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  • 1.
    Albahaca, Juan Carlos
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Analytical and Numerical Study of the Poincaré Map with Applications on the Computation of Periodic Orbits2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 2.
    Amiri, Saeid
    et al.
    Univ Wisconsin, Dept Nat & Appl Sci, Green Bay, WI 54302 USA..
    Modarres, Reza
    George Washington Univ, Dept Stat, Washington, DC 20052 USA..
    Zwanzig, Silvelyn
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Tests of perfect judgment ranking using pseudo-samples2017In: Computational statistics (Zeitschrift), ISSN 0943-4062, E-ISSN 1613-9658, Vol. 32, no 4, p. 1309-1322Article in journal (Refereed)
    Abstract [en]

    Ranked set sampling (RSS) is a sampling approach that can produce improved statistical inference when the ranking process is perfect. While some inferential RSS methods are robust to imperfect rankings, other methods may fail entirely or provide less efficiency. We develop a nonparametric procedure to assess whether the rankings of a given RSS are perfect. We generate pseudo-samples with a known ranking and use them to compare with the ranking of the given RSS sample. This is a general approach that can accommodate any type of raking, including perfect ranking. To generate pseudo-samples, we consider the given sample as the population and generate a perfect RSS. The test statistics can easily be implemented for balanced and unbalanced RSS. The proposed tests are compared using Monte Carlo simulation under different distributions and applied to a real data set.

  • 3.
    Andersson, Björn
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Validated Enclosures of Rotation Numbers2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 4.
    Andersson, Jesper
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Houghtransformen – ett verktyg för bildigenkänning2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 5.
    Aoki, Yasunori
    et al.
    Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics. Department of Mathematics, Uppsala University.
    Nordgren, Rikard
    Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.
    Hooker, Andrew C.
    Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.
    Preconditioning of Nonlinear Mixed Effects Models for Stabilisation of Variance-Covariance Matrix Computations2016In: AAPS Journal, ISSN 1550-7416, E-ISSN 1550-7416, Vol. 18, no 2, p. 505-518Article in journal (Refereed)
    Abstract [en]

    As the importance of pharmacometric analysis increases, more and more complex mathematical models are introduced and computational error resulting from computational instability starts to become a bottleneck in the analysis. We propose a preconditioning method for non-linear mixed effects models used in pharmacometric analyses to stabilise the computation of the variance-covariance matrix. Roughly speaking, the method reparameterises the model with a linear combination of the original model parameters so that the Hessian matrix of the likelihood of the reparameterised model becomes close to an identity matrix. This approach will reduce the influence of computational error, for example rounding error, to the final computational result. We present numerical experiments demonstrating that the stabilisation of the computation using the proposed method can recover failed variance-covariance matrix computations, and reveal non-identifiability of the model parameters.

  • 6.
    Aoki, Yasunori
    et al.
    Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Sundqvist, Monika
    AstraZeneca R&D.
    Hooker, Andrew C.
    Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.
    Gennemark, Peter
    AstraZeneca R&D.
    PopED lite: an optimal design software for preclinical pharmacokinetic and pharmacodynamic studiesManuscript (preprint) (Other academic)
    Abstract [en]

    Optimal experimental design approaches are seldom used in pre-clinical drug discovery. Main reasons for this lack of use are that available software tools require relatively high insight in optimal design theory, and that the design-execution cycle of in vivo experiments is short, making time-consuming optimizations infeasible. We present the publicly available software PopED lite in order to increase the use of optimal design in pre-clinical drug discovery. PopED lite is designed to be simple, fast and intuitive. Simple, to give many users access to basic optimal design calculations. Fast, to fit the short design-execution cycle and allow interactive experimental design (test one design, discuss proposed design, test another design, etc). Intuitive, so that the input to and output from the software can easily be understood by users without knowledge of the theory of optimal design. In this way, PopED lite is highly useful in practice and complements existing tools. Key functionality of PopED lite is demonstrated by three case studies from real drug discovery projects. 

  • 7. Barrio, Roberto
    et al.
    Dena, Angeles
    Tucker, Warwick
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    A database of rigorous and high-precision periodic orbits of the Lorenz model2015In: Computer Physics Communications, ISSN 0010-4655, E-ISSN 1879-2944, Vol. 194, p. 76-83Article in journal (Refereed)
    Abstract [en]

    A benchmark database of very high-precision numerical and validated initial conditions of periodic orbits for the Lorenz model is presented. This database is a "computational challenge" and it provides the initial conditions of all periodic orbits of the Lorenz model up to multiplicity 10 and guarantees their existence via computer-assisted proofs methods, The orbits are computed using high-precision arithmetic and mixing several techniques resulting in 1000 digits of precision on the initial conditions of the periodic orbits, and intervals of size 10100 that prove the existence of each orbit. Program summary Program title: Lorenz-Database Catalogue identifier: AEWM_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEWM_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 8515 No. of bytes in distributed program, including test data, etc.: 6964501 Distribution format: tar.gz Programming language: Data. Computer: Any computer. Operating system: Any. RAM: Database, no requirements Classification: 4.3, 4.12. Nature of problem: Database of all periodic orbits of the Lorenz model up to multiplicity 10 with 1000 precision digits. Solution method: Advanced search methods for locating unstable periodic orbits combined with the Taylor series method for multiple precision integration of ODEs and interval methods for providing Computer-Assisted proofs of the periodic orbits. Unusual features: The database gives 100 digits rigorously proved using Computer-Assisted techniques and 1000 digits using an optimal adaptive Taylor series method. Running time: Not Applicable.

