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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 förutsÀttning för skoglig planering pÄ alla nivÄer Àr att man har en god uppfattning
om tillstÄndet i den stÄende skogen. K
valiten pÄ de beslut som fattas kommer dÀrför
att vara direkt beroende av mÀngden och kvaliten pÄ den information som samlats in.
Sensorer som radar, lidar och olika typer av digitala kameror anvÀnds idag med
framgÄng för fjÀrranalys dÀr skogen avbildas frÄn ovan. Föreliggande arbete syftar till
att belysa de tekniska förutsÀttningarna för att utnyttja modem sensorteknik Àven för
markbaserade mÀtningar. Detta skulle i sÄ fall öppna möjligheter att automatisera
fÄngsten av skogliga data som dÀrmed skulle bli kostnadseffektivare samtidigt som
nya typer av data skulle bli tillgÀngliga.
PÄ ett tidigt stadium valdes följande tekniker ut för att nÀrmare studeras med avseende
pÄ lÀmplighet att ingÄ i ett inventeringskoncept:
âą
Lidar. Lidar Àr en laserbaserad teknik för att mÀta avstÄnd och riktning till
objekt. Laserns fördelar gentemot andra typer av sensorer Àr att mycket hög
vinkelupplösning kan erhÄllas pÄ signalen. Laser baserade sensorer framstÄr dÀrför
som mycket lÀmpliga för olika typer av scanning eller avstÄndsmÀtning.
Nackdelen Àr att laserstrÄlen mÄste ha fri sikt för att kunna registrera ett objekt
samt att det i dagslÀget handlar om dyr och avancerad teknik.
âą
Fotogrammetri i digitala bilder. Om avstÄndet till objektet i en bild och
kamerans inre geometri Àr kÀnda kan geometriska mÀtningar av exempelvis
stamdiametrar göras i bilden. Genom att anvÀnda digitala bilder och bildanalys
borde det vara möjligt att skapa program som mer eller mindre automatiskt
detekterar och mÀter diametrar pÄ de stammar som Àr synliga i en bild.
ObjektavstÄnden tas lÀmpligen ut genom separat avstÄndsmÀtning med lidar eller
genom stereomatchning av tvÄ eller flera bilder.
âą
Radar. Radarsignalen anvÀnder betydligt lÀgre frekvenser Àn laser, vilket ger
den intressanta egenskaper i skogsuppskatt
ningssammanhang dÄ man kan se
igenom objekt mindre Àn halva vÄglÀngden. Nackdelen med lÄgfrekventa signaler
Àr att man fÄr en för dÄlig vinkelupplösning om man försöker att genom scanning
ta ut vinkel och avstÄnd till de enskilda stammarna. Radar verkar dÀremot vara en
mer framkomlig vÀg om man avser att hÀmta information ur den totala
retursignalen. En viss uppfattning om diameter fördelningen skulle i sÄ fall kunna
fÄs genom att studera skillnaden i retursignalen frÄn olika vÄglÀngder.
âą
Ultraljud. Ultraljud kan anvÀndas enligt samma principer som radar. Fördelarna
med ultraljudssensorer Àr att det finns enkla och billiga standardkomponenter.
Nackdelen Àr att signalen dÀmpas under fÄrden genom luften och mÄste dÀrför
kalibreras för förÀndringar i luftens temperatur och fuktighet. Inventeringens upplÀggning har ocksÄ betydelse för de olika teknikernas
anvÀndbarhet. Om man inventerar enligt principen för tvÄfassampling stÀlls olika krav
pÄ utrustningen beroende pÄ om det Àr det stora primÀra samplet eller det mer
noggranna sekundÀra samplet man samlar in. Vid insamlingen av det primÀra samplet
försöker man samla in stora mÀngder data som Àr korrelerat med den variabel som
man önskar mÀta för att fÄ ett sÄ lÄgt representativt fel som möjligt. Generellt kan man
dÀrför sÀga att kvantiteten data Àr viktigare Àn kvaliteten pÄ det samma vid insamling
av det primÀra samplet. Detta gör att tekniker som samlar in data kostnadseffektivt
men med lÄg precision blir intressanta, exempelvis radar och ultraljuds sensorer som
registrerar ekon kontinuerligt medan utrustningen förs lÀngs en linje. Om man
dÀremot vill mÀta in det sekundÀra samplet med sensorer krÀvs utrustning som mÀter
med hög precision pÄ den enskilda provytan, vilket talar för tekniker som lidar och
fotogrammetri i digitala bilder. Ett kanske mer realistiskt alternativ Àr annars att
inventera det primÀra samplet med automatiska kostnadseffektiva metoder medan det
sekundÀra samplet mÀts in med traditionella manuella metoder.This MSc thesis was done at the Department of Forest Resources and Geomatics SLU,
UmeÄ 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:
âą
Lidar. Lidar is an abbreviation for light detection and ranging and is a laserÂ
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.
âą
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.
âą
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.
âą
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 flowâestimating algorithms are not well suited to low-quality videoâhence, 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 objectâthat 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 vehicleâs 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 âobjectsâ 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 âFiddlersâ Movementâ in Halland, Sweden, during the twentieth century
Publisher PD
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