Construction and benchmarking of adaptive parameterized linear multistep methods

A recent publication introduced a new way to define all k-step linear multistep methods of order k and k+1, in a parametric form that builds in variable step-size. In this framework it is possible to continuously change method and step-size, making it possible to create better behaving adaptive numerical solvers. In this thesis general numerical solvers based on this framework have been implemented, utilizing variable step-size and variable order, based on control theory and digital filters. To test and analyze the solvers, libraries of test problems, methods and filters have been implemented. In the analysis, the solvers were also compared to commercial (Matlab) solvers. The conclusion of this investigation is that the solvers show potential to become competitive in the field.Many important problems in engineering and science need to be solved using computers. Unlike people, computers do not make mistakes, and they are much faster at certain tasks. However, computers have a big weakness: they do not know what to do without being instructed. These instructions are created by people designing algorithms, and constructing software. Our thesis project involves implementing and testing an algorithm designed to solve a particular type of mathematical equations. To simply explain how the solver works, we use the following example: You are dropping a stone from your roof. According to physics, the stone will accelerate constantly 9.82 ms$^{-2}$ by gravity towards the ground. If you know at what height the stone was dropped, you are able to calculate where the stone will be a second later. This new approximated position can then be used to calculate where the stone will be two seconds and so forth. This is exactly what our software --- which we call a numerical solver --- does. The time passed between each calculation of the position of the stone in the previous example, is called a time-step, and generally, the longer a time-step is, the less precise will the next position approximation be. Herein lies a problem: We would like as few calculations as possible, but at the same time as accurate a solution as possible. By taking longer steps, we do not need as many calculations, but at the same time, longer steps means less accuracy. A numerical solver can be compared to a car. Assume a self-driving car only able to use one speed. This speed is chosen in the beginning of your car ride and can not be changed during the same ride, only in the beginning of the next. The speed might be adequate in some situations, on some roads, but in others it might be too fast or too slow, which means that you have to choose the speed carefully in the beginning of your ride. This is analogous to a numerical solver only able to use one step-size throughout the same calculation. Instead we let the car use different speeds during the ride. However, it is only allowed to half the speed or double the speed at every change. This would lead to a pretty ``bumpy'' ride. Most numerical solvers today use this kind of regulation to change the step-size. Since the roads we drive on might change character a lot very fast, we would instead like the car to continuously be able to change the speed, such that we always manage to stay on the road and at the same time do not need to spend all day in the car. In the corresponding way, a mathematical problem can change character very fast. In our solver we let the step-size change continuously, removing this bad ``bumpy'' behavior. The solver can not only vary the length of the time-step, but also change the underlying numerical method during the calculation of a particular problem. The difference between these methods is what we call order. Higher order methods often allow us to take longer time-steps, while still getting the same amount of precision as a lower order method would get using a shorter time-step. This means getting the same precision for less work. The order can be compared to the gears in a car. Depending on the surface of the road, the slope, and other factors, we want to use the correct gear to be able to drive as efficiently as possible. The problem with using the highest order method all the time, which may seem like the best way to go, is that all problems are not alike, just like all roads are not alike. One method working well with one problem, may not work as well with another. Also, the character of a problem may change during the calculation in such a way that a method that was working well two seconds ago, is no longer a good choice. Our thesis has focused on these two control systems, that is, a system controlling the step-size during the calculation, and a system controlling the method/order during the calculation. The software we have built, is using a certain type of numerical methods called linear multistep methods, and the control systems mentioned, are based on control theory, which is a branch of science and mathematics, used to build systems controlling everything from thermostats to jets, and of course, cars. The software package was tested after the implementation, and it turns out that it has the potential of becoming better than the corresponding packages used today, that do not use control theory

Use of granulocyte colony-stimulating factor and risk of relapse in pediatric patients treated for acute myeloid leukemia according to NOPHO-AML 2004 and DB AML-01

