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  • 101. Backlund, Ulf
    et al.
    Carlsson, Linus
    Fällström, Anders
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Persson, Håkan
    Semi-Bloch Functions in Several Complex Variables2016Ingår i: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 26, nr 1, s. 463-473Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Let M be an n-dimensional complex manifold. A holomorphic function f : M -> C is said to be semi-Bloch if for every lambda is an element of C the function g(lambda) = exp(lambda f(z)) is normal on M. We characterize semi-Bloch functions on infinitesimally Kobayashi non-degenerate M in geometric as well as analytic terms. Moreover, we show that on such manifolds, semi-Bloch functions are normal.

  • 102. Backman, Anders
    et al.
    Bodin, Kenneth
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Lacoursière, Claude
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Servin, Martin
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Democratizing CAE with Interactive Multiphysics Simulation and Simulators2012Konferensbidrag (Övrigt vetenskapligt)
  • 103. Baculikova, Blanka
    et al.
    Dzurina, Jozef
    Rogovchenko, Yuri V.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Oscillation of third order trinomial delay differential equations2012Ingår i: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 218, nr 13, s. 7023-7033Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The purpose of this paper is to study oscillation and asymptotic behavior of solutions to a third order linear delay differential equation y'''(t) + p(t)y'(t) + q(t)y(tau(t)) = 0. New comparison theorems deduce oscillation of the given third order delay differential equation via application of known oscillation criteria to associated first order delay differential equations or inequalities. Contrary to most known results, we establish oscillation of all solutions to a given delay differential equation. Conditions in all theorems are not difficult to verify; computer algebra systems can be efficiently used to assist the computations. Main results in the paper are illustrated with a number of examples.

  • 104.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Fysik.
    Bernhardsson, Sebastian
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Fysik.
    Equilibrium solution to the lowest unique positive integer game2010Ingår i: Fluctuation and Noise Letters, ISSN 0219-4775, E-ISSN 1793-6780, Vol. 9, nr 1, s. 61-68Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We address the equilibrium concept of a reverse auction game so that no one can enhance the individual payoff by a unilateral change when all the others follow a certain strategy. In this approach the combinatorial possibilities to consider become very much involved even for a small number of players, which has hindered a precise analysis in previous works. We here present a systematic way to reach the solution for a general number of players, and show that this game is an example of conflict between the group and the individual interests.

  • 105.
    Baek, Seung Ki
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Choi, Jung-Kyoo
    Kim, Beom Jun
    Dworkin's Paradox2012Ingår i: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 7, nr 6, s. e38529-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    How to distribute welfare in a society is a key issue in the subject of distributional justice, which is deeply involved with notions of fairness. Following a thought experiment by Dworkin, this work considers a society of individuals with different preferences on the welfare distribution and an official to mediate the coordination among them. Based on a simple assumption that an individual's welfare is proportional to how her preference is fulfilled by the actual distribution, we show that an egalitarian preference is a strict Nash equilibrium and can be favorable even in certain inhomogeneous situations. These suggest how communication can encourage and secure a notion of fairness.

  • 106. Balmus, Maximilian
    et al.
    Massing, André
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway.
    Hoffman, Johan
    Razavi, Reza
    Nordsletten, David A.
    A partition of unity approach to fluid mechanics and fluid-structure interaction2020Ingår i: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 362, artikel-id 112842Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    For problems involving large deformations of thin structures, simulating fluid-structure interaction (FSI) remains a computationally expensive endeavour which continues to drive interest in the development of novel approaches. Overlapping domain techniques have been introduced as a way to combine the fluid-solid mesh conformity, seen in moving-mesh methods, without the need for mesh smoothing or re-meshing, which is a core characteristic of fixed mesh approaches. In this work, we introduce a novel overlapping domain method based on a partition of unity approach. Unified function spaces are defined as a weighted sum of fields given on two overlapping meshes. The method is shown to achieve optimal convergence rates and to be stable for steady-state Stokes, Navier-Stokes, and ALE Navier-Stokes problems. Finally, we present results for FSI in the case of 2D flow past an elastic beam simulation. These initial results point to the potential applicability of the method to a wide range of FSI applications, enabling boundary layer refinement and large deformations without the need for re-meshing or user-defined stabilization.

