Conjugacy of Coxeter elements

For a Coxeter group (W,S), a permutation of the set S is called a Coxeter word and the group element represented by the product is called a Coxeter element. Moving the first letter to the end of the word is called a rotation and two Coxeter elements are rotation equivalent if their words can be transformed into each other through a sequence of rotations and legal commutations. We prove that Coxeter elements are conjugate if and only if they are rotation equivalent. This was known for some special cases but not for Coxeter groups in general

Multi-Adaptive Time-Integration

Time integration of ODEs or time-dependent PDEs with required resolution of the fastest time scales of the system, can be very costly if the system exhibits multiple time scales of different magnitudes. If the different time scales are localised to different components, corresponding to localisation in space for a PDE, efficient time integration thus requires that we use different time steps for different components. We present an overview of the multi-adaptive Galerkin methods mcG(q) and mdG(q) recently introduced in a series of papers by the author. In these methods, the time step sequence is selected individually and adaptively for each component, based on an a posteriori error estimate of the global error. The multi-adaptive methods require the solution of large systems of nonlinear algebraic equations which are solved using explicit-type iterative solvers (fixed point iteration). If the system is stiff, these iterations may fail to converge, corresponding to the well-known fact that standard explicit methods are inefficient for stiff systems. To resolve this problem, we present an adaptive strategy for explicit time integration of stiff ODEs, in which the explicit method is adaptively stabilised by a small number of small, stabilising time steps