  • 8. Bartha, Ferenc A.
    et al.
    Tucker, Warwick
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Fixed points of a destabilized Kuramoto-Sivashinsky equation2015In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 266, p. 339-349Article in journal (Refereed)
    Abstract [en]

    We consider the family of destabilized Kuramoto-Sivashinsky equations in one spatial dimension u(t) + nu u(xxx) + beta u(xx) + gamma uu(x) - alpha u for alpha, nu >= 0 and beta, gamma is an element of R. For certain parameter values, shock like stationary solutions have been numerically observed. In this work we verify the existence of several such solutions using the framework of self consistent bounds and validated numerics. Published by Elsevier Inc.

  • 9.
    Bartoszek, Krzysztof
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Phylogenetic effective sample size2016In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 407, p. 371-386Article in journal (Refereed)
    Abstract [en]

    In this paper I address the question—how large is a phylogenetic sample? I propose a definition of a phylogenetic effective sample size for Brownian motion and Ornstein-Uhlenbeck processes-the regression effective sample size. I discuss how mutual information can be used to define an effective sample size in the non-normal process case and compare these two definitions to an already present concept of effective sample size (the mean effective sample size). Through a simulation study I find that the AICc is robust if one corrects for the number of species or effective number of species. Lastly I discuss how the concept of the phylogenetic effective sample size can be useful for biodiversity quantification, identification of interesting clades and deciding on the importance of phylogenetic correlations.

  • 10.
    Bartoszek, Krzysztof
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Pietro, Lio'
    Cambridge University.
    A novel algorithm to reconstruct phylogenies using gene sequences and expression data2014In: International Proceedings of Chemical, Biological & Environmental Engineering; Environment, Energy and Biotechnology III, 2014, p. 8-12Conference paper (Refereed)
    Abstract [en]

    Phylogenies based on single loci should be viewed with caution and the best approach for obtaining robust trees is to examine numerous loci across the genome. It often happens that for the same set of species trees derived from different genes are in conflict between each other. There are several methods that combine information from different genes in order to infer the species tree. One novel approach is to use informationfrom different -omics. Here we describe a phylogenetic method based on an Ornstein–Uhlenbeck process that combines sequence and gene expression data. We test our method on genes belonging to the histidine biosynthetic operon. We found that the method provides interesting insights into selection pressures and adaptive hypotheses concerning gene expression levels.

  • 11.
    Bartoszek, Krzysztof
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Pulka, Malgorzta
    Gdansk University of Technology.
    Asymptotic properties of quadratic stochastic operators acting on the L1 space2015In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 114, p. 26-39Article in journal (Refereed)
    Abstract [en]

    Quadratic stochastic operators can exhibit a wide variety of asymptotic behaviours andthese have been introduced and studied recently in the l1 space. It turns out that inprinciple most of the results can be carried over to the L1 space. However, due to topologicalproperties of this space one has to restrict in some situations to kernel quadratic stochasticoperators. In this article we study the uniform and strong asymptotic stability of quadratic stochastic operators acting on the L1 space in terms of convergence of the associated (linear)nonhomogeneous Markov chains.

  • 12.
    Bartoszek, Krzysztof
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Pułka, Małgorzata
    Gdansk University of Technology.
    Prevalence Problem in the Set of Quadratic Stochastic Operators Acting on L12018In: Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, Vol. 41, no 1, p. 159-173Article in journal (Refereed)
    Abstract [en]

    This paper is devoted to the study of the problem of prevalence in the classof quadratic stochastic operators acting on the L1 space for the uniform topology.We obtain that the set of norm quasi-mixing quadratic stochastic operators is a denseand open set in the topology induced by a very natural metric. This shows the typicallong-term behaviour of iterates of quadratic stochastic operators.

  • 13.
    Bartoszek, Krzysztof
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Sagitov, Serik
    A consistent estimator of the evolutionary rate2015In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 371, p. 69-78Article in journal (Refereed)
    Abstract [en]

    We consider a branching particle system where particles reproduce according to the pure birth Yule process with the birth rate 2, conditioned on the observed number of particles to be equal to n. Particles are assumed to move independently on the real line according to the Brownian motion with the local variance sigma(2). In this paper we treat n particles as a sample of related species. The spatial Brownian motion of a particle describes the development of a trait value of interest (e.g. log-body-size). We propose an unbiased estimator 4 of the evolutionary rate rho(2) - sigma(2)/lambda. The estimator R-n(2) is proportional to the sample variance S-n(2) computed from n trait values. We find an approximate formula for the standard error of R-n(2), based on a neat asymptotic relation for the variance of S-n(2). (C) 2015 Elsevier Ltd. All rights reserved.

