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  • 201.
    Bodin, Mats
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Harmonic functions and Lipschitz spaces on the Sierpinsky gasket2005Rapport (Övrigt vetenskapligt)
  • 202.
    Bodin, Mats
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Wavelets and Besov spaces on Mauldin-Williams fractals2005Rapport (Övrigt vetenskapligt)
  • 203.
    Bodin, Mats
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Wavelets and function spaces on Mauldin-Williams fractals2005Ingår i: Research Report in Mathematics, Vol. 7Artikel i tidskrift (Refereegranskat)
  • 204.
    Bodin, Mats
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för ekologi, miljö och geovetenskap.
    Brännström, Åke
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Dieckmann, U.
    Evolution and Ecology Program, International Institute for Applied Systems Analysis, 2361, Laxenburg, Austria.
    A systematic overview of Harvesting-Induced Maturation Evolution in Predator-Prey systems with three different Life-History Tradeoffs2012Ingår i: Bulletin of Mathematical Biology, ISSN 0092-8240, E-ISSN 1522-9602, Vol. 74, nr 12, s. 2842-2860Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    There are concerns that anthropogenic harvesting may cause phenotypic adaptive changes in exploited wild populations, in particular maturation at a smaller size and younger age. In this paper, we study the evolutionarily stable size at maturation of prey subjected to size-selective harvesting in a simple predator-prey model, taking into account three recognized life-history costs of early maturation, namely reduced fecundity, reduced growth, and increased mortality. Our analysis shows that harvesting large individuals favors maturation at smaller size compared to the unharvested system, independent of life-history tradeoff and the predator's prey-size preference. In general, however, the evolutionarily stable maturation size can either increase or decrease relative to the unharvested system, depending on the harvesting regime, the life-history tradeoff, and the predator's preferred size of prey. Furthermore, we examine how the predator population size changes in response to adaptive change in size at maturation of the prey. Surprisingly, in some situations, we find that the evolutionarily stable maturation size under harvesting is associated with an increased predator population size. This occurs, in particular, when early maturation trades off with growth rate. In total, we determine the evolutionarily stable size at maturation and associated predator population size for a total of forty-five different combinations of tradeoff, harvest regime, and predated size class.

  • 205.
    Boesen, Jesper
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Assessing mathematical creativity: comparing national and teacher-made tests, explaining differences and examining impact2006Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    Students’ use of superficial reasoning seems to be a main reason for learning difficulties in mathematics. It is therefore important to investigate the reasons for this use and the components that may affect students’ mathematical reasoning development. Assessments have been claimed to be a component that significantly may influence students’ learning.

    The purpose of the study in Paper 1 was to investigate the kind of mathematical reasoning that is required to successfully solve tasks in the written tests students encounter in their learning environment. This study showed that a majority of the tasks in teacher-made assessment could be solved successfully by using only imitative reasoning. The national tests however required creative mathematically founded reasoning to a much higher extent.

    The question about what kind of reasoning the students really use, regardless of what theoretically has been claimed to be required on these tests, still remains. This question is investigated in Paper 2.

    Here is also the relation between the theoretically established reasoning requirements, i.e. the kind of reasoning the students have to use in order to successfully solve included tasks, and the reasoning actually used by students studied. The results showed that the students to large extent did apply the same reasoning as were required, which means that the framework and analysis procedure can be valuable tools when developing tests. It also strengthens many of the results throughout this thesis. A consequence of this concordance is that as in the case with national tests with high demands regarding reasoning also resulted in a higher use of such reasoning, i.e. creative mathematically founded reasoning. Paper 2 can thus be seen to have validated the used framework and the analysis procedure for establishing these requirements.

    Paper 3 investigates the reasons for why the teacher-made tests emphasises low-quality reasoning found in paper I. In short the study showed that the high degree of tasks solvable by imitative reasoning in teacher-made tests seems explainable by amalgamating the following

    factors: (i) Limited awareness of differences in reasoning requirements, (ii) low expectations of students abilities and (iii) the desire to get students passing the tests, which was believed easier when excluding creative reasoning from the tests.

    Information about these reasons is decisive for the possibilities of changing this emphasis. Results from this study can also be used heuristically to explain some of the results found in paper 4, concerning those teachers that did not seem to be influenced by the national tests.

    There are many suggestions in the literature that high-stake tests affect practice in the classroom. Therefore, the national tests may influence teachers in their development of classroom tests. Findings from paper I suggests that this proposed impact seem to have had a limited effect, at least regarding the kind of reasoning required to solve included tasks. What about other competencies described in the policy documents?

    Paper 4 investigates if the Swedish national tests have had such an impact on teacher-made classroom assessment. Results showed that impact in terms of similar distribution of tested competences is very limited. The study however showed the existence of impact from the national tests on teachers test development and how this impact may operate.