  • 107.
    Baltz, Andreas
    et al.
    Christian-Albrechts Universität Kiel.
    El Ouali, Mourad
    Christian-Albrechts Universität Kiel.
    Jäger, Gerold
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Sauerland, Volkmar
    Christian-Albrechts Universität Kiel.
    Srivastav, Anand
    Christian-Albrechts Universität Kiel.
    Exact and heuristic algorithms for the Travelling Salesman Problem with Multiple Time Windows and Hotel Selection2015Ingår i: Journal of the Operational Research Society, ISSN 0160-5682, E-ISSN 1476-9360, Vol. 66, nr 4, s. 615-626Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We introduce and study the Travelling Salesman Problem with Multiple Time Windows and Hotel Selection (TSP-MTWHS), which generalises the well-known Travelling Salesman Problem with Time Windows and the recently introduced Travelling Salesman Problem with Hotel Selection. The TSP-MTWHS consists in determining a route for a salesman (eg, an employee of a services company) who visits various customers at different locations and different time windows. The salesman may require a several-day tour during which he may need to stay in hotels. The goal is to minimise the tour costs consisting of wage, hotel costs, travelling expenses and penalty fees for possibly omitted customers. We present a mixed integer linear programming (MILP) model for this practical problem and a heuristic combining cheapest insert, 2-OPT and randomised restarting. We show on random instances and on real world instances from industry that the MILP model can be solved to optimality in reasonable time with a standard MILP solver for several small instances. We also show that the heuristic gives the same solutions for most of the small instances, and is also fast, efficient and practical for large instances.

  • 108.
    Baltz, Andreas
    et al.
    Christian-Albrechts Universität Kiel, Germany.
    Jäger, Gerold
    Christian-Albrechts Universität Kiel, Germany.
    Srivastav, Anand
    Christian-Albrechts Universität Kiel, Germany.
    Construction of Sparse Asymmetric Connectors2003Ingår i: Proceedings of European Conference on Combinatorics, Graph Theory and Applications (Eurocomb 2003), 2003Konferensbidrag (Refereegranskat)
  • 109.
    Baltz, Andreas
    et al.
    Christian-Albrechts-Universität Kiel, Germany.
    Jäger, Gerold
    Christian-Albrechts-Universität Kiel, Germany.
    Srivastav, Anand
    Christian-Albrechts-Universität Kiel, Germany.
    Constructions of Sparse Asymmetric Connectors2003Ingår i: Proceedings of 23rd Conference of Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2003) / [ed] P.K. Lodaya and J. Radhakrishnan, Berlin-Heidelberg: Springer Berlin/Heidelberg, 2003, s. 13-22Konferensbidrag (Refereegranskat)
  • 110.
    Baltz, Andreas
    et al.
    Mathematisches seminar, Christian-Albrechts-Universität zu Kiel, Germany.
    Jäger, Gerold
    Mathematisches seminar, Christian-Albrechts-Universität zu Kiel, Germany.
    Srivastav, Anand
    Mathematisches seminar, Christian-Albrechts-Universität zu Kiel, Germany.
    Constructions of Sparse Asymmetric Connectors with Number Theoretic Methods2005Ingår i: Networks, ISSN 0028-3045, E-ISSN 1097-0037, Vol. 45, nr 3, s. 119-124Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the problem of connecting a set I of n inputs to a set O of N outputs (n ≤ N) by as few edges as possible such that for every injective mapping f : I → O there are n vertex disjoint paths from i to f(i) of length k for a given k . For k = Ω(log N + logn) Oruς (1994) gave the presently best (n,N)-connector with O(N+n·log n) edges. For k=2 and N the square of a prime, Richards and Hwang (1985) described a construction using edges. We show by a probabilistic argument that an optimal (n,N)-connector has Θ (N) edges, if for some ε>0. Moreover, we give explicit constructions based on a new number theoretic approach that need at most edges for arbitrary choices of n and N. The improvement we achieve is based on applying a generalization of the Erdös-Heilbronn conjecture on the size of restricted sums.

  • 111. Banerjee, M.
    et al.
    Zhang, Lai
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Stabilizing Role of Nonlocal Interaction on Spatio-temporal Pattern Formation2016Ingår i: Mathematical Modelling of Natural Phenomena, ISSN 0973-5348, E-ISSN 1760-6101, Vol. 11, nr 5, s. 103-118Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Here we study a spatio-temporal prey-predator model with ratio-dependent functional response and nonlocal interaction term in the prey growth. For a clear understanding of the effect of nonlocal interaction on the resulting stationary and non-stationary patterns, we consider the nonlocal interaction term in prey growth only to describe the nonlocal intra-specific competition due to limited resources for the prey. First we obtain the patterns exhibited by the basic model in the absence of nonlocal interaction and then explore the effect of nonlocal interaction on the resulting patterns. We demonstrate the stabilizing role of nonlocal interaction as it induces stationary pattern from periodic and chaotic regimes with an increase in the range of nonlocal interaction. The existence of multiple branches of stationary solutions, bifurcating from homogeneous steady-state as well as non-stationary patterns, is illustrated with the help of numerical continuation technique.

  • 112. Banerjee, Malay
    et al.
    Zhang, Lai
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Influence of discrete delay on pattern formation in a ratio-dependent prey-predator model2014Ingår i: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 67, s. 73-81Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we explore how the two mechanisms, Turing instability and Hopf bifurcation, interact to determine the formation of spatial patterns in a ratio-dependent prey predator model with discrete time delay. We conduct both rigorous analysis and extensive numerical simulations. Results show that four types of patterns, cold spot, labyrinthine, chaotic as well as mixture of spots and labyrinthine can be observed with and without time delay. However, in the absence of time delay, the two aforementioned mechanisms have a significant impact on the emergence of spatial patterns, whereas only Hopf bifurcation threshold is derived by considering the discrete time delay as the bifurcation parameter. Moreover, time delay promotes the emergence of spatial patterns via spatio-temporal Hopf bifurcation compared to the non-delayed counterpart, implying the destabilizing role of time delay. In addition, the destabilizing role is prominent when the magnitude of time delay and the ratio of diffusivity are comparatively large. 