  • 14.
    Bartoszek, Krzysztof
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Sagitov, Serik
    Chalmers University of Technology and the University of Gothenburg.
    A consistent estimator of the evolutionary rate2015In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 371, p. 69-78Article in journal (Refereed)
    Abstract [en]

    We consider a branching particle system where particles reproduce according to the pure birth Yule process with the birth rate λ, conditioned on the observed number of particles to be equal to n. Particles are assumed to move independently on the real line according to the Brownian motion with the local variance σ2. In this paper we treat n particles as a sample of related species. The spatial Brownian motion of a particle describes the development of a trait value of interest (e.g. log-body-size). We propose an unbiased estimator Rn2 of the evolutionary rate ρ22/λ. The estimator Rn2 is proportional to the sample variance Sn2 computed from n trait values. We find an approximate formula for the standard error of Rn2 based on a neat asymptotic relation for the variance of Sn2.

  • 15.
    Bartoszek, Krzysztof
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Sagitov, Serik
    Chalmers University of Technology and the Unversity of Gothenburg.
    Phylogenetic confidence intervals for the optimal trait value2015In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 52, no 4, p. 1115-1132Article in journal (Refereed)
    Abstract [en]

    We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree ismodelled by a Yule process conditioned on n contemporary nodes. The trait value is assumed to evolve along lineages as an Ornstein–Uhlenbeck process. As a result, the trait values of the n species form a sample with dependent observations. We establish three limit theorems for the samplemean corresponding to three domains for the adaptation rate. In the case of fast adaptation, we show that for large n the normalized sample mean isapproximately normally distributed. Using these limit theorems, we develop novel confidence interval formulae for the optimal trait value.

  • 16.
    Berggren, Mathias
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Exploding dice: A special case of summing a random number of randomvariables decided by a branching process2017Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 17.
    Bertolino, Mattias
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Jonnarth, Arvi
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Monte Carlo methods applied to tree-structured decision processes2017Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 18.
    Björnberg, Dag
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Wavelets: Introduction and Applications for Economic Time Series2017Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 19.
    Bommier, Esther
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Peaks-Over-Threshold Modelling of Environmental Data2014Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
  • 20.
    Bottinelli, Arianna
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Modelling collective movement and transport network formation in living systems2016Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The emergence of collective patterns from repeated local interactions between individuals is a common feature to most living systems, spanning a variety of scales from cells to animals and humans. Subjects of this thesis are two aspects of emergent complexity in living systems: collective movement and transport network formation. For collective movement, this thesis studies the role of movement-mediated information transfer in fish decision-making. The second project on collective movement takes inspiration from granular media and soft mode analysis and develops a new approach to describe the emergence of collective phenomena from physical interactions in extremely dense crowds. As regards transport networks, this thesis proposes a model of network growth to extract simple, biologically plausible rules that reproduce topological properties of empirical ant trail networks.  In the second project on transport networks, this thesis starts from the simple rule of “connecting each new node to the closest one”, that describes ants building behavior, to study how balancing local building costs and global maintenance costs influences the growth and topological properties of transport networks. These projects are addressed through a modeling approach and with the aim of identifying minimal sets of basic mechanisms that are most likely responsible of large-scale complex patterns. Mathematical models are always based on empirical observations and are, when possible, compared to experimental data.

    List of papers
    1. Local cost minimization in ant transport networks: from small-scale data to large-scale trade-offs
    Open this publication in new window or tab >>Local cost minimization in ant transport networks: from small-scale data to large-scale trade-offs
    2015 (English)In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 12, no 112, article id 20150780Article in journal (Refereed) Published
    Abstract [en]

    Transport networks distribute resources and information in many human and biological systems. Their construction requires optimization and balance of conflicting criteria such as robustness against disruptions, transport efficiency and building cost. The colonies of the polydomous Australian meat ant Iridomyrmex purpureus are a striking example of such a decentralized network, consisting of trails that connect spatially separated nests. Here we study the rules that underlie network construction in these ants. We find that a simple model of network growth, which we call the minimum linking model (MLM), is sufficient to explain the growth of real ant colonies. For larger networks, the MLM shows a qualitative similarity with a Euclidean minimum spanning tree, prioritizing cost and efficiency over robustness. We introduce a variant of our model to show that a balance between cost, efficiency and robustness can be also reproduced at larger scales than ant colonies. Remarkably, such a balance is influenced by a parameter reflecting the specific features of the modelled transport system. The extended MLM could thus be a suitable source of inspiration for the construction of cheap and efficient transport networks with non-zero robustness, suggesting possible applications in the design of human-made networks.