  • 206.
    Boesen, Jesper
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    The national course tests’ impact on teachers’ written classroom assessmentArtikel i tidskrift (Refereegranskat)
  • 207.
    Boesen, Jesper
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Why emphasise imitative reasoning?: teacher made testsArtikel i tidskrift (Refereegranskat)
  • 208.
    Boesen, Jesper
    et al.
    Göteborgs universitet.
    Helenius, Ola
    Göteborgs universitet och Örebro universitet.
    Bergqvist, Ewa
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM).
    Bergqvist, Tomas
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Samhällsvetenskapliga fakulteten, Institutionen för tillämpad utbildningsvetenskap.
    Lithner, Johan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM).
    Palm, Torulf
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM).
    Palmberg, Björn
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM).
    Developing mathematical competence: from the intended to the enacted curriculum2014Ingår i: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 33, s. 72-87Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This study investigates the impact of a national reform in Sweden introducing mathematical competency goals. Data were gathered through interviews, classroom observations, and online surveys with nearly 200 teachers. Contrasting to most studies of this size, qualitative analyses were conducted. The results show that teachers are positive to the message, but the combination of using national curriculum documents and national tests to convey the reform message has not been sufficient for teachers to identify the meaning of the message. Thus, the teachers have not acquired the functional knowledge of the competence message required to modify their teaching in alignment with the reform. The results indicate that for complex reform messages, such as the competency message, to have intended impact on classroom practice, special attention needs to be put on the clarity of the message. To have high-stakes tests, for example, does not alone seem to be sufficient. 

  • 209.
    Boesen, Jesper
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Lithner, Johan
    Palm,
    The relation between test task requirements and the reasoning used by students: an analysis of an authentic national test situationIngår i: Artikel i tidskrift (Refereegranskat)
  • 210.
    Boesen, Jesper
    et al.
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Palm, Torulf
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Vilka typer av resonemang (ut)värderas i skolmatematiken?: En analys av svenska gymnasieprov2005Ingår i: Nordisk konferense i matematikkdidaktikk, 2004: Vurdering i matematikk - Hvorfor og vhordan? Fra småskole til voksenopplaering, 2005, s. 171-186Konferensbidrag (Refereegranskat)
  • 211. Bohlin, Katja S.
    et al.
    Ankardal, Maud
    Stjerndahl, Jan-Henrik
    Lindkvist, Håkan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Milsom, Ian
    Influence of the modifiable life-style factors body mass index and smoking on the outcome of hysterectomy2016Ingår i: Acta Obstetricia et Gynecologica Scandinavica, ISSN 0001-6349, E-ISSN 1600-0412, Vol. 95, nr 1, s. 65-73Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Introduction

    The aim of this study was to study the impact of body mass index (BMI) and smoking on the outcome of hysterectomy and whether effects of these factors vary between abdominal, laparoscopic and vaginal hysterectomy.

    Material and methods

    Pre-, per- and postoperative (8 weeks) data were retrieved from the Swedish National Register for Gynecological Surgery on 28 537 hysterectomies performed because of a benign indication between 2004 and 2013. Multivariable logistic regression analyses were used to identify independent factors affecting the rate of complications, presented as adjusted odds ratios (adjOR) with 95% confidence intervals (CI).

    Results

    Overweight and obesity had the strongest impact on complications in the abdominal hysterectomy group. In women with a BMI 30 an increased adjOR could be seen for bleeding >1000 mL (2.90; 95% CI 2.23-3.77), peroperative complications (1.54; 95% CI 1.26-1.88), operation time >120 min (2.67; 95% CI 2.33-3.03), postoperative complications (1.21; 95% CI 1.08-1.34) and postoperative infections (1.73; 95% CI 1.50-1.99). With vaginal hysterectomy, the effect of BMI 30 could be seen in relation to excessive bleeding >500 mL (1.63; 95% CI 1.22-2.17) and operative time >120 min (2.00; 95% CI 1.60-2.50). With laparoscopic hysterectomy (LH), a BMI 30 had a higher adjOR for prolonged surgery (1.71; 95% CI 1.30-2.26). Smokers had an increased risk of postoperative infection in the abdominal hysterectomy (1.23; 95% CI 1.07-1.40) and vaginal hysterectomy groups (1.21; 95% CI 1.02-1.43) but not in the LH group.

    Conclusions

    Body mass index and smoking had a negative effect with all hysterectomy approaches but to a lesser extent in vaginal and laparoscopic hysterectomies. This should be taken into consideration in advance of surgery to improve outcome.

