av den algebraiska topologins mer centrala satser och samband, bland annat: Jordans kurvsats, Cauchys integralformel, Brouwers fixpunktssats, Lefschetz fixpunktssats och satsens relation till Eulerkaraktäristik samt helt översiktligt, differentialtopologi, där ”the hairy ball theorem” behandlas. Uppsatsens målgrupp är personer med grundläggande kunskaper i matematik på högskolenivå och som vill få en grundläggande orientering eller ökad insikt i ämnet.

Given a multiplicative cohomology theory represented by a spectrum, E,we define its associated geometric homology theory by means of bordism. Restrictedto CW pairs, we show how the geometric homology theory is naturally equivalent to the homology theory associated E. This was done by M. Jakob in 2000, and we give an expositionfollowing his approach. We also consider a naturally occurring cap product.

SCADA is the primary system for control and monitoring of distribution grids. As the expectations on how the grid must operate changes with the increased use of renewable energy sources, it also requires new methods of monitoring. Phasor Measurement Units (PMU) measures the phase angle and amplitude synchronously with GPS. A collaboration between U.C Berkeley and Power Standard Lab researches the possibilities of implementing synchrophasors in distribution grids. These devices are called micro-PMU and will provide similar services available for transmission grids, though adapted for lower voltage levels. Synchrophasors are useful in the development of a smarter distribution network, which consequently makes them interesting for the Swedish electricity market. Martin Gahr, a student at Berkeley / ETH, has developed a method to determine the topology of a distribution grid using micro-PMU's. The method compares calculated values from SCADA with values from micro-PMU's. The smallest difference between the two readings clarifies the topology. In this thesis the method is used to study an existing distribution grid in central parts of a medium-sized Swedish city. The method gives a satisfactory result when it is implemented on the mashed parts of the distribution grid. There are also indications that micro-PMU's must not be placed at every node to provide a reliable result. Although the method seems to be working on mashed parts of a Swedish distribution grid, it is not particulary interesting to implement the method in reality.

Diss. (sammanfattning) Uppsala : Univ., 2004. / Härtill 2 uppsatser.

Diss. (sammanfattning) Uppsala : Univ., 2003. / Härtill 3 uppsatser.

I denna uppsats undersöker vi Game/Media Jam, Hackathon och liknande koncept och försökerskapa en metod för att ta fram en modell för deras topologi. Vi ämnar att undersöka degemensamma punkterna Jams och Hackathons har via deras regler, samt jämföra detta med JamSessions. Vidare kommer vi försöka identifiera reglernas syften. Dessa syften sätter vi i entopologiskt mätbar intervall som sedan kan överföras på den topologisk modellen. Sedan användsdessa resultat för att jämföra regelrätta Jams/Hackathons, närliggande koncept och arrangemangsom endast har vissa gemensamma punkter med Jams, för att se om modellen kan påvisa om ettarrangemang har en känsla av Jam utan att faktiskt vara det. / In this thesis we will study Game/Media-Jams, Hackathons and similar concepts and try to establisha method to create a model for their topology. We intend to investigate what these concepts have incommon through their rules and compare that to Jam Sessions. Following this we will try to extractthe purpose of the rules. These purposes will then be put in topologically measurable intervals thatcan be transfered onto the topological model. The results will then be used to compareJams/Hackathons, similar concepts and events that only have a few things in common with Jams, tosee if the model can determine if an event is in the spirit of a Jam without actually being one.