    Keyword
    transport networks, network growth model, graph theory, ant collective behaviour, ant colony, network optimization
    National Category
    Other Natural Sciences Mathematics Other Biological Topics
    Identifiers
    urn:nbn:se:uu:diva-268402 (URN)10.1098/rsif.2015.0780 (DOI)000363987900009 ()
    Available from: 2015-12-09 Created: 2015-12-04 Last updated: 2017-12-01Bibliographically approved
    2. Emergent Structural Mechanisms for High-Density Collective Motion Inspired by Human Crowds
    Open this publication in new window or tab >>Emergent Structural Mechanisms for High-Density Collective Motion Inspired by Human Crowds
    2016 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 117, no 22, article id 228301Article in journal (Refereed) Published
    Abstract [en]

    Collective motion of large human crowds often depends on their density. In extreme cases like heavy metal concerts and black Friday sales events, motion is dominated by physical interactions instead of conventional social norms. Here, we study an active matter model inspired by situations when large groups of people gather at a point of common interest. Our analysis takes an approach developed for jammed granular media and identifies Goldstone modes, soft spots, and stochastic resonance as structurally driven mechanisms for potentially dangerous emergent collective motion.

    National Category
    Physical Sciences
    Identifiers
    urn:nbn:se:uu:diva-303941 (URN)10.1103/PhysRevLett.117.228301 (DOI)000388630000032 ()
    Available from: 2016-09-27 Created: 2016-09-27 Last updated: 2017-11-21Bibliographically approved
    3. How Do Fish Use the Movement of Other Fish to Make Decisions?: From Individual Movement to Collective Decision Making
    Open this publication in new window or tab >>How Do Fish Use the Movement of Other Fish to Make Decisions?: From Individual Movement to Collective Decision Making
    2013 (English)In: Proceedings of the European Conference on Complex Systems 2012 / [ed] Thomas Gilbert, Markus Kirkilionis, Gregoire Nicolis, 2013, Vol. V, p. 591-606Conference paper, Published paper (Other academic)
    Series
    Springer Proceedings in Complexity, ISSN 2213-8684
    Keyword
    Collective animal behaviour, Decision making, SPP models, Fish
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-301517 (URN)10.1007/978-3-319-00395-5_73 (DOI)9783319003948 (ISBN)9783319003955 (ISBN)
    Conference
    European Conference on Complex Systems 2012
    Available from: 2016-08-23 Created: 2016-08-23 Last updated: 2016-10-04Bibliographically approved
    4. Balancing building and maintenance costs in growing transport networks
    Open this publication in new window or tab >>Balancing building and maintenance costs in growing transport networks
    2017 (English)In: Physical revview E, ISSN 2470-0045, Vol. 96, no 3, article id 032316Article in journal (Refereed) Published
    Abstract [en]

    The costs associated to the length of links impose unavoidable constraints to the growth of natural and artificial transport networks. When future network developments cannot be predicted, the costs of building and maintaining connections cannot be minimized simultaneously, requiring competing optimization mechanisms. Here, we study a one-parameter nonequilibrium model driven by an optimization functional, defined as the convex combination of building cost and maintenance cost. By varying the coefficient of the combination, the model interpolates between global and local length minimization, i.e., between minimum spanning trees and a local version known as dynamical minimum spanning trees. We show that cost balance within this ensemble of dynamical networks is a sufficient ingredient for the emergence of tradeoffs between the network's total length and transport efficiency, and of optimal strategies of construction. At the transition between two qualitatively different regimes, the dynamics builds up power-law distributed waiting times between global rearrangements, indicating a point of nonoptimality. Finally, we use our model as a framework to analyze empirical ant trail networks, showing its relevance as a null model for cost-constrained network formation.

    National Category
    Mathematics Physical Sciences
    Identifiers
    urn:nbn:se:uu:diva-303938 (URN)10.1103/PhysRevE.96.032316 (DOI)000411991200004 ()
    Available from: 2016-09-27 Created: 2016-09-27 Last updated: 2017-12-20Bibliographically approved
  • 21.
    Bottinelli, Arianna
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Louf, Remi
    UCL, Ctr Adv Spatial Anal, 90 Tottenham Court Rd, London W1T 4TJ, England.
    Gherardi, Marco
    UPMC Univ Paris 06, Sorbonne Univ, UMR 7238, Computat & Quantitat Biol, 15 Rue Ecole Med, Paris, France.; Univ Milan, Dipartimento Fis, Via Celoria 16, I-20133 Milan, Italy..
    Balancing building and maintenance costs in growing transport networks2017In: Physical revview E, ISSN 2470-0045, Vol. 96, no 3, article id 032316Article in journal (Refereed)
    Abstract [en]

    The costs associated to the length of links impose unavoidable constraints to the growth of natural and artificial transport networks. When future network developments cannot be predicted, the costs of building and maintaining connections cannot be minimized simultaneously, requiring competing optimization mechanisms. Here, we study a one-parameter nonequilibrium model driven by an optimization functional, defined as the convex combination of building cost and maintenance cost. By varying the coefficient of the combination, the model interpolates between global and local length minimization, i.e., between minimum spanning trees and a local version known as dynamical minimum spanning trees. We show that cost balance within this ensemble of dynamical networks is a sufficient ingredient for the emergence of tradeoffs between the network's total length and transport efficiency, and of optimal strategies of construction. At the transition between two qualitatively different regimes, the dynamics builds up power-law distributed waiting times between global rearrangements, indicating a point of nonoptimality. Finally, we use our model as a framework to analyze empirical ant trail networks, showing its relevance as a null model for cost-constrained network formation.