  • 212. Bohlin, Katja Stenstrom
    et al.
    Ankardal, Maud
    Nüssler, Emil
    Umeå universitet, Medicinska fakulteten, Institutionen för klinisk vetenskap, Obstetrik och gynekologi.
    Lindkvist, Håkan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Milsom, Ian
    Factors influencing the outcome of surgery for pelvic organ prolapse2018Ingår i: International Urogynecology Journal, ISSN 0937-3462, E-ISSN 1433-3023, Vol. 29, nr 1, s. 81-89Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Pelvic organ prolapse (POP) surgery is a common gynecological procedure. Our aim was to assess the influence of obesity and other risk factors on the outcome of anterior and posterior colporrhaphy with and without mesh. Data were retrieved from the Swedish National Register for Gynecological Surgery on 18,554 women undergoing primary and repeat POP surgery without concomitant urinary incontinence (UI) surgery between 2006 and 2015. Multivariate logistic regression analyses were used to identify independent risk factors for a sensation of a vaginal bulge, de novo UI, and residual UI 1 year after surgery. The overall subjective cure rate 1 year after surgery was 80% (with mesh 86.4% vs 77.3% without mesh, p < 0.001). The complication rate was low, but was more frequent in repeat surgery that were mainly mesh related. The use of mesh was also associated with more frequent de novo UI, but patient satisfaction and cure rates were higher compared with surgery without mesh. Preoperative sensation of a vaginal bulge, severe postoperative complications, anterior colporrhaphy, prior hysterectomy, postoperative infections, local anesthesia, and body mass index (BMI) 30 were risk factors for sensation of a vaginal bulge 1 year postsurgery. Obesity had no effect on complication rates but was associated increased urinary incontinence (UI) after primary surgery. Obesity had no influence on cure or voiding status in women undergoing repeat surgery. Obesity had an impact on the sensation of a vaginal bulge and the presence of UI after primary surgery but not on complications.

  • 213. Boiveau, Thomas
    et al.
    Burman, Erik
    Claus, Susanne
    Larson, Mats G.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Fictitious domain method with boundary value correction using penalty-free Nitsche method2018Ingår i: Journal of Numerical Mathematics, ISSN 1570-2820, E-ISSN 1569-3953, Vol. 26, nr 2, s. 77-95Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we consider a fictitious domain approach based on a Nitsche type method without penalty. To allow for high order approximation using piecewise affine approximation of the geometry we use a boundary value correction technique based on Taylor expansion from the approximate to the physical boundary. To ensure stability of the method a ghost penalty stabilization is considered in the boundary zone. We prove optimal error estimates in the H1-norm and estimates suboptimal by 𝓞(h1/2) in the L2-norm. The suboptimality is due to the lack of adjoint consistency of our formulation. Numerical results are provided to corroborate the theoretical study.

  • 214.
    Bolin, David
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Spatial Matern Fields Driven by Non-Gaussian Noise2014Ingår i: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 41, nr 3, s. 557-579Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The article studies non-Gaussian extensions of a recently discovered link between certain Gaussian random fields, expressed as solutions to stochastic partial differential equations (SPDEs), and Gaussian Markov random fields. The focus is on non-Gaussian random fields with Matern covariance functions, and in particular, we show how the SPDE formulation of a Laplace moving-average model can be used to obtain an efficient simulation method as well as an accurate parameter estimation technique for the model. This should be seen as a demonstration of how these techniques can be used, and generalizations to more general SPDEs are readily available.

  • 215.
    Bondesson, Lennart
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    A class of probability distributions that is closed with respect to addition as well as multiplication of independent random variables2015Ingår i: Journal of theoretical probability, ISSN 0894-9840, E-ISSN 1572-9230, Vol. 28, nr 3, s. 1063-1081Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Thorin’s class of generalized gamma convolutions (GGCs) is closed with respect to change in scale, weak limits, and addition of independent random variables. Here, it is shown that the GGC class also has the remarkable property of being closed with respect to multiplication of independent random variables. This novel result, which has a simple extension to symmetric distributions on R, has many consequences and applications. In particular, it follows that X∼ GGC implies that exp(X)∼ GGC. The latter result is used to find a large class of explicit probability functions on {0,1,2,…} which are generalized negative binomial convolutions (GNBCs). The paper ends with several open problems.

  • 216.
    Bondesson, Lennart
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Conditional and restricted Pareto sampling: two new methods for unequal probability sampling2010Ingår i: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 37, nr 3, s. 514-530Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Two new unequal probability sampling methods are introduced: conditional and restricted Pareto sampling. The advantage of conditional Pareto sampling compared with standard Pareto sampling, introduced by Rosén (J. Statist. Plann. Inference, 62, 1997, 135, 159), is that the factual inclusion probabilities better agree with the desired ones. Restricted Pareto sampling, preferably conditioned or adjusted, is able to handle cases where there are several restrictions on the sample and is an alternative to the recent cube method for balanced sampling introduced by Deville and Tillé (Biometrika, 91, 2004, 893). The new sampling designs have high entropy and the involved random numbers can be seen as permanent random numbers.

  • 217.
    Bondesson, Lennart
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Dear reader,2001Ingår i: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 28, nr 1, s. 1-1Artikel i tidskrift (Övrigt vetenskapligt)
  • 218.
    Bondesson, Lennart
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Is there a best fixed size pps sampling design?2006Ingår i: Workshop on Survey Sampling and Methodology, Ventpils, Latvia, 2006, s. 6-16Konferensbidrag (Refereegranskat)
  • 219.
    Bondesson, Lennart
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    On a minimum correlation problem2003Ingår i: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 62, nr 4, s. 361-370Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A stationary sequence of Bernoulli(p) distributed variables is considered. For a general class of 1-dependent sequences the minimum and the maximum of the lag 1 autocorrelation is found. The correlation is never below −1/3 and attains this value only for certain values of p.