  • 113. Banerjee, Malay
    et al.
    Zhang, Lai
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Time delay can enhance spatio-temporal chaos in a prey-predator model2016Ingår i: Ecological Complexity: An International Journal on Biocomplexity in the Environment and Theoretical Ecology, ISSN 1476-945X, E-ISSN 1476-9840, Vol. 27, s. 17-28Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we explore how the time delay induced Hopf-bifurcation interacts with Turing instability to determine the resulting spatial patterns. For this study, we consider a delayed prey-predator model with Holling type-II functional response and intra-specific competition among the predators. Analytical criteria for the delay induced Hopf-bifurcation and for the delayed spatio-temporal model are provided with numerical example to validate the analytical results. Exhaustive numerical simulation reveals the appearance of three types of stationary patterns, cold spot, labyrinthine, mixture of stripe-spot and two non-stationary patterns, quasi-periodic and spatio-temporal chaotic patterns. The qualitative features of the patterns for the non-delayed and the delayed spatio-temporal model are the same but their occurrence is solely controlled by the temporal parameters, rate of diffusivity and magnitude of the time delay. It is evident that the magnitude of time delay parameter beyond the Hopf-bifurcation threshold mostly produces spatio-temporal chaotic patterns. 

  • 114. Barban, Nicola
    et al.
    de Luna, Xavier
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Lundholm, Emma
    Umeå universitet, Samhällsvetenskapliga fakulteten, Institutionen för geografi och ekonomisk historia. Umeå universitet, Samhällsvetenskapliga fakulteten, Enheten för demografi och åldrandeforskning (CEDAR).
    Svensson, Ingrid
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Billari, F. C.
    Causal Effects of the Timing of Life-course Events: Age at Retirement and Subsequent Health2020Ingår i: Sociological Methods & Research, ISSN 0049-1241, E-ISSN 1552-8294, Vol. 49, nr 1, s. 216-249Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this article, we combine the extensive literature on the analysis of life-course trajectories as sequences with the literature on causal inference and propose a new matching approach to investigate the causal effect of the timing of life-course events on subsequent outcomes. Our matching approach takes into account pre-event confounders that are both time-independent and time-dependent as well as life-course trajectories. After matching, treated and control individuals can be compared using standard statistical tests or regression models. We apply our approach to the study of the consequences of the age at retirement on subsequent health outcomes, using a unique data set from Swedish administrative registers. Once selectivity in the timing of retirement is taken into account, effects on hospitalization are small, while early retirement has negative effects on survival. Our approach also allows for heterogeneous treatment effects. We show that the effects of early retirement differ according to preretirement income, with higher income individuals tending to benefit from early retirement, while the opposite is true for individuals with lower income.

  • 115.
    Barkhordari, Mahnaz
    et al.
    Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran.
    Padyab, Mojgan
    Umeå universitet, Samhällsvetenskapliga fakulteten, Enheten för demografi och åldrandeforskning (CEDAR).
    Hadaegh, Farzad
    Prevention of Metabolic Disorders Research Center, Research Institute for Endocrine Sciences, Shahid Beheshti University of Medical Sciences, Tehran, IR Iran.
    Azizi, Fereidoun
    Research Center, Research Institute for Endocrine Sciences, Shahid Beheshti University of Medical Sciences, Tehran, IR Iran.
    Bozorgmanesh, Mohammadreza
    Prevention of Metabolic Disorders Research Center, Research Institute for Endocrine Sciences, Shahid Beheshti University of Medical Sciences, Tehran, IR Iran.
    Stata Modules for Calculating Novel Predictive Performance Indices for Logistic Models2016Ingår i: International Journal of Endocrinology and Metabolism, ISSN 1726-9148, Vol. 14, nr 1, artikel-id e26707Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Background: Prediction is a fundamental part of prevention of cardiovascular diseases (CVD). The development of prediction algorithms based on the multivariate regression models loomed several decades ago. Parallel with predictive models development, biomarker researches emerged in an impressively great scale. The key question is how best to assess and quantify the improvement in risk prediction offered by new biomarkers or more basically how to assess the performance of a risk prediction model. Discrimination, calibration, and added predictive value have been recently suggested to be used while comparing the predictive performances of the predictive models’ with and without novel biomarkers.Objectives: Lack of user-friendly statistical software has restricted implementation of novel model assessment methods while examining novel biomarkers. We intended, thus, to develop a user-friendly software that could be used by researchers with few programming skills.Materials and Methods: We have written a Stata command that is intended to help researchers obtain cut point-free and cut point-based net reclassification improvement index and (NRI) and relative and absolute Integrated discriminatory improvement index (IDI) for logistic-based regression analyses.We applied the commands to a real data on women participating the Tehran lipid and glucose study (TLGS) to examine if information of a family history of premature CVD, waist circumference, and fasting plasma glucose can improve predictive performance of the Framingham’s “general CVD risk” algorithm.Results: The command is addpred for logistic regression models.Conclusions: The Stata package provided herein can encourage the use of novel methods in examining predictive capacity of ever-emerging plethora of novel biomarkers.