Markbaserade sensorer för insamling av skogliga data : en förstudie

En förutsättning för skoglig planering på alla nivåer är att man har en god uppfattning om tillståndet i den stående skogen. K valiten på de beslut som fattas kommer därför att vara direkt beroende av mängden och kvaliten på den information som samlats in. Sensorer som radar, lidar och olika typer av digitala kameror används idag med framgång för fjärranalys där skogen avbildas från ovan. Föreliggande arbete syftar till att belysa de tekniska förutsättningarna för att utnyttja modem sensorteknik även för markbaserade mätningar. Detta skulle i så fall öppna möjligheter att automatisera fångsten av skogliga data som därmed skulle bli kostnadseffektivare samtidigt som nya typer av data skulle bli tillgängliga. På ett tidigt stadium valdes följande tekniker ut för att närmare studeras med avseende på lämplighet att ingå i ett inventeringskoncept: • Lidar. Lidar är en laserbaserad teknik för att mäta avstånd och riktning till objekt. Laserns fördelar gentemot andra typer av sensorer är att mycket hög vinkelupplösning kan erhållas på signalen. Laser baserade sensorer framstår därför som mycket lämpliga för olika typer av scanning eller avståndsmätning. Nackdelen är att laserstrålen måste ha fri sikt för att kunna registrera ett objekt samt att det i dagsläget handlar om dyr och avancerad teknik. • Fotogrammetri i digitala bilder. Om avståndet till objektet i en bild och kamerans inre geometri är kända kan geometriska mätningar av exempelvis stamdiametrar göras i bilden. Genom att använda digitala bilder och bildanalys borde det vara möjligt att skapa program som mer eller mindre automatiskt detekterar och mäter diametrar på de stammar som är synliga i en bild. Objektavstånden tas lämpligen ut genom separat avståndsmätning med lidar eller genom stereomatchning av två eller flera bilder. • Radar. Radarsignalen använder betydligt lägre frekvenser än laser, vilket ger den intressanta egenskaper i skogsuppskatt ningssammanhang då man kan se igenom objekt mindre än halva våglängden. Nackdelen med lågfrekventa signaler är att man får en för dålig vinkelupplösning om man försöker att genom scanning ta ut vinkel och avstånd till de enskilda stammarna. Radar verkar däremot vara en mer framkomlig väg om man avser att hämta information ur den totala retursignalen. En viss uppfattning om diameter fördelningen skulle i så fall kunna fås genom att studera skillnaden i retursignalen från olika våglängder. • Ultraljud. Ultraljud kan användas enligt samma principer som radar. Fördelarna med ultraljudssensorer är att det finns enkla och billiga standardkomponenter. Nackdelen är att signalen dämpas under fården genom luften och måste därför kalibreras för förändringar i luftens temperatur och fuktighet. Inventeringens uppläggning har också betydelse för de olika teknikernas användbarhet. Om man inventerar enligt principen för tvåfassampling ställs olika krav på utrustningen beroende på om det är det stora primära samplet eller det mer noggranna sekundära samplet man samlar in. Vid insamlingen av det primära samplet försöker man samla in stora mängder data som är korrelerat med den variabel som man önskar mäta för att få ett så lågt representativt fel som möjligt. Generellt kan man därför säga att kvantiteten data är viktigare än kvaliteten på det samma vid insamling av det primära samplet. Detta gör att tekniker som samlar in data kostnadseffektivt men med låg precision blir intressanta, exempelvis radar och ultraljuds sensorer som registrerar ekon kontinuerligt medan utrustningen förs längs en linje. Om man däremot vill mäta in det sekundära samplet med sensorer krävs utrustning som mäter med hög precision på den enskilda provytan, vilket talar för tekniker som lidar och fotogrammetri i digitala bilder. Ett kanske mer realistiskt alternativ är annars att inventera det primära samplet med automatiska kostnadseffektiva metoder medan det sekundära samplet mäts in med traditionella manuella metoder.This MSc thesis was done at the Department of Forest Resources and Geomatics SLU, Umeå during the fall 1996 and spring 1997. A requirement for accurate forestry planning at all levels is knowledge about the condition of the forests today. The quality of the decisions made will therefore be proportional to the quality and amount of information collected. Sensors like radar, lidar and different types of digital cameras are today used quite successfully for remote sensing from aircraft or satellites. The purp ose of the thesis is to make a feasibility-study about ground-based use of these kinds of sensors in order to rationalise and improve forest inventory work. Following techniques where selected for a closer study oftheir qualities as ingredients in an inventory concept: • Lidar. Lidar is an abbreviation for light detection and ranging and is a laser­ hased technique to measure distance and reflection of an object. Compared to other kinds of sensors the lidar has a very high angular resolution. Therefor it is well suited for scanning and ranging where high accuracy is required. The disadvantage of the method isthat a clear sight to the object is needed and that the technique must still be considered advanced and expensive. • Photogrammetry in digital images. If the distance to the object and the intemal geometry of the camera is known for an image, measurements of for example tree diameters or the shape of the whole trunk can be made. By using digital pietmes and image processing it seerus possible to develop programs that more or less automatically detects and measure the desired variables. • Radar. The radar-based sensors are using much lower frequencies than the laser. This gives radar the characteristic of being able to see through objects half the size of the wavelength or less. This could be very valuable if radar are supposed to be used for forest inventory work since there will be a problem with undergrowth covering stems if methods that demands visual sight will be used. The disadvantage with using the appropriate wavelengths is that the angular resolution will be to low for scanning where the purpose is to measure each stem individually. If on the other hand the total sum of the signals in a seanned sector is analysed in order to extract information about the standing volume, radar seems like a very feasible technique for developing an effective forest inventory concept. • Ultras o nie. Ultrasonic can be used by the same theories as for radar. The advantage for ultrasonic compared to radar is that there is a supply of comparatively cheap and simple standard components. The disadvantage is that how much the signal will be reduced while transmitting through the air depends to a high grade of the atmospheric humidity and temperature, which means that calibration must be made. Another negative characteristic of ultrasonic is that the signal is sensitive for wind. The methods of in ventory used al so have an effect on the feasibility of the techniques. If double sampling is used there will be different requirements for the equipment depending on if it is data from the large primary sample or the more accurate secondary sample being collected. When collecting the primary sample i t' s necessary to collect a large amount of data to prevent errors that originates from the representation of the population. The quality of the collected data will therefore be less important. This means that techniques that collects large arnounts of data with high cost-efficiency but lacks in precision will be interesting, for example radar or ultra-sonie sensors that collects data continuously while moving. On the other hand if the purpose is to collect the secondary sample, equipment that measures with high accuracy, like lidar or photogrammetry in digital pictures will be required. Another, maybe more realistic alternative, is to use a cost-efficient sensor-hased technique to collect data from the primary sample and then use traditional manual circular plot sampling for the secondary sample