  • 220.
    Bondesson, Lennart
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    On minimum and maximum autocorrelation for 1- and m-dependent Bernouilli processes2006Rapport (Övrigt vetenskapligt)
  • 221.
    Bondesson, Lennart
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    On Sampling with Prescribed Second-order Inclusion Probabilities2012Ingår i: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 39, nr 4, s. 813-829Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Methods to perform fixed size sampling with prescribed second-order inclusion probabilities are presented. The focus is on a conditional Poisson design of order 2, a CP(2) design. It is an exponential design of quadratic type and it is carefully studied. In particular, methods to find the suitable values of the parameters and methods to sample are described. Small examples illustrate.

  • 222.
    Bondesson, Lennart
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    On the Lévy measure of the lognormal and logCauchy distributions2002Ingår i: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 4, nr 3, s. 243-256Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The densities of the Lévy measure and the Thorin measure of the standard lognormal distribution are approximated and presented in graphs. Moreover, the behavior of these densities at 0 and ∞ is studied. Laplace and saddlepoint approximations are used. The infinite divisibility of the standard logCauchy distribution is given some attention in passing.

  • 223.
    Bondesson, Lennart
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    On univariate and bivariate generalized gamma convolutions2009Ingår i: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 139, nr 11, s. 3759-3765Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper has two parts. In the first part some results for generalized gamma convolutions (GGCs) are reviewed. A GGC is a limit distribution for sums of independent gamma variables. In the second part, bivariate gamma distributions and bivariate GGCs are considered. New bivariate gamma distributions are derived from shot-noise models. The remarkable property hyperbolic complete monotonicity (HCM) for a function is considered both in the univariate case and in the bivariate case.

  • 224.
    Bondesson, Lennart
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Pareto sampling2010Ingår i: International Encyclopedia of Statistical Sciences, Springer, 2010Kapitel i bok, del av antologi (Refereegranskat)
  • 225.
    Bondesson, Lennart
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Recursion formulas for inclusion probabilities of all orders for Conditional Poisson, Samford, Pareto, and more general sampling designs2010Ingår i: Official Statistics: Methodology and Applications in Honour of Daniel Thorburn / [ed] Carlsson, Nyquist, and Villani, Stockholm: Department of Statistics, Stockholm University , 2010, s. 67-78Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    Simple recursion formulas are presented for the calculation of inclusion probabilities of allorders for conditional Poisson, Sampford, Pareto, and other sampling designs. For CPsampling, the formulas date partially back to work by Chen et al. in 1994.

  • 226.
    Bondesson, Lennart
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    The splitting method for unequal probability sampling2008Ingår i: Encyclopedia of Statistical Sciences / [ed] Samuel Kotz, Campbell B. Read, N. Balakrishnan and Brani Vidakovi, John Wiley & Sons, 2008, Second editionKapitel i bok, del av antologi (Övrig (populärvetenskap, debatt, mm))
  • 227.
    Bondesson, Lennart
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Unequal probability sampling designs with high entropy2008Ingår i: Encyclopedia of Statistical Sciences / [ed] Samuel Kotz, Campbell B. Read, N. Balakrishnan and Brani Vidakovi, John Wiley & Sons, 2008, Second editionKapitel i bok, del av antologi (Refereegranskat)
  • 228.
    Bondesson, Lennart
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Variants of the splitting method for unequal probability sampling2008Ingår i: Baltic-Nordic workshop on survey sampling theory and methodology, Tallinn: Statistics Estonia , 2008, s. 22-31Konferensbidrag (Övrigt vetenskapligt)
  • 229.
    Bondesson, Lennart
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Fahlén, Jessica
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Mean and variance of vacancy for hard-core Disc processes and applications2003Ingår i: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 30, nr 4, s. 797-816Artikel i tidskrift (Refereegranskat)
  • 230.
    Bondesson, Lennart
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Grafström, Anton
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    An extension of Sampford's method for unequal probability sampling2011Ingår i: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 38, nr 2, s. 377-392Artikel i tidskrift (Övrigt vetenskapligt)
    Abstract [en]

    Sampford's (1967) unequal probability sampling method is extended to the case that the inclusion probabilities do not sum to an integer. In this case the sampling outcome is left open for exactly one randomly chosen unit and that unit gets a new inclusion probability. Three applications are presented. Two of them challenge traditional sampling routines. The simple Pareto sampling design, which was introduced by Rosén (1997a,b), is also extended. The extended Pareto design is shown to be close to the extended Sampford design.

  • 231.
    Bondesson, Lennart
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Grafström, Anton
    department of Forest Resource Management, Swedish University of Agricultural Sciences, Umeå, Sweden.
    Traat, Imbi
    Institute of Mathematical Statistics, University of Tartu, Tartu, Estonia.
    Sampling Designs with Linear and Quadratic Probability Functions2014Ingår i: Open Journal of Statistics, ISSN 2161-718X, E-ISSN 2161-7198, Vol. 4, s. 178-187Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Fixed size without replacement sampling designs with probability functions that are linear or quadratic functions of the sampling indicators are defined and studied. Generality, simplicity, remarkable properties, and also somewhat restricted flexibility characterize these designs. It is shown that the families of linear and quadratic designs are closed with respect to sample complements and with respect to conditioning on sampling outcomes for specific units. Relations between inclusion probabilities and parameters of the probability functions are derived and sampling procedures are given. 