  • 116.
    Bartlett, Roscoe A.
    et al.
    Sandia National Laboratories.
    Van Bloemen Waanders, Bart
    Sandia National Laboratories.
    Berggren, Martin
    Department of Information Technology, Uppsala University.
    Hybrid Differentiation Strategies for Simulation and Analysis of Applications in C++2008Ingår i: ACM Transactions on Mathematical Software, ISSN 0098-3500, E-ISSN 1557-7295, Vol. 35, nr 1Artikel i tidskrift (Refereegranskat)
  • 117.
    Bartolini Bussi, M G
    et al.
    Universita' di Modena e Reggio Emilia, Modena, Itlay.
    Gade, Sharada
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik.
    Janvier, M
    Kahane, J-P
    Matsko, V
    Maschietto, M
    Ouvrier-Buffet, C
    Saul, M
    Mathematics in context: focusing on students2009Ingår i: Challenging Mathematics In and Beyond the Classroom – The 16th ICMI Study / [ed] E. J. Barbeau and P. J. Taylor, New York: Springer Science+Business Media B.V., 2009, s. 171-203Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    This chapter presents nine case studies in which school students engage in challenging mathematics outside their immediate classroom environment. In each case, students are encouraged to collaborate in investigations that go beyond the standard curriculum and creatively use the ingredients of the particular context. In Italy, students visit a mathematical laboratory to understand and utilize mathematical machines. Morning assembly at an Indian school brings students from many classes together in the solution of mathematical problems. Four of the projects are from France: students analyze the configuration of a heap of sand, pursue astronomical investigations with software, obtain a flavor of research by having secondary school teams investigate interesting problems, and are presented at all levels with open-ended research problems. There are three programs from the United States, the first, an advanced geometry sequence for secondary students completing the regular syllabus early, the second, activities arising from exhibits in an art museum, and the third, using the school lawn to deepen student understanding of geometric constructions. All such activities need to be evaluated for their effectiveness, so that they move from just being initiatives of dynamic individuals to serve as the foundation for systemic improvements in the way in which students learn, understand and use mathematics. In the early part of this chapter, we briefly mention how research into such activities might be approached.

  • 118.
    Baudin, Anders
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten.
    On the Application of Short-term Causal Models1977Doktorsavhandling, monografi (Övrigt vetenskapligt)
    Abstract [en]

    Causal (econometric) models are often employed as instruments for for-casting in short-term planning within organizations. The aim of this work is to contribute to an understanding of the short-term aspects of causal model building. The interest focuses mainly on the adjustment problem (as one of a number of data problems) and the problem of auto-correlated disturbances. The general considerations for and against trend and seasonal adjustment in a short-term context are discussed. Furthermore different principles for chosing an appropriate adjustment technique are considered. Imperfections in data and operations performed on the original data, e.g. different adjustments, are some of the causes of auto-correlated disturbances. A multivariate ARMA-process is proposed as one means of taking account of the autocorrelation. An estimation procedure is suggested for recursive systems, the consistency of the estimator is proved and the procedure is applied to an empirical situation: a model for the pulp and paper industry in the United States. Different specifications of the disturbances are compared in the application with regard to fit in observation period and forecasting. Although the model with a multivariate ARMA-specification in disturbances gives a better fit than its alternatives it does not provide better forecasts in a period subsequent to the observation period.

  • 119.
    Bayisa, Fekadu
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Kuljus, Kristi
    Institute of Mathematics and Statistics, University of Tartu, Tartu, Estonia.
    Johansson, Adam
    Umeå universitet, Medicinska fakulteten, Institutionen för strålningsvetenskaper.
    Bolin, David
    Department of Mathematical Sciences, Chalmers and University of Gothenburg, Gothenburg, Sweden.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Prediction of CT images from MR images with hidden Markov and random field models2016Ingår i: Proceedings of the 8th International Workshop on Spatio-Temporal Modelling / [ed] A. Iftimi, J. Mateu and F. Montes, 2016, s. 163-163Konferensbidrag (Övrigt vetenskapligt)
  • 120.
    Bayisa, Fekadu L.
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Liu, Xijia
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Garpebring, Anders
    Umeå universitet, Medicinska fakulteten, Institutionen för strålningsvetenskaper.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Computed Tomography Image Estimation by Statistical Learning MethodsManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    There is increasing interest in computed tomography (CT) image estimations from magnetic resonance (MR) images. The estimated CT images canbe utilised for attenuation correction, patient positioning, and dose planningin diagnostic and radiotherapy workflows. This study presents a statisticallearning method for CT image estimation. We have used predefined tissuetype information in a Gaussian mixture model to explore the estimation.The performance of our method was evaluated using cross-validation on realdata. In comparison with the existing model-based CT image estimationmethods, the proposed method has improved the estimation, particularly inbone tissues. Evaluation of our method shows that it is a promising methodto generate CT image substitutes for the implementation of fully MR-basedradiotherapy and PET/MRI applications.