  • 22.
    Bottinelli, Arianna
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Perna, Andrea
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Ward, Ashley
    The University of Sydney, NSW, Australia.
    Sumpter, David TJ
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    How Do Fish Use the Movement of Other Fish to Make Decisions?: From Individual Movement to Collective Decision Making2013In: Proceedings of the European Conference on Complex Systems 2012 / [ed] Thomas Gilbert, Markus Kirkilionis, Gregoire Nicolis, 2013, Vol. V, p. 591-606Conference paper (Other academic)
  • 23.
    Bottinelli, Arianna
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Sumpter, David
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Silverberg, Jesse
    Wyss Institute for Biologically Inspired Engineering, Harvard University.
    Emergent Structural Mechanisms for High-Density Collective Motion Inspired by Human Crowds2016In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 117, no 22, article id 228301Article in journal (Refereed)
    Abstract [en]

    Collective motion of large human crowds often depends on their density. In extreme cases like heavy metal concerts and black Friday sales events, motion is dominated by physical interactions instead of conventional social norms. Here, we study an active matter model inspired by situations when large groups of people gather at a point of common interest. Our analysis takes an approach developed for jammed granular media and identifies Goldstone modes, soft spots, and stochastic resonance as structurally driven mechanisms for potentially dangerous emergent collective motion.

  • 24.
    Bottinelli, Arianna
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    van Wilgenburg, E.
    Fordham Univ, Dept Biol Sci, Bronx, NY 10458 USA..
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Latty, T.
    Univ Sydney, Sch Biol Sci, Sydney, NSW 2006, Australia..
    Local cost minimization in ant transport networks: from small-scale data to large-scale trade-offs2015In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 12, no 112, article id 20150780Article in journal (Refereed)
    Abstract [en]

    Transport networks distribute resources and information in many human and biological systems. Their construction requires optimization and balance of conflicting criteria such as robustness against disruptions, transport efficiency and building cost. The colonies of the polydomous Australian meat ant Iridomyrmex purpureus are a striking example of such a decentralized network, consisting of trails that connect spatially separated nests. Here we study the rules that underlie network construction in these ants. We find that a simple model of network growth, which we call the minimum linking model (MLM), is sufficient to explain the growth of real ant colonies. For larger networks, the MLM shows a qualitative similarity with a Euclidean minimum spanning tree, prioritizing cost and efficiency over robustness. We introduce a variant of our model to show that a balance between cost, efficiency and robustness can be also reproduced at larger scales than ant colonies. Remarkably, such a balance is influenced by a parameter reflecting the specific features of the modelled transport system. The extended MLM could thus be a suitable source of inspiration for the construction of cheap and efficient transport networks with non-zero robustness, suggesting possible applications in the design of human-made networks.

  • 25.
    Brodersson, Anna Lilly
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Flygbesiktning av Luftledningar: Modellering av samband mellan besiktningsanmärkningar och systemtillförlitlighet2014Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This paper thoroughly investigates needs and requirements for overhead distribution feeder inspection and develops models to investigate possible relations between short term inspections remarks and outages. The study was conducted in collaboration with Fortum Distribution AB that supplied extensive information about their overhead power feeders concerning both inspection and power outages. The investigated models where lognormal linear model, Poisson generalized linear model and negative binomial generalized linear model. All models were implemented utilizing offset terms to compensate for differences in feeder length and amount of overhead versus underground feeders. The Poisson generalized linear model was rejected at an early stage due to overdispersion and neither of the remaining models fit the data perfectly. There for conclusions were primarily concluded from similarities and differences amongst the models. The results either implicate that maintenance is scheduled sufficiently fast, with respect to short term inspection, to ensure a high system reliability or no relationships between short term inspection and feeder outages exist. Therefore the final conclusion was that maintenance and reinvestment decisions should not be based on short cycle inspection data.