Background Supportive-care use of granulocyte colony-stimulating factor (G-CSF) in pediatric acute myeloid leukemia (AML) remains controversial due to a theoretical increased risk of relapse and limited impact on neutropenic complications. We describe the use of G-CSF in patients treated according to NOPHO-AML 2004 and DB AML-01 and investigated associations with relapse. Procedure Patients diagnosed with de novo AML completing the first week of therapy and not treated with hematopoietic stem cell transplantation in the first complete remission were included (n = 367). Information on G-CSF treatment after each course (yes/no) was registered prospectively in the study database and detailed information was gathered retrospectively from each center. Descriptive statistics were used to describe G-CSF use and Cox regression to assess the association between G-CSF and risk of relapse. Results G-CSF as supportive care was given to 128 (35%) patients after 268 (39%) courses, with a large variation between centers (0-93%). The use decreased with time-the country-adjusted odds ratio was 0.8/diagnostic year (95% confidence interval [CI] 0.7-0.9). The median daily dose was 5 mu g/kg (range 3-12 mu g/kg) and the median cumulative dose was 75 mu g/kg (range 7-1460 mu g/kg). Filgrastim was used in 82% of G-CSF administrations and infection was the indication in 44% of G-CSF administrations. G-CSF was associated with increased risk of relapse-the adjusted hazard ratio was 1.5 (95% CI 1.1-2.2). Conclusions G-CSF as supportive care was used in a third of patients, and use decreased with time. Our results indicate that the use of G-CSF may be associated with an increased risk of relapse.Peer reviewe

DNA methylation holds prognostic information in relapsed precursor B-cell acute lymphoblastic leukemia

Background: Few biological markers are associated with survival after relapse of B-cell precursor acute lymphoblastic leukemia (BCP-ALL). In pediatric T-cell ALL, we have identified promoter-associated methylation alterations that correlate with prognosis. Here, the prognostic relevance of CpG island methylation phenotype (CIMP) classification was investigated in pediatric BCP-ALL patients. Methods: Six hundred and one BCP-ALL samples from Nordic pediatric patients (age 1-18) were CIMP classified at initial diagnosis and analyzed in relation to clinical data. Results: Among the 137 patients that later relapsed, patients with a CIMP-profile (n = 42) at initial diagnosis had an inferior overall survival (pOS(5years) 33%) compared to CIMP+ patients (n = 95, pOS(5years) 65%) (p = 0.001), which remained significant in a Cox proportional hazards model including previously defined risk factors. Conclusion: CIMP classification is a strong candidate for improved risk stratification of relapsed BCP-ALL.Peer reviewe

DNA methylation-based subtype prediction for pediatric acute lymphoblastic leukemia

Peer reviewe

Islet Autoimmunity and HLA Markers of Presymptomatic and Clinical Type 1 Diabetes: Joint Analyses of Prospective Cohort Studies in Finland, Germany, Sweden, and the US

OBJECTIVETo combine prospective cohort studies, by including HLA harmonization, and estimate risk of islet autoimmunity and progression to clinical diabetes.RESEARCH DESIGN AND METHODSFor prospective cohorts in Finland, Germany, Sweden, and the U.S., 24,662 children at increased genetic risk for development of islet autoantibodies and type 1 diabetes have been followed. Following harmonization, the outcomes were analyzed in 16,709 infants-toddlers enrolled by age 2.5 years.RESULTSIn the infant-toddler cohort, 1,413 (8.5%) developed at least one autoantibody confirmed at two or more consecutive visits (seroconversion), 865 (5%) developed multiple autoantibodies, and 655 (4%) progressed to diabetes. The 15-year cumulative incidence of diabetes varied in children with one, two, or three autoantibodies at seroconversion: 45% (95% CI 40–52), 85% (78–90), and 92% (85–97), respectively. Among those with a single autoantibody, status 2 years after seroconversion predicted diabetes risk: 12% (10–25) if reverting to autoantibody negative, 30% (20–40) if retaining a single autoantibody, and 82% (80–95) if developing multiple autoantibodies. HLA-DR-DQ affected the risk of confirmed seroconversion and progression to diabetes in children with stable single-autoantibody status. Their 15-year diabetes incidence for higher- versus lower-risk genotypes was 40% (28–50) vs. 12% (5–38). The rate of progression to diabetes was inversely related to age at development of multiple autoantibodies, ranging from 20% per year to 6% per year in children developing multipositivity in ≤2 years or >7.4 years, respectively.CONCLUSIONSThe number of islet autoantibodies at seroconversion reliably predicts 15-year type 1 diabetes risk. In children retaining a single autoantibody, HLA-DR-DQ genotypes can further refine risk of progression.</div

Kvinnors erfarenheter av att bli inducerad efter beräknat förlosningsdatum : En kvalitativ webbaserad enkätundersökning