  • 121.
    Bayisa, Fekadu Lemessa
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Statistical methods in medical image estimation and sparse signal recovery2018Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [sv]

    Denna avhandling presenterar arbete kring metoder för skattning av datortomografibilder (CT) från magnetiska resonanstomografibilder (MR) för ett antal diagnostiska och terapeutiska arbetsflöden. Studien demonstrerar även en metod för gles signalrekonstruktion, vilket är en mellanliggande metod för rekonstruktion av MR-bilder. Avhandlingen består av fyra artiklar. De tre första artiklarna handlar om att utveckla statistiska metoder för uppskattning av CT-bilder från MR-bilder. Här formuleras rumsliga och icke-rumsliga modeller för skattning av CT-bilder från MR-bilder, där de rumsliga modellerna inkluderar dolda Markov-modeller (HMM) och dolda Markov-slumpfältmodeller (HMRF), medan de icke-rumsliga modellerna består av Gaussiska mix-modeller (GMM) och skeva Gaussiska mixmodeller (SGMM). De statistiska modellerna skattas via en maximum-likelihoodansats, där EM-algoritmen används för GMM och SGMM, EM-gradientalgoritmen för HMRF samt Baum-Welch-algoritmen för HMM. Vi har även undersökt CTbildskattning med hjälp av GMM och övervakade statistiska inlärningsmetoder. Modellernas prestanda har utvärderats med hjälp av korsvalidering på faktiska data. Genom att jämföra prestandan hos modellernas CT-bildskattningar har vi observerat att GMM kombinerat med övervakad statistisk inlärning har den bästa prestandan, i synnerhet ifråga om benvävnad. Den fjärde artikeln behandlar en gles modellering inom signalrekonstruktion. Med hjälp av så kallade ”spike and slab priors” för signalen formulerade vi ett glest signalrekonstruktionsproblem och utvecklade en adaptiv algoritm för gles signalrekonstruktion. Den utvecklade algoritmen har bättre prestanda än den nyligen föreslagna iterativ konvex förfining (ICR)-algoritmen. De metoder som introducerats i detta arbete är bidrag till litteraturen inom så kallade ”lattice-processer” och signalbehandling. Resultaten levererar ett bidrag till forskningen kring ersättandet av CT-bilder med syntetiska eller pseudo-CTbilder, samt till effektiv gles signalrekonstruktion.

  • 122.
    Bayisa, Fekadu
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Liu, Xijia
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Garpebring, Anders
    Umeå universitet, Medicinska fakulteten, Institutionen för strålningsvetenskaper.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Statistical learning in computed tomography image estimation2018Ingår i: Medical physics (Lancaster), ISSN 0094-2405, Vol. 45, nr 12, s. 5450-5460Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Purpose: There is increasing interest in computed tomography (CT) image estimations from magneticresonance (MR) images. The estimated CT images can be utilized for attenuation correction, patientpositioning, and dose planning in diagnostic and radiotherapy workflows. This study aims to introducea novel statistical learning approach for improving CT estimation from MR images and to compare theperformance of our method with the existing model-based CT image estimation methods.

    Methods: The statistical learning approach proposed here consists of two stages. At the trainingstage, prior knowledge about tissue types from CT images was used together with a Gaussian mixturemodel (GMM) to explore CT image estimations from MR images. Since the prior knowledge is notavailable at the prediction stage, a classifier based on RUSBoost algorithm was trained to estimatethe tissue types from MR images. For a new patient, the trained classifier and GMMs were used topredict CT image from MR images. The classifier and GMMs were validated by using voxel-leveltenfold cross-validation and patient-level leave-one-out cross-validation, respectively.

    Results: The proposed approach has outperformance in CT estimation quality in comparison withthe existing model-based methods, especially on bone tissues. Our method improved CT image estimationby 5% and 23% on the whole brain and bone tissues, respectively.

    Conclusions: Evaluation of our method shows that it is a promising method to generate CTimage substitutes for the implementation of fully MR-based radiotherapy and PET/MRI applications

  • 123.
    Bayisa, Fekadu
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Model-based computed tomography image estimation: partitioning approach2019Ingår i: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 46, nr 14, s. 2627-2648Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    There is a growing interest to get a fully MR based radiotherapy. The most important development needed is to obtain improved bone tissue estimation. The existing model-based methods perform poorly on bone tissues. This paper was aimed at obtaining improved bone tissue estimation. Skew-Gaussian mixture model and Gaussian mixture model were proposed to investigate CT image estimation from MR images by partitioning the data into two major tissue types. The performance of the proposed models was evaluated using the leaveone-out cross-validation method on real data. In comparison with the existing model-based approaches, the model-based partitioning approach outperformed in bone tissue estimation, especially in dense bone tissue estimation.