  • 232.
    Bondesson, Lennart
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Grandell, Jan
    Department of Mathematics, Royal Institute of Technology, Stockholm.
    Peetre, Jaak
    Department of Mathematics, Lund University, Lund.
    The life and work of Olof Thorin (1912-2004)2008Ingår i: Proceedings of the Estonian Academy of Sciences, ISSN 1736-6046, E-ISSN 1736-7530, Vol. 57, s. 18-25Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper reviews Olof Thorin’s contributions to mathematical analysis, actuarial mathematics, and probability theory, though in reversed order. In probability theory he is known for his path-breaking work on infinite divisibility. In actuarial mathematics he contributed significantly to the ruin problem. However, his international fame very much relies on his work in mathematical analysis and his share in the Riesz–Thorin theorem. Data about his life and some personal recollections are also given.

  • 233.
    Bondesson, Lennart
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Nilsson, Thomas
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Wikstrand, Greger
    YAHM Sweden AB, SE–224 78 Lund, Sweden.
    Probability calculus for silent elimination: A method for medium access control2007Rapport (Övrigt vetenskapligt)
    Abstract [en]

    A probability problem arising in the context of medium access control in wireless networks is considered. It is described as a problem with n urns, each one having one ball at time 0. Each ball leaves its urn after a geometrically distributed time. Then there is a first time T such that no departures take place at the times T +1, T +2, . . . , T +k, where k is fixed. The focus is on the probability distribution of (XT , ST , T), where XT is the number of balls that leave their urns at time T and ST is the number of balls remaining there at that time. Efficient recursion formulas are derived. Asymptotics and continuous time approximations are considered. For k = ∞, T is the maximum of n geometrically distributed variables. This case has earlier got a large literature.

  • 234.
    Bondesson, Lennart
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Persson, Anna
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Matematisk statistik.
    Semi-Bayesian methods for adjusting coordinate mesurements and for estimating the area of a polygonManuskript (Övrigt vetenskapligt)
  • 235.
    Bondesson, Lennart
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Simon, Thomas
    Stieltjes functions of finite order and hyperbolic monotonicity2018Ingår i: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 370, nr 6, s. 4201-4222Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A class of Stieltjes functions of finite type is introduced. These satisfy Widder's conditions on the successive derivatives up to some finite order and are not necessarily smooth. We show that such functions have a unique integral representation along some generic kernel which is a truncated Laurent series approximating the standard Stieltjes kernel. We then obtain a two-to-one correspondence, via the logarithmic derivative, between these functions and a subclass of hyperbolically monotone functions of finite type. This correspondence generalizes a representation of HCM functions in terms of two Stieltjes transforms earlier obtained by the first author.

  • 236.
    Bondesson, Lennart
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Steutel, Fred
    Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
    A class of infinitely divisible distributions connected to branching processes and random walks2004Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, Vol. 295, nr 1, s. 134-143Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A class of infinitely divisible distributions on {0,1,2,…} is defined by requiring the (discrete) Lévy function to be equal to the probability function except for a very simple factor. These distributions turn out to be special cases of the total offspring distributions in (sub)critical branching processes and can also be interpreted as first passage times in certain random walks. There are connections with Lambert's W function and generalized negative binomial convolutions.

  • 237.
    Bondesson, Lennart
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Thorburn, Daniel
    Department of Statistics, University of Stockholm.
    A list sequential sampling method suitable for real time sampling2008Ingår i: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 35, nr 3, s. 466-483Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A flexible list sequential πps sampling method is introduced and studied. It can reproduce any given sampling design without replacement, of fixed or random sample size. The method is a splitting method and uses successive updating of inclusion probabilities. The main advantage of the method is in real-time sampling situations where it can be used as a powerful alternative to Bernoulli and Poisson sampling and can give any desired second-order inclusion probabilities and thus considerably reduce the variability of the sample size.

  • 238.
    Bondesson, Lennart
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Traat, Imbi
    Institute of Mathematical Statistics , University of Tartu , 50409 Tartu, Estonia.
    A non-symmetric matrix with integer eigenvalues2007Ingår i: Linear and Multilinear Algebra, ISSN 0308-1087, 1563-5139, Vol. 55, nr 3, s. 239-247Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A nonsymmetric N × N matrix with elements as certain simple functions of N distinct real or complex numbers r 1, r 2, …, rN is presented. The matrix is special due to its eigenvalues − the consecutive integers 0,1,2, …, N−1. Theorems are given establishing explicit expressions of the right and left eigenvectors and formulas for recursive calculation of the right eigenvectors. A special case of the matrix has appeared in sampling theory where its right eigenvectors, if properly normalized, give the inclusion probabilities of the conditional Poisson sampling design.