Syfte: Att beskriva kvinnors erfarenheter av att bli inducerad i samband medförlossning från graviditetsvecka 41. Metod: En kvalitativ webbaserad undersökning genom ett frågeformulär med öppna frågor. Kvalitativ innehållsanalys med induktiv ansats valdes som analysmetod. Resultat: Totalt inkluderades 28 deltagare i undersökningen. I resultatet framkom fyra huvudkategorier och elva subkategorier. Kvinnorna reagerade olika beträffande beslutet om induktion av förlossning. Flera tog emot beslutet positivt, en del accepterade beslutet och andra hade önskat spontan förlossningsstart. Kvinnorna beskrev att det inte togs hänsyn till personliga önskemål eller möjlighet att ifrågasätta. Det framkom en besvikelse över att kroppen inte startade igång förlossningen spontant och naturligt. Kvinnorna hade olika erfarenheter av information, delaktighet, stöd och närvaro i samband med induktion av förlossning. Det kunde konstateras att kvinnorna erfor förloppet antingen som långdraget eller snabbt. Slutsats: Barnmorskor som bistår kvinnor vid induktion av förlossning behöver särskilt Information från barnmorskor har stor betydelse för att stilla oro, stress och förvirring samtidigt som det skapar lugn och samhörighet. uppmärksamma att induktionen kan skapa varierade reaktioner och känslor.

Kvinnors erfarenheter av att bli inducerad efter beräknat förlosningsdatum : En kvalitativ webbaserad enkätundersökning

Syfte: Att beskriva kvinnors erfarenheter av att bli inducerad i samband medförlossning från graviditetsvecka 41. Metod: En kvalitativ webbaserad undersökning genom ett frågeformulär med öppna frågor. Kvalitativ innehållsanalys med induktiv ansats valdes som analysmetod. Resultat: Totalt inkluderades 28 deltagare i undersökningen. I resultatet framkom fyra huvudkategorier och elva subkategorier. Kvinnorna reagerade olika beträffande beslutet om induktion av förlossning. Flera tog emot beslutet positivt, en del accepterade beslutet och andra hade önskat spontan förlossningsstart. Kvinnorna beskrev att det inte togs hänsyn till personliga önskemål eller möjlighet att ifrågasätta. Det framkom en besvikelse över att kroppen inte startade igång förlossningen spontant och naturligt. Kvinnorna hade olika erfarenheter av information, delaktighet, stöd och närvaro i samband med induktion av förlossning. Det kunde konstateras att kvinnorna erfor förloppet antingen som långdraget eller snabbt. Slutsats: Barnmorskor som bistår kvinnor vid induktion av förlossning behöver särskilt Information från barnmorskor har stor betydelse för att stilla oro, stress och förvirring samtidigt som det skapar lugn och samhörighet. uppmärksamma att induktionen kan skapa varierade reaktioner och känslor.

Rumslig Modellering av Ekodukt: GIS-baserad Modellering för att identifiera Habitat Flaskhalsar Längst en Transport Korridor.

In this report, connectivity modeling has been performed using land cover data to find habitat pinch-points for deer along the study area Norrortsleden in Stockholm. Norrortsleden was chosen because there are a high number of deer accidents in the area, and is a priority area for action according to a barrier analysis for deer made by the Swedish Transport Administration. After interviews and research, it was found that a tool named LinkageMapper using CircuitScape theory is one good way to find habitat pinch-points along transport corridors. Firstly, a habitat resistance raster map and zone data are needed. The habitat resistance layer was made using ground cover data and given resistance values specifically for deer. An edge-zone layer was also added on top using built-in ArcGIS tools. Lastly all the road and railway data was transformed into raster and added to the final resistance layer. To find the pinch-points in the natural habitat for deer, different settings for the ArcGIS tool LinkageMapper have been tested and variations of the zone layer have been used. LinkageMapper is an external free to download tool and uses CircuitScape theory to find habitat pinch points. Different settings were tested for a 2-zone version on a 2 km buffer on each side of the road. In addition, two main settings are available, all-to-one mode and pairwise mode in LinkageMapper. Input width must also be entered to limit the number of results. Corridor width was set to 50 m for all of the produced results. After preparation of the raw data, processing zones and resistance layers it was found that usually only one corridor was showing, so a version with 6 zones on each side of the road with a 4 km buffer was made and produced more continuous results. All of the pinch-points found were marked on a map and the ones not already near an existing wildlife passage are located just south of Lake Vallentuna. The research found that the GIS-based approach is effective for Identifying high-priority locations of defragmentation across transport corridors. Using CircuitScape theory can be a great compliment too regular least cost-path.