  • 124.
    Bayisa, Fekadu
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Model-based Estimation of Computed Tomography Images2017Konferensbidrag (Övrigt vetenskapligt)
  • 125.
    Bayisa, Fekadu
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Model-based Estimation of Computed Tomography Images2017Manuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    There is a growing interest to get a fully MR based radiotherapy. The most important development needed is to obtain improved bone tissue estimation. Existing model-based methods have performed poorly on bone tissues. This paper aims to obtainimproved estimation of bone tissues. Skew-Gaussian mixture model (SGMM) isproposed to further investigate CT image estimation from MR images. The estimation quality of the proposed model is evaluated using leave-one-out cross-validation method on real data. In comparison with the existing model-based approaches, the approach utilized in this paper outperforms in estimation of bone tissues, especiallyon dense bone tissues.

  • 126.
    Bayisa, Fekadu
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Zhou, Zhiyong
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Cronie, Ottmar
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Adaptive algorithm for sparse signal recovery2019Ingår i: Digital signal processing (Print), ISSN 1051-2004, E-ISSN 1095-4333, Vol. 87, s. 16s. 10-18Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The development of compressive sensing in recent years has given much attention to sparse signal recovery. In sparse signal recovery, spike and slab priors are playing a key role in inducing sparsity. The use of such priors, however, results in non-convex and mixed integer programming problems. Most of the existing algorithms to solve non-convex and mixed integer programming problems involve either simplifying assumptions, relaxations or high computational expenses. In this paper, we propose a new adaptive alternating direction method of multipliers (AADMM) algorithm to directly solve the suggested non-convex and mixed integer programming problem. The algorithm is based on the one-to-one mapping property of the support and non-zero element of the signal. At each step of the algorithm, we update the support by either adding an index to it or removing an index from it and use the alternating direction method of multipliers to recover the signal corresponding to the updated support. Moreover, as opposed to the competing “adaptive sparsity matching pursuit” and “alternating direction method of multipliers” methods our algorithm can solve non-convex problems directly. Experiments on synthetic data and real-world images demonstrated that the proposed AADMM algorithm provides superior performance and is computationally cheaper than the recently developed iterative convex refinement (ICR) and adaptive matching pursuit (AMP) algorithms.

  • 127. Bech, Morten L
    et al.
    Bergstrom, Carl T
    Rosvall, Martin
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Garratt, Rodney J
    Mapping change in the overnight money market2015Ingår i: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 424, s. 44-51Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We use an information-theoretic approach to describe changes in lending relationships between financial institutions around the time of the Lehman Brothers failure. Unlike previous work that conducts maximum likelihood estimation on undirected networks our analysis distinguishes between borrowers and lenders and looks for broader lending relationships (multi-bank lending cycles) that extend beyond the immediate counter-parties. We detect significant changes in lending patterns following implementation of the Interest on Required and Excess Reserves policy by the Federal Reserve in October 2008. Analysis of micro-scale rates of change in the data suggests these changes were triggered by the collapse of Lehman Brothers a few weeks before.

  • 128. Behme, Anita
    et al.
    Bondesson, Lennart
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    A class of scale mixtures of Gamma(k)-distributions that are generalized gamma convolutions2017Ingår i: Bernoulli, ISSN 1350-7265, E-ISSN 1573-9759, Vol. 23, nr 1, s. 773-787Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Let k > 0 be an integer and Y a standard Gamma(k) distributed random variable. Let X be an independent positive random variable with a density that is hyperbolically monotone (HIM) of order k. Then Y . X and Y/X both have distributions that are generalized gamma convolutions (GGCs). This result extends a result of Roynette et al. from 2009 who treated the case k = 1 but without use of the HM-concept. Applications in excursion theory of diffusions and in the theory of exponential functionals of Levy processes are mentioned.

  • 129.
    Behrstock, Jason
    et al.
    Lehman College, CUNY.
    Falgas-Ravry, Victor
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Hagen, Mark
    University of Cambridge.
    Susse, Tim
    University of Nebraska-Lincoln.
    Global Structural Properties of Random Graphs2018Ingår i: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, nr 5, s. 1411-1441Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study two global structural properties of a graph , denoted AS and CFS, which arise in a natural way from geometric group theory. We study these properties in the Erd ˝os–Rényi random graph model G(n, p), proving the existence of a sharp threshold for a random graph to have the AS property asymptotically almost surely, and giving fairly tight bounds for the corresponding threshold for the CFS property. As an application of our results, we show that for any constant p and any ∈ G(n, p), the right-angled Coxeter group W asymptotically almost surely has quadratic divergence and thickness of order 1, generalizing and strengthening a result of Behrstock–Hagen–Sisto [8]. Indeed, we show that at a large range of densities a random right-angled Coxeter group has quadratic divergence. 1