  • 239.
    Bondesson, Lennart
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Traat, Imbi
    On Sampling Designs with Ordered Conditional Inclusion Probabilities2013Ingår i: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 40, nr 4, s. 724-733Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we consider a family of sampling designs for which increasing first-order inclusion probabilities imply, in a specific sense, increasing conditional inclusion probabilities. It is proved that the complementary Midzuno, the conditional Poisson, and the Sampford designs belong to this family. It is shown that designs of the family are more efficient than a comparable with-replacement design. Furthermore, the efficiency gain is explicitly given for these designs.

  • 240.
    Bondesson, Lennart
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Traat, Imbi
    Institute of Mathematical Statistics , University of Tartu , Estonia.
    Lundquist, Anders
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Pareto sampling versus Sampford and Conditional Poisson sampling2006Ingår i: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 33, nr 4, s. 699-720Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Pareto sampling was introduced by Rosén in the late 1990s. It is a simple method to get a fixed size πps sample though with inclusion probabilities only approximately as desired. Sampford sampling, introduced by Sampford in 1967, gives the desired inclusion probabilities but it may take time to generate a sample. Using probability functions and Laplace approximations, we show that from a probabilistic point of view these two designs are very close to each other and asymptotically identical. A Sampford sample can rapidly be generated in all situations by letting a Pareto sample pass an acceptance–rejection filter. A new very efficient method to generate conditional Poisson (CP) samples appears as a byproduct. Further, it is shown how the inclusion probabilities of all orders for the Pareto design can be calculated from those of the CP design. A new explicit very accurate approximation of the second-order inclusion probabilities, valid for several designs, is presented and applied to get single sum type variance estimates of the Horvitz–Thompson estimator.

  • 241.
    Borggren, My
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    En statistisk undersökning av turtäthet och dess inverkan på resebeteenden: En fallstudie på Arriva Sverige AB2017Självständigt arbete på avancerad nivå (yrkesexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    En gemensam målsättning för kollektivtrafikoperatörer är att effektivisera trafiken samt att generera fler och nöjdare resenärer. Arriva Sverige AB bedriver buss- och spårvagnsverksamhet åt Storstockholms Lokaltrafik (SL) i Stockholmsområdet och precis som övriga operatörer inom kollektivtrafik arbetar Arriva mot att öka antalet kollektivt resande. Forskning visar att turtäthet har en stor inverkan på resebeteenden, men i dagsläget saknar Arriva ett systematiskt sätt att internt beräkna den optimala turtätheten. En ökad förståelse för resebeteenden kopplat till turtäthet skulle bidra till ett bättre beslutsunderlag i frågor som rör turtäthet. Denna studie undersöker hur en reducering i turtäthet påverkar antalet resande i Stockholms busstrafik, baserat på sekundärdata tillhandahållen av Arriva. Studien avgränsades i ett första steg till busstrafik tillhörande E20-avtalen och i ett andra steg till busstrafik i Brommaområdet (Västerort). Studien utgick från befintliga teorier och tog en deduktiv ansats. Sambandet mellan den procentuella förändringen i turtäthet och den procentuella förändringen i antal resande undersöktes med multipel linjär regression och resulterade i en skattning på produktionselasticiteten. Dataunderlaget bestod av VBP-data (statistik över antalet verifierade betalande passagerare), baserat på SL accesskortsvalideringar. För att besvara frågeställningen undersöktes två delfrågor, varav den ena utredde effekten av en reducering i turtäthet och den andra huruvida effekten av en reducering är densamma vid lågturtäthet som vid hög turtäthet. Resultatet visade på att ett linjärt samband mellan en reducering i turtäthet och en förändring i antal resande existerar. De framtagna regressionsmodellerna hade låga förklaringsvärden (0,1818 och 0,1857) och kunde inte förklara det exakta sambandet. Andra icke-linjära samband kunde inte uteslutas på grund av det begränsade antalet bussturer och den låga variation i turtäthetsförändringar. Produktionselasticiteten för det studerade datasetet skattades till 0,3886. Vid införandet av en dummyvariabel för hög turtäthet skattades produktionselasticiteten till 0,4546. Regressionskoefficienten för dummyvariabeln antog värdet 0,0779. Resultatet tyder på att en reducering i turtäthet påverkar antal resande i högre grad vid låg turtäthet än vid hög turtäthet. Skattade värden på produktionselasticitet ligger i spannet av skattade värden i tidigare forskning. Detta är en indikation på att resultatet, och därmed insamlat VBP-data, är relevant för analys av produktionselasticitet.

  • 242.
    Brandl, Michael
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Newton’s Method for a Finite Element Approach to the Incompressible Navier-Stokes Equations2016Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [en]

    The cG(1)cG(1)-method is a finite element method for solving the incompressible Navier-Stokes equations, using a splitting scheme and fixed-point iteration to resolve the nonlinear term u · ∇u. In this thesis, Newton’s method has been implemented on a formulation of the cG(1)cG(1)-method without splitting, resulting in equal results for the velocity and pressure computation, but higher computation times and slower convergence.