Effect of voluntary exercise on BDNF/TrkB gene expression and alcohol intake.

Voluntary wheel running is rewarding and believed to activate the same brain reward system as in alcohol and drug addiction. Brain-derived neurotrophic factor (BDNF), a well-known growth factor widely expressed in the brain, is modulated by both voluntary exercise and alcohol consumption. The aim of this study was to evaluate how voluntary exercise affects the expression levels of BDNF and its receptor TrkB in brain regions involved in positive and negative reinforcement. Additionally we wanted to evaluate the effect it may have on alcohol drinking behaviors in C57BL/6 mice, a mouse model which are naturally prone for engaging in voluntary exercise and voluntary alcohol consumption. We found a small upregulation in DG and CA1 after three weeks of exercise, confirming findings by others, and a significant 3-fold downregulation of BDNF in NAc after both three weeks of exercise and exercise followed by a five week period of either ethanol intake or not. Interestingly, we here show a significant 100-fold increase in BDNF after exercise and a 120-fold increase after both exercise and alcohol consumption in amygdala, a region involved in regulation of anxiety-related behavior and negative reinforcement. Additionally a slightly lower 10-fold increase in BDNF was seen after exercise and a 15-fold increase after exercise followed by ethanol in prefrontal cortex, a structure contributing to reward-related behavior. Behaviorally, we could not either directly following exercise or at five weeks post-exercise detect any significant effect of wheel-running on depression-related behavior. However, we did find that exercise significantly increased the alcohol intake

To structure and calculate mathematical expressions : A study on how 5th grade students handle longer arithmetic expressions

En del svårigheter som elever upplever i algebra kan bero på saknad förståelse av strukturen i matematiska uttryck. Struktur, i det här sammanhanget, syftar på hur en matematisk enhet består av delar, och hur dessa delar är relaterade till varandra. Tidigare studier indikerar också att elevers svårigheter inom algebra beror på bristande aritmetiska kunskaper. Inom aritmetiken kan elever ofta använda informella metoder, medan algebraiska aktiviteter kräver en större medvetenhet om matematiska strukturer. Man har därför hävdat att elevers svårigheter att hantera algebraiska uttryck kan bero på saknad förståelse av strukturen i aritmetiska uttryck.  Syftet med denna studie är att undersöka hur elever i årskurs 5 beräknar och strukturerar utvecklade aritmetiska uttryck, det vill säga, numeriska uttryck med flera räkneoperationer, som exempelvis 5 · 6 + 4 · 2 · 3. I denna studie behandlas numeriska uttryck med tre eller fyra operationer.  I studien ingick 116 elever från tre olika skolor. Analysen baseras på data från lösningar av uppgifter på ett skriftligt arbetsblad. Arbetsbladet bestod av tio aritmetiska räkneuppgifter, som eleverna arbetade med individuellt. I analysen av data framkom olika metoder, som eleverna använde för att strukturera och beräkna de aritmetiska uttrycken, speciellt fyra metoder var återkommande i flera uppgifter. Genom de olika tillvägagångssätten som eleverna använde för att beräkna matematiska uttryck kunde olika sätt att skapa struktur upptäckas. Många elever utgick från uttryckens ytliga struktur och endast få elever visade förmåga att urskilja uttryckens dolda struktur. Some of the difficulties students experience in algebra can be due to lack of understanding of the structure in mathematical expressions. Structure, in this context, refers to how a mathematical entity consists of its parts, and how these parts are related to each other. Previous studies also indicate that students’ difficulties in algebra devolve upon a lack of arithmetical knowledge. In arithmetic, students can manage by using informal methods, while algebraic activities require a greater awareness of mathematical structures. It has therefore been argued that students’ difficulties with algebraic expressions are caused by a lack of knowledge of the structure in arithmetic expressions.  The purpose of this study is to investigate how 5th grade students calculate and structure longer arithmetic expressions, meaning numerical expressions with several operations, for example, 5 · 6 + 4 · 2 · 3. This study covers numerical expressions with three or four operations.  The study includes 116 students from three different schools. The analysis is based on data from solutions of tasks on a written worksheet. The worksheet consisted of ten arithmetic calculation assignments that the students worked with individually. The analysis of the data revealed different approaches that students used to structure and calculate the arithmetic expressions, particularly four methods were used in several tasks. Through the different approaches that students used to calculate mathematical expressions, different ways to create structure could be discovered. Many students based their calculations on the surface structure of an expression and only a few students seemed to be able to identify the hidden structure of an expression.