  • 130.
    Belitskii, Genrich
    et al.
    Ben-Gurion University of the Negev, Israel.
    Dmytryshyn, Andrii
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Lipyanski, Ruvim
    Ben-Gurion University of the Negev, Israel.
    Sergeichuk, Vladimir
    Institute of Mathematics, Kiev, Ukraine.
    Tsurkov, Arkady
    Ben-Gurion University of the Negev, Israel.
    Problems of classifying associative or Lie algebras over a field of characteristic not 2 and finite metabelian groups are wild2009Ingår i: The Electronic Journal of Linear Algebra, ISSN 1537-9582, E-ISSN 1081-3810, Vol. 18, s. 516-529Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Let F be a field of characteristic different from 2. It is shown that the problems of classifying

    (i) local commutative associative algebras over F with zero cube radical,

    (ii) Lie algebras over F with central commutator subalgebra of dimension 3, and

    (iii) finite p-groups of exponent p with central commutator subgroup of order  are hopeless since each of them contains

    • the problem of classifying symmetric bilinear mappings UxU → V , or

    • the problem of classifying skew-symmetric bilinear mappings UxU → V ,

    in which U and V are vector spaces over F (consisting of p elements for p-groups (iii)) and V is 3-dimensional. The latter two problems are hopeless since they are wild; i.e., each of them contains the problem of classifying pairs of matrices over F up to similarity.

  • 131.
    Belyaev, Yu. K.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    This issue is devoted to the memory of Boris Vladimirovich Gnedenko2014Ingår i: Markov Processes and Related Fields, ISSN 1024-2953, Vol. 20, nr 3, s. 385-389Artikel i tidskrift (Refereegranskat)
  • 132.
    Belyaev, Yu.K.
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Rydén, Patrik
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    On Non-Parametric Estimation of Poission Point Processes Related to Failure Stresses of Fibres2000Rapport (Övrigt vetenskapligt)
    Abstract [en]

    We consider statistical analysis of the reliability of fibres. The problem is to estimate the distribution law of random failure stresses of fibres (i.e. the critical level of stresses that destroy fibres) by using data obtained in a special kind of test, where several fibres are tested until they break. All new pieces resulting from this test will also be tested, if they are long enough. The test ends when all the remaining pieces are too short to be tested further. We refer to these as binary tree structured tests. We assume that the cumulative hazard function (c.h.f.) of the failure stresses of these fibres is continuous, and that the fibres are statistically identical. Under these assumptions we obtain, as the number of tested fibres increases, a strongly consistent Nelson-Aalen type estimator of the c.h.f. The functional central limit resampling theorem in Skorohod space is proved. It justifies the possibility of using resampling for estimating the accuracy of these estimators. The theorem shows that resampling can be used to asymptotically consistently estimate distribution laws of continuous functionals of the random deviations between the estimator and the true c.h.f.. For example, resampling can be used to estimate the distribution law of the maximum distance between estimators and estimands. Numerical examples suggest that resampling works well for a moderate number of tested fibres.

  • 133.
    Belyaev, Yuri
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Matematisk statistik.
    Application of Resampling Methods to Linear Heteroscedastic Regression with Vector Responses2004Rapport (Övrigt vetenskapligt)
  • 134.
    Belyaev, Yuri
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Vivid recollections on A.N. Kolmogorov2006Ingår i: Kolmogorov in Recollections of his PhD students, Moscow Publishing Company MHLIMO , 2006, s. 100-103Kapitel i bok, del av antologi (Övrigt vetenskapligt)
  • 135.
    Belyaev, Yuri K
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Analysis of contingent valuation data with self-selected rounded WTP-intervals collected by two-steps sampling plans2011Ingår i: Abstracts of the 9th Tartu Conference on Multivariate Statistics & 20th International Workshop on Matrices and Statistics / [ed] Tönu Kollo, Kelli Sander, Ants Kaasik, University of Tartu, 2011, s. 11-12Konferensbidrag (Övrigt vetenskapligt)
  • 136.
    Belyaev, Yuri K.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Application of consistent resampling to linear heteroscedastic regression2003Ingår i: Bulletin of the 54th Session of the International Statistical Institute, 2003Konferensbidrag (Övrigt vetenskapligt)
  • 137.
    Belyaev, Yuri K
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Approaching sequences of random distribution laws with applications to resampling1996Rapport (Övrigt vetenskapligt)
  • 138.
    Belyaev, Yuri K
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Assessing accuracy of statistical inferences by resamplings2010Ingår i: Mathematical and Statistical Models and Methods in Reliability: Applications to Medicine, Finance, and Quality Control / [ed] V.V. Rykov, N. Balakrishnan, M.S. Nikulin, New York: Birkhäuser Verlag, 2010, s. 193-206Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    Suppose that a list of explanatory variables and corresponding random responses was obtained during a series of regression experiments. The characteristic of interest is the mean value of responses considered as a regression function of corresponding values of explanatory variables. For example, if responses are failure times of tested elements, then the conditional mean value of life time given the value of explanatory variable is one of the important reliability characteristics of the tested elements. The analysis of this type of data can be realized in the framework of linear heteroscedastic regression models. Here, one of the central problems is a consistent estimation of the unknown regression function when the size of data grows unboundedly. The problems related to analysis of regression data attracted many researches, see Wu [Ann. Statist. 14, 1261–1350 (1986)]. We give an approach to consistent solution of the problems under the assumption that values of explanatory variables are real numbers and the regression function is a polynomial with unknown degree and coefficients. The selection of regression function is based on resamplings from terms in the sum of the residuals estimated by the ordinary least squares method with various values of polynomial degree. In a similar way, resamplings from the weighted estimated residuals are used for consistent estimation of the deviations distributions of estimated coefficients from their true unknown values. The consistency of applied resamplings methods holds under certain assumptions, e.g. it is assumed that the residuals distributions have uniformly integrable second moments (assumption AW 2). Given in Appendix a variant of the Central Limit Resampling Theorem is used in the proofs of Theorems 1 and 2.