  • 243. Brignall, Robert
    et al.
    Sliacan, Jakub
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Combinatorial specifications for juxtapositions of permutation classes2019Ingår i: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 26, nr 4, artikel-id P4.4Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We show that, given a suitable combinatorial specification for a permutation class C, one can obtain a specification for the juxtaposition (on either side) of C with Av(21) or Av(12), and that if the enumeration for C is given by a rational or algebraic generating function, so is the enumeration for the juxtaposition. Furthermore this process can be iterated, thereby providing an effective method to enumerate any 'skinny' k x 1 grid class in which at most one cell is non-monotone, with a guarantee on the nature of the enumeration given the nature of the enumeration of the non-monotone cell.

  • 244. Brinkmann, Gunnar
    et al.
    Goedgebeur, Jan
    Hägglund, Jonas
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Markström, Klas
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Generation and properties of snarks2013Ingår i: Journal of combinatorial theory. Series B (Print), ISSN 0095-8956, E-ISSN 1096-0902, Vol. 103, nr 4, s. 468-488Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    For many of the unsolved problems concerning cycles and matchings in graphs it is known that it is sufficient to prove them for snarks, the class of non-trivial 3-regular graphs which cannot be 3-edge coloured.

    In the first part of this paper we present a. new algorithm for generating all non-isomorphic snarks of a given order. Our implementation of the new algorithm is 14 times faster than previous programs for generating snarks, and 29 times faster for generating weak snarks. Using this program we have generated all non-isomorphic snarks on n <= 36 vertices. Previously lists up to n = 28 vertices have been published.

    In the second part of the paper we analyze the sets of generated snarks with respect to a number of properties and conjectures. We find that some of the strongest versions of the cycle double cover conjecture hold for all snarks of these orders, as does Jaeger's Petersen colouring conjecture, which in turn implies that Fulkerson's conjecture has no small counterexamples. In contrast to these positive results we also find counterexamples to eight previously published conjectures concerning cycle coverings and the general cycle structure of cubic graphs.

    (C) 2013 Published by Elsevier Inc.

  • 245.
    Britse, Oscar
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Jarnmo, Johan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Greenhouse Gas Footprint Minimization of Credit Default Swap Baskets2018Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [en]

    Global bond market capitalization amounts to approximately $100 trillion, compared to $60 trillion in the equity markets. Despite debt financing being a large part of the global financial market, the measurements and greenhouse gas reduction investment strategies to date are not nearly as thorough as for equity financing. More recently, the problem has been brought into light by the World Bank, expressing concerns about the crucial role of debt financing activities in the current and upcoming threats caused by climate change.

    A commonly used credit derivative in debt financing is credit default swaps (CDS), which is an agreement between two parties to exchange the credit risk of a reference entity. The buyer of the contract makes fixed periodic payments to the seller of the contract, who collects the premiums in exchange for making the protection buyer whole in the case of a defaulting reference entity.

    This thesis aims to minimize the greenhouse gas emission exposure for two CDS indices, iTraxx Main and CDX.IG, each consisting of 125 equally weighted constituents, or companies. The CDS indices are widely used high liquid fixed income instruments. In 2017, iTraxx Main had a monthly trading volume of $330-440 billion notional, and CDX.IG a corresponding volume of $200-275 billion. In order to rate the greenhouse gas emissions of the constituents, the ECOBAR model was used. The model utilizes a discrete ranking score system, where the aim is to obtain as low score as possible. To minimize the ECOBAR score for the baskets, Markowitz Modern Portfolio Theory was used, implemented by using a quadratic programming algorithm. By optimizing the portfolios while retaining a low tracking error and high correlation toward the CDS indices, underlying investment properties were retained.

    We show that one can construct replicated portfolios of the CDS indices that have significantly lower ECOBAR scores than the indices themselves, whilst still maintaining a low tracking error and high correlation with the actual indices. When constructing baskets of fewer constituents, one can replicate the indices with merely 10-30 constituents, without worsening the tracking error or correlation substantially, and obtain an even lower ECOBAR score for the respective portfolios.

  • 246.
    Brodin, Andreas
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Kreativitet: En studie av matematikuppgifterna i PISA 20032009Självständigt arbete på avancerad nivå (yrkesexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Forskning har visat att uppgifter i prov inverkar på vad elever lär sig genom deras förväntningar på vad testet ska innehålla (Virta, 2004). Boesen (2006b) konstaterar att uppgifter i nationella prov påverkar lärares undervisning vilket indirekt också bör inverka på vad elever lär sig. Lithner (2008) menar att det finns risk att en elev som använder ett imitativt resonemang i alltför hög grad vid lösning av matematikuppgifter får sämre matematikkunskaper. Genom att som lärare förse eleven med uppgifter som kräver ett kreativt resonemang, i vilka det inte är möjligt för eleven att använda ett imitativt resonemang, bör en sådan utveckling hindras. Syftet med detta examensarbete är att med ett klassificeringsverktyg tidigare använt av bland andra Boesen, Lithner och Palm (2005) och Bergqvist (2007) undersöka alla 85 matematikuppgifter i PISA 2003 med avseende på vilken grad av matematiskt kreativt resonemang som krävs för att lösa dem. Klassificeringen av uppgifterna visar att endast 9% är möjliga att lösa med ett imitativt resonemang medan resten av uppgifterna kräver ett kreativt resonemang. Några egenskaper typiska för uppgifterna i PISA jämfört med uppgifter i läroboken Matte Direkt har också noterats. Dessa egenskaper har även omformulerats till konkreta tips riktade till lärare vilka önskar konstruera uppgifter som kräver ett matematiskt kreativt resonemang.