  • 26. Cederbaum, Carla
    et al.
    Cabrera Pacheco, Armando
    McCormick, Stephen
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Miao, Pengzi
    Asymptotically flat extensions of CMC Bartnik data2017In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382Article in journal (Refereed)
  • 27.
    Cox, Sander
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Dynamical modelling2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 28.
    Cribäck, Kevin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Skattningsmetoder för den generaliserade extremvärdesfördelningen2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 29.
    Dahne, Joel
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Enclosing Zeros for Systems of Two Analytic Functions2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 30.
    David, Jäderberg
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Sentiment and topic classification of messages on Twitter: and using the results to interact with Twitter users2016Independent thesis Basic level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    We classify messages posted to social media network Twitter based on the sentiment and topic of the messages. We use the results of the classification to sometimes generate responses that are sent to the original user and their network on Twitter using natural language processing. A network of users who post science related content is used as the sources of data. The classifications of the dataset show worse results than others have achieved for sentiment analysis of content on Twitter, possibly due to the data sets that were used. 

  • 31.
    Delshams, Amadeu
    et al.
    Univ Politecn Cataluna, Dept Matemat, Barcelona 08028, Spain..
    Gonchenko, Marina
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Gutierrez, Pere
    Univ Politecn Cataluna, Dept Matemat, Barcelona 08028, Spain..
    Exponentially Small Splitting of Separatrices and Transversality Associated to Whiskered Tori with Quadratic Frequency Ratio2016In: SIAM Journal on Applied Dynamical Systems, ISSN 1536-0040, E-ISSN 1536-0040, Vol. 15, no 2, p. 981-1024Article in journal (Refereed)
    Abstract [en]

    The splitting of invariant manifolds of whiskered (hyperbolic) tori with two frequencies in a nearly integrable Hamiltonian system, whose hyperbolic part is given by a pendulum, is studied. We consider a torus with a fast frequency vector w/root epsilon with w = (1, Omega), where the frequency ratio Omega is a quadratic irrational number. Applying the Poincare-Melnikov method, we carry out a careful study of the dominant harmonics of the Melnikov potential. This allows us to provide an asymptotic estimate for the maximal splitting distance and show the existence of transverse homoclinic orbits to the whiskered tori with an asymptotic estimate for the transversality of the splitting. Both estimates are exponentially small in epsilon, with the functions in the exponents being periodic with respect to Ins, and can be explicitly constructed from the continued fraction of Omega. In this way, we emphasize the strong dependence of our results on the arithmetic properties of Omega. In particular, for quadratic ratios Omega with a 1-periodic or 2-periodic continued fraction (called metallic and metallic-colored ratios, respectively), we provide accurate upper and lower bounds for the splitting. The estimate for the maximal splitting distance is valid for all sufficiently small values of epsilon, and the transversality can be established for a majority of values of epsilon, excluding small intervals around some transition values where changes in the dominance of the harmonics take place, and bifurcations could occur.

  • 32.
    Dumanois, Stephane
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Least Squares Radial Basis Function generated Finite Differences for Option Pricing2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
  • 33.
    Dyrssen, Hannah
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    The perpetual American put option in jump-to-default models2017In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 89, no 2, p. 510-520Article in journal (Refereed)
    Abstract [en]

    We study the perpetual American put option in a general jump-to-default model, deriving an explicit expression for the price of the option.

    We find that in some cases the optimal stopping boundary vanishes and thus it is not optimal to exercise the option before default occurs. Precise conditions for when this situation arises are given.

    Furthermore we present a necessary and sufficient condition for convexity of the option price, and also show that a nonincreasing intensity is sufficient, but not necessary, to have convexity.

    From this we also get conditions for when option prices are monotone in the model parameters.

  • 34.
    Dyrssen, Hannah
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Valuation and Optimal Strategies in Markets Experiencing Shocks2017Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis treats a range of stochastic methods with various applications, most notably in finance. It is comprised of five articles, and a summary of the key concepts and results these are built on.

    The first two papers consider a jump-to-default model, which is a model where some quantity, e.g. the price of a financial asset, is represented by a stochastic process which has continuous sample paths except for the possibility of a sudden drop to zero. In Paper I prices of European-type options in this model are studied together with the partial integro-differential equation that characterizes the price. In Paper II the price of a perpetual American put option in the same model is found in terms of explicit formulas. Both papers also study the parameter monotonicity and convexity properties of the option prices.

    The third and fourth articles both deal with valuation problems in a jump-diffusion model. Paper III concerns the optimal level at which to exercise an American put option with finite time horizon. More specifically, the integral equation that characterizes the optimal boundary is studied. In Paper IV we consider a stochastic game between two players and determine the optimal value and exercise strategy using an iterative technique.

    Paper V employs a similar iterative method to solve the statistical problem of determining the unknown drift of a stochastic process, where not only running time but also each observation of the process is costly.

    List of papers
    1. Pricing equations in jump-to-default models
    Open this publication in new window or tab >>Pricing equations in jump-to-default models
    2014 (English)In: Int. J. Theor. Appl. Finance, ISSN 0219-0249, Vol. 17, no 3Article in journal (Refereed) Published
    National Category
    Probability Theory and Statistics
    Identifiers
    urn:nbn:se:uu:diva-313325 (URN)10.1142/S0219024914500198 (DOI)
    Available from: 2017-01-19 Created: 2017-01-19 Last updated: 2017-03-14
    2. The perpetual American put option in jump-to-default models
    Open this publication in new window or tab >>The perpetual American put option in jump-to-default models
    2017 (English)In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 89, no 2, p. 510-520Article in journal (Refereed) Published
    Abstract [en]

    We study the perpetual American put option in a general jump-to-default model, deriving an explicit expression for the price of the option.