  • 139.
    Belyaev, Yuri K
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Asymptotical properties of nonparametric point estimators based on complexly structured reliability data with right-censoring1991Ingår i: Statistics (Berlin), ISSN 0233-1888, E-ISSN 1029-4910, Vol. 22, nr 4, s. 589-612Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper presents a general approach to nonparametric estimation of unknown distribution functions and related characteristics such as cumulative hazard functions. It is based on the notion of portions of statistical data and on the property of discertely separated distributions of statistical data General assumptions are given under which the corresponding generalized maximum likelihood estimators are consistent and their deviations have asymptotically normal distributions, if the number of portions increases to indinity.

  • 140.
    Belyaev, Yuri K.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Bootstrap, Resampling and Mallows Metric1995Rapport (Övrigt vetenskapligt)
  • 141.
    Belyaev, Yuri K
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Central limit theorems for m-dependent heterogeneous random variables1996Rapport (Övrigt vetenskapligt)
  • 142.
    Belyaev, Yuri K.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Comment (on the paper Singpurwalla, N. Some Cracks in the Empire of Chance)2002Ingår i: International Statistical Review, ISSN 0306-7734, E-ISSN 1751-5823, Vol. 70, nr 1, s. 65-67Artikel i tidskrift (Övrigt vetenskapligt)
  • 143.
    Belyaev, Yuri K.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Computer Intensive Methods Based on Resampling in Analysis of Reliability and Survival Data2000Ingår i: Resent Advances in Reliability, Boston: Birkhäuser Verlag, 2000, s. 195-208Kapitel i bok, del av antologi (Övrigt vetenskapligt)
  • 144.
    Belyaev, Yuri K.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Methoden der Wahrscheinlichkeitsrechnung und Statistik bei der Analise von Zuverlassigkeitsdaten2000Bok (Övrigt vetenskapligt)
  • 145.
    Belyaev, Yuri K
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Methods of mathematical statistics in the reliability theory2012Ingår i: Математические методы в теории надежности: основные характеристики надежности и их статистический анализ / [ed] Belyaev, Y.K., Gnedenko, B.V. and Solovjev, A.D., Moscow: URSS Librokom , 2012, 2nd, s. 551-571Kapitel i bok, del av antologi (Övrigt vetenskapligt)
  • 146.
    Belyaev, Yuri K.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    My communication2003Ingår i: Bulletin of the International Statistical Institute, 50th Session of ISI, Berlin, Germany, 2003Kapitel i bok, del av antologi (Refereegranskat)
  • 147.
    Belyaev, Yuri K.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    My PhD scientific supervisor - Kolmogorov, A.N. Letters of Elets State University2008Ingår i: Pedagogics, History and Theory of Mathematical Education, Vol. 17, s. 24-29Artikel i tidskrift (Övrigt vetenskapligt)
  • 148.
    Belyaev, Yuri K
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Necessary and sufficient conditions for consistency of resampling, centre of biostochastics2003Rapport (Övrigt vetenskapligt)
  • 149.
    Belyaev, Yuri K.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Non-Parametric Estimators of Risk Functions of Tensile Strengths of Wires and Their Deviations1997Ingår i: Theory of Stochastic Processes, Vol. 3 (19), nr 1-2, s. 110-120Artikel i tidskrift (Refereegranskat)
  • 150.
    Belyaev, Yuri K
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    On the accuracy of classifiers and corresponding digital discretely colored images2002Ingår i: Theory of Probability and Mathematical Statistics. American Mathematical Society, ISSN 0094-9000, Vol. 65, s. 15-25Artikel i tidskrift (Refereegranskat)
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