  • 247.
    Brodin, Andreas
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Multiwavelet analysis on fractals2007Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This thesis consists of an introduction and a summary, followed by two papers, both of them on the topic of function spaces on fractals.

    Paper I: Andreas Brodin, Pointwise Convergence of Haar type Wavelets on Self-Similar Sets, Manuscript.

    Paper II: Andreas Brodin,

    Regularization of Wavelet Expansion characterizes Besov Spaces on Fractals, Manuscript.

    Properties of wavelets, originally constructed by A. Jonsson, are studied in both papers. The wavelets are piecewise polynomial functions on self-similar fractal sets.

    In Paper I, pointwise convergence of partial sums of the wavelet expansion is investigated. On a specific fractal set, the Sierpinski gasket, pointwise convergence of the partial sums is shown by calculating the kernel explicitly, when the wavelets are piecewise constant functions. For more general self-similar fractals, pointwise convergence of the partial sums and their derivatives, in case the expanded function has higher regularity, is shown using a different technique based on Markov's inequality.

    A. Jonsson has shown that on a class of totally disconnected self-similar sets it is possible to characterize Besov spaces by means of the magnitude of the coefficients in the wavelet expansion of a function. M. Bodin has extended his results to a class of graph directed self-similar sets introduced by Mauldin and Williams. Unfortunately, these results only holds for fractals such that the sets in the first generation of the fractal are disjoint. In Paper II we are able to characterize Besov spaces on a class of fractals not necessarily sharing this condition by making the wavelet expansion smooth. We create continuous regularizations of the partial sums of the wavelet expansion and show that properties of these regularizations can be used to characterize Besov spaces.

  • 248.
    Brodin, Andreas
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Pointwise convergence of Haar type wavelets on self-similar sets2006Rapport (Övrigt vetenskapligt)
  • 249.
    Brodin, Andreas
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Regularization of wavelet expansion characterizes Besov spaces on fractalsManuskript (Övrigt vetenskapligt)
  • 250.
    Brorsson, Camilla
    et al.
    Umeå universitet, Medicinska fakulteten, Institutionen för kirurgisk och perioperativ vetenskap, Anestesiologi och intensivvård.
    Dahlqvist, Per
    Umeå universitet, Medicinska fakulteten, Institutionen för folkhälsa och klinisk medicin, Medicin.
    Nilsson, Leif
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Naredi, Silvana
    Umeå universitet, Medicinska fakulteten, Institutionen för kirurgisk och perioperativ vetenskap, Anestesiologi och intensivvård.
    Saliva stimulation with glycerine and citric acid does not affect salivary cortisol levels2014Ingår i: Clinical Endocrinology, ISSN 0300-0664, E-ISSN 1365-2265, Vol. 81, nr 2, s. 244-248Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    OBJECTIVE:

    In critically ill patients with hypotension, who respond poorly to fluids and vasoactive drugs, cortisol insufficiency may be suspected. In serum over 90% of cortisol is protein-bound, thus routine measures of total serum cortisol may yield 'false lows' due to hypoproteinaemia. Thus, the occurrence of cortisol insufficiency could be overestimated in critically ill patients. Salivary cortisol can be used as a surrogate for free serum cortisol, but in critically ill patients saliva production is decreased, and insufficient volume of saliva for analysis is a common problem. The aim of this study was to investigate if a cotton-tipped applicator with glycerine and citric acid could be used for saliva stimulation without affecting salivary cortisol levels.

    DESIGN:

    Prospective, observational study.

    PARTICIPANTS:

    Thirty-six volunteers (six males, 30 females), age 49 ± 9 years, without known oral mucus membrane rupture in the mouth.

    MEASUREMENTS:

    Forty-two pairs of saliva samples (22 paired morning samples, 20 paired evening samples) were obtained before and after saliva stimulation with glycerine and citric acid. Salivary cortisol was analysed using Spectria Cortisol RIA (Orion Diagnostica, Finland).

    RESULTS:

    The paired samples correlated significantly (P < 0·0001) and there was no significant difference between un-stimulated and stimulated salivary cortisol levels.

    CONCLUSIONS:

    Saliva stimulation with a cotton-tipped applicator containing glycerine and citric acid did not significantly influence salivary cortisol levels in healthy volunteers. This indicates that salivary cortisol measurement after saliva stimulation may be a useful complement when evaluating cortisol status in critically ill patients.

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