    We find that in some cases the optimal stopping boundary vanishes and thus it is not optimal to exercise the option before default occurs. Precise conditions for when this situation arises are given.

    Furthermore we present a necessary and sufficient condition for convexity of the option price, and also show that a nonincreasing intensity is sufficient, but not necessary, to have convexity.

    From this we also get conditions for when option prices are monotone in the model parameters.

    National Category
    Probability Theory and Statistics
    Research subject
    Mathematics with specialization in Applied Mathematics
    Identifiers
    urn:nbn:se:uu:diva-313326 (URN)10.1080/17442508.2016.1267177 (DOI)000392492800004 ()
    Available from: 2017-01-19 Created: 2017-01-19 Last updated: 2017-11-29Bibliographically approved
    3. The integral equation for the American put boundary in models with jumps
    Open this publication in new window or tab >>The integral equation for the American put boundary in models with jumps
    (English)Article in journal (Other academic) Submitted
    Abstract [en]

    The price of the American put option is frequently studied as the solution to an associated free-boundary problem. This free boundary, the optimal exercise boundary, determines the value of the option. In spectrally negative models the early exercise premium representation for the value of the option gives rise to an integral equation for the boundary. We study this integral equation and prove that the optimal exercise boundary is the unique solution and thus that the equation characterizes the free boundary. In a spectrally positive model, this approach does not give an equation for the boundary. We instead find lower and upper bounds for the true boundary which can be found by solving related equations.

    National Category
    Probability Theory and Statistics
    Research subject
    Mathematics with specialization in Applied Mathematics
    Identifiers
    urn:nbn:se:uu:diva-316576 (URN)
    Available from: 2017-03-03 Created: 2017-03-03 Last updated: 2017-03-14
    4. Optimal stopping games for a process with jumps
    Open this publication in new window or tab >>Optimal stopping games for a process with jumps
    (English)Article in journal (Other academic) Submitted
    Abstract [en]

    This paper presents a study of a general two-player optimal stopping game in a jump-diffusion model. An iterative scheme to find the value of this game is derived, specifically the value is shown to be the limit of a sequence of stopping games for a related diffusion but with a running reward. Furthermore the convergence is uniform and exponential. The special case of a cancellable put option is studied.

    National Category
    Probability Theory and Statistics
    Identifiers
    urn:nbn:se:uu:diva-316577 (URN)
    Available from: 2017-03-03 Created: 2017-03-03 Last updated: 2017-03-14
    5. Sequential testing of a Wiener process with costly observations
    Open this publication in new window or tab >>Sequential testing of a Wiener process with costly observations
    (English)Article in journal (Other academic) Submitted
    Abstract [en]

    We consider the sequential testing of two simple hypotheses for the drift of a Brownian motion when each observation of the underlying process is associated with a positive cost. In this setting where continuous monitoring of the underlying process is not feasible, the question is not only whether to stop or to continue at a given observation time, but also, if continuing,how to distribute the next observation time. Adopting a Bayesian methodology, we show that the value function can be characterized as the unique fixed point of an associated operator, and that it can be constructed using an iterative scheme. Moreover, the optimal sequential distribution of observation times can be described in terms of the fixed point.

    National Category
    Probability Theory and Statistics
    Research subject
    Mathematics with specialization in Applied Mathematics
    Identifiers
    urn:nbn:se:uu:diva-316571 (URN)
    Available from: 2017-03-03 Created: 2017-03-03 Last updated: 2017-03-22
  • 35.
    Dyrssen, Hannah
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Ekström, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Sequential testing of a Wiener process with costly observationsArticle in journal (Other academic)
    Abstract [en]

    We consider the sequential testing of two simple hypotheses for the drift of a Brownian motion when each observation of the underlying process is associated with a positive cost. In this setting where continuous monitoring of the underlying process is not feasible, the question is not only whether to stop or to continue at a given observation time, but also, if continuing,how to distribute the next observation time. Adopting a Bayesian methodology, we show that the value function can be characterized as the unique fixed point of an associated operator, and that it can be constructed using an iterative scheme. Moreover, the optimal sequential distribution of observation times can be described in terms of the fixed point.

  • 36.
    Dyrssen, Hannah
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Ekström, Erik
    Tysk, Johan
    Pricing equations in jump-to-default models2014In: Int. J. Theor. Appl. Finance, ISSN 0219-0249, Vol. 17, no 3Article in journal (Refereed)
  • 37.
    Dyrssen, Hannah
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Ekström, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Tysk, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Pricing equations in jump-to-default models2014In: International Journal of Theoretical and Applied Finance, ISSN 0219-0249Article in journal (Refereed)
    Abstract [en]

    We study pricing equations in jump-to-default models, and we provide conditions under which the option price is the unique classical solution, with a special focus on boundary conditions. In particular, we find precise conditions ensuring that the option price at the default boundary coincides with the recovery payment. We also study spatial convexity of the option price, and we explore the connection between preservation of convexity and parameter monotonicity.