Milk production from leguminous forage, roots and potatoes

The aim of the present work was to investigate the effects of replacing grain concentrates with roots and potatoes in dairy cow diets based upon large amounts of grass/alfalfa silage. The emphasis was on the possible improvement of microbial protein synthesis and nitrogen balance. Alfalfa dominated silage has a large excess of ruminally degradable protein that must be balanced with feed carbohydrates to avoid urinary nitrogen losses. The effects on ruminal fermentation pattern, intake and production were also studied. The thesis is based on two batch culture in vitro experiments and three animal experiments. The in vitro experiments compared fodder beets, barley/oats and raw, boiled or frozen potatoes as supplements to a silage diet incubated with rumen fluid from cows fed different diets. With respect to amounts fermented during 5 h incubation, supplements were ranked (P barley/oats > raw potatoes = frozen potatoes = unsupplemented silage. Substrates were numerically ranked in the same order with respect to microbial protein production, but due to larger variation they could only be divided into two groups, where fodder beets, boiled potatoes and barley/oats gave microbial yields not different from each other, but higher than for raw potatoes, frozen potatoes or unsupplemented silage. Butyrate proportion was little affected by incubation substrate but fodder beets fed to rumen fluid donor cows increased butyrate molar proportion in vitro from 10.7 to 13.0%. A change-over design experiment compared barley supplementation with fodder beet and potato supplementation of a silage diet for lactating cows. The fodder beet/potato diet lowered ad libitum silage intake by 0.9 kg DM/d and milk yield decreased correspondingly by 1.7 to 2.3 kg/d. Microbial protein production and nitrogen balance were not increased by the fodder beet supplementation, but a part of N excretion was redirected from urine to feces. Fodder beets tended to decrease the ratio lipogenic/glucogenic VFA, by increasing propionate and butyrate at the expense of acetate. In an intake experiment, most of the cows consumed the maximum allowance of fodder beets (4.6 kg DM/d) while there was a huge variation in the potato intake. A more synchronous feeding of degradable protein and readily available carbohydrates lowered the urinary nitrogen loss and increased allantoin excretion numerically but not significantly. A close correlation (R2 = 0.94) was found between total urinary N excretion and the ratio urea/creatinine in urine, which implies that spot sampling of urine may be a way to facilitate N balance measurements in lactating cows. In conclusion, a full replacement of grain by roots and potatoes can be done and the effects will be lowered urinary N losses but also a reduction in silage consumption and hence also milk production

Leveraging Traffic and Surveillance Video Cameras for Urban Traffic

The objective of this project was to investigate the use of existing video resources, such as traffic cameras, police cameras, red light cameras, and security cameras for the long-term, real-time collection of traffic statistics. An additional objective was to gather similar statistics for pedestrians and bicyclists. Throughout the course of the project, we investigated several methods for tracking vehicles under challenging conditions. The initial plan called for tracking based on optical flow. However, it was found that current optical flow–estimating algorithms are not well suited to low-quality video—hence, developing optical flow methods for low-quality video has been one aspect of this project. The method eventually used combines basic optical flow tracking with a learning detector for each tracked object—that is, the object is tracked both by its apparent movement and by its appearance should it temporarily disappear from or be obscured in the frame. We have produced a prototype software that allows the user to specify the vehicle trajectories of interest by drawing their shapes superimposed on a video frame. The software then tracks each vehicle as it travels through the frame, matches the vehicle’s movements to the most closely matching trajectory, and increases the vehicle count for that trajectory. In terms of pedestrian and bicycle counting, the system is capable of tracking these “objects” as well, though at present it is not capable of distinguishing between the three classes automatically. Continuing research by the principal investigator under a different grant will establish this capability as well.Illinois Department of Transportation, R27-131Ope

The growth of the organized ‘Fiddlers’ Movement’ in Halland, Sweden, during the twentieth century

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Genetic aspects of calving, growth, and carcass traits in beef cattle

The aim of this thesis was to learn more about the genetic background of calving, growth and carcass traits of beef cattle breeds in Sweden, and to assess the possibility of including calving traits and commercial carcass traits in the genetic evaluation. In addition, the genetic relationship between field-recorded growth rate and daily weight gain at station performance testing was investigated. The breeds studied were Charolais, Hereford and Simmental. Records of birth weight, pre-weaning gain, post-weaning gain, carcass fleshiness grade, carcass fatness grade, carcass weight, calving difficulty score and stillbirth were analysed using linear animal models. The estimated direct heritabilities were moderate to high for birth and carcass weight, moderate for pre- and post-weaning gain, carcass fleshiness and fatness grades, low for calving difficulty score and very low for stillbirth. Maternal heritabilities tended to be lower than the direct ones. Genetic relationships between direct and maternal genetic effects were generally antagonistic. Moderate to high genetic correlations were estimated between post-weaning gain in the field and at the station, showing considerable breed differences, and the added value of station testing was questioned. Genetic relationships were generally weaker between growth traits and both carcass fleshiness and fatness grade than between growth and carcass weight. Male and female birth weights were found to be the same trait genetically, and strong genetic relationships were estimated between birth weight and calving traits. Less than unity genetic correlations between calving difficulty at first and later parities indicated that partly different sets of genes control these traits. Some antagonistic relationships were found between carcass and calving traits. It was concluded that it would be feasible to include commercial carcass records and calving difficulty score in the genetic evaluation, and that both direct and maternal effects should be considered for pre-weaning traits. Information on correlated traits should be used for selection against stillbirth as direct selection would be inefficient due to small progeny group size and very low heritability. Joint genetic evaluation of pre-weaning gain and carcass weight was recommended to reduce selection bias