  • 38.
    Dyrssen, Hannah
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Vannestål, Martin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Optimal stopping games for a process with jumpsArticle in journal (Other academic)
    Abstract [en]

    This paper presents a study of a general two-player optimal stopping game in a jump-diffusion model. An iterative scheme to find the value of this game is derived, specifically the value is shown to be the limit of a sequence of stopping games for a related diffusion but with a running reward. Furthermore the convergence is uniform and exponential. The special case of a cancellable put option is studied.

  • 39.
    Dyrssen, Hannah
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Vannestål, Martin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    The integral equation for the American put boundary in models with jumpsArticle in journal (Other academic)
    Abstract [en]

    The price of the American put option is frequently studied as the solution to an associated free-boundary problem. This free boundary, the optimal exercise boundary, determines the value of the option. In spectrally negative models the early exercise premium representation for the value of the option gives rise to an integral equation for the boundary. We study this integral equation and prove that the optimal exercise boundary is the unique solution and thus that the equation characterizes the free boundary. In a spectrally positive model, this approach does not give an equation for the boundary. We instead find lower and upper bounds for the true boundary which can be found by solving related equations.

  • 40.
    Eggers, Julia
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    On Statistical Methods for Zero-Inflated Models2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 41.
    Ekström, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Janson, Svante
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    The inverse first-passage problem and optimal stopping2016In: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 26, no 5, p. 3154-3177Article in journal (Refereed)
    Abstract [en]

    Given a survival distribution on the positive half-axis and a Brownian motion, a solution of the inverse first-passage problem consists of a boundary so that the first passage time over the boundary has the given distribution. We show that the solution of the inverse first-passage problem coincides with the solution of a related optimal stopping problem. Consequently, methods from optimal stopping theory may be applied in the study of the inverse first passage problem. We illustrate this with a study of the associated integral equation for the boundary.

  • 42.
    Ekström, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Tysk, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Comparison of two methods for superreplication2012In: Applied Mathematical Finance, ISSN 1350-486X, E-ISSN 1433-4313Article in journal (Refereed)
  • 43.
    Ekström, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Tysk, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Dupire's equation for bubbles2012In: International Journal of Theoretical and Applied Finance, ISSN 0219-0249Article in journal (Refereed)
  • 44.
    Ekström, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Tysk, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Lindberg, Carl
    Optimal liquidation of a pairs trade2011In: Advanced Mathematical Methods in Finance, Springer-Verlag New York, 2011Chapter in book (Refereed)
  • 45.
    Ekström, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Vaicenavicius, Juozas
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Optimal liquidation of an asset under drift uncertainty2016In: SIAM Journal on Financial Mathematics, ISSN 1945-497X, E-ISSN 1945-497XArticle in journal (Refereed)
    Abstract [en]

    We study a problem of finding an optimal stopping strategy to liquidate an asset with unknown drift. Taking a Bayesian approach, we model the initial beliefs of an individual about the drift by allowing an arbitrary probability distribution to characterize the uncertainty about the drift parameter. Filtering theory is used to describe the evolution of the posterior beliefs about the drift once the price process is being observed. An optimal stopping time is determined as the first passage time of the posterior mean below a monotone boundary, which can be characterized as the unique solution to a nonlinear integral equation. We also study monotonicity properties with respect to the prior distribution and the asset volatility.

  • 46.
    Ekström, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Vaicenavicius, Juozas
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Optimal stopping of a Brownian bridge with an unknown pinning pointArticle in journal (Other academic)
  • 47.
    Ekström, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Vaicenavicius, Juozas
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Wiener disorder detection under disorder magnitude uncertaintyManuscript (preprint) (Other academic)
  • 48.
    Ekström, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Vannestål, Martin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Momentum liquidation under partial information2016In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 53, no 2, p. 341-359Article in journal (Refereed)
    Abstract [en]

    Momentum is the notion that an asset that has performed well in the past will continue to do so for some period. We study the optimal liquidation strategy for a momentum trade in a setting where the drift of the asset drops from a high value to a smaller one at some random change-point. This change-point is not directly observable for the trader, but it is partially observable in the sense that it coincides with one of the jump times of some exogenous Poisson process representing external shocks, and these jump times are assumed to be observable. Comparisons with existing results for momentum trading under incomplete information show that the assumption that the disappearance of the momentum effect is triggered by observable external shocks significantly improves the optimal strategy.

  • 49.
    Falk Soylu, Denniz
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Dimension Reduction Methods for Predicting Financial Data2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 50.
    Falk Soylu, Denniz
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Recovery Rate Modelling of Non-performing Consumer Loans2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
1234 1 - 50 